2.4 – Experimental Design and rise of statistics in medical research

Experiments and observations: Finding answers.

.

How to identify cause and effect, and the kinds of evidence that can be inferred from the various approaches to study causes of  disease has became a major source of disagreement in the news. In a fascinating study, Pew Research Center reported “half of U.S. adults under 50 say they get health and wellness information from social media influencers or podcasts,” and, only about 17% of these influencers report “conventional medicine” training (Report, May 7 2026).  For our purposes, I made substantial updates to this page in the fifth month after WHO had declared the Covid-19 pandemic (CDC timeline), and continue to do so today. 

The pandemic left many life-lessons, for scientists and public-health supporters, but also for everyone who lived through those times. One of the lessons was how to deal with the challenges of finding treatments in real time. If you followed the news early in the pandemic, you know of the appeal from some (including Donald Trump, the then-President of the United States, Boseley 2020), for use of an anti-parasite drug, hydroxychloroquine, as prophylactic or treatment for active Covid-19 infection (cf. Liu et al 2020). The FDA as well as other institutions rapidly advised against use, in part because experimental design concerns were raised for early studies (Kupferschmidt, 2020). The issue remains contentious for some (eg, Health and Human Services Secretary Robert F. Kennedy Jr., CNN August 2, 2026 interview).

Thus, job number one for students of biostatistics is to learn how to weigh arguments for or against therapies or treatments offered. The purpose of this page is to introduce these issues — how to judge whether a treatment is effective or not. 

We will spend some time later on statistical aspects of experimental design (Chapter 5), but we begin with Randomized Control Trials, or RCT, as a model for our discussion of experimental studies. The RCT we recognize today owes its beginning to the 1948 studies on streptomycin use to treat tuberculosis (British Medical Research Council 1948), but of course, the foundations of RCT and experimental design in general, go back much earlier than that date (Chalmers 2011, Hairton and Locascio 2018). For a number of reasons the RCT — experimental, prospective, double-blind clinical trial with random selection of subjects from a reference population and random assignment of subjects to a treatment group or an appropriate placebo treatment control group — is considered the “gold standard” method for producing knowledge (Kaptchuk 2001, Hairton and Locascio 2018). 

Technically, RCT are intervention trials, a specific application of the more general definition of an experiment. That is, the researchers tests a potential drug or therapy in people to observe its effect while holding other variables constant.  Experimental studies imply that the researcher imposed treatments or controls onto subjects. The subjects are followed and outcomes are recorded. Thus, experiments by definition are also prospective studies — the outcome is recorded for subjects after some period of time. With a well-designed experiment, the researcher may have evidence to support the claim that, for example, Treatment A causes the outcome.

RCT applied to human health can have profound impact on lives.

The ALLHAT-LLT (JAMA, 2002) trial tested whether adding the cholesterol-lowering drug pravastatin to standard care would reduce heart attacks and deaths in people with high blood pressure and moderately high cholesterol. The study found no significant benefit compared to usual care, suggesting that statin therapy may not always provide extra protection in this group. Its results helped refine how doctors balance blood pressure and cholesterol treatment in heart disease prevention.

The Women’s Health Initiative (JAMA, 2002) trial tested the effects of combined estrogen and progestin therapy in healthy postmenopausal women. It found that while the therapy slightly reduced the risk of fractures and colon cancer, it increased the risk of heart disease, stroke, and breast cancer. These results transformed medical guidance by showing that hormone therapy should not be routinely used to prevent chronic disease in postmenopausal women.

The Du Toit et al. (NEJM, 2015) study showed that introducing peanut-containing foods early in life — rather than avoiding them — greatly reduced the risk of developing peanut allergies in high-risk infants. This landmark randomized trial changed how doctors think about food allergies, leading to new guidelines that encourage early introduction instead of avoidance.

And more recently, we have study reported by Deanfield et al (Lancet, 2025), which found that semaglutide reduced the risk of major adverse cardiovascular events (MACE) in adults with overweight or obesity and established cardiovascular disease—even if they did not lose much weight or had lower baseline adiposity.

In contrast, observational studies are those in which treatments arise by acts of nature. In both experiments and observational studies, there can be treatment and control groups; the distinction between the types of studies is how assignment of subjects to treatments were affected. Observational studies generally are retrospective studies — the outcome has already occurred, the researcher follows up to identify differences among the groups that may account for different outcomes. Examples of observational, retrospective study designs include cross-sectional and case control; cohort studies are prospective studies. Observational studies are discussed further in Chapter 5.4 – Clinical trials.

Compared to observational studies, in principle, experiments can establish cause and effect. Cause and effect refers to an explanation about relationship between two events or objects. In biology, Ernst Mayr (1904 – 2005) distinguished between two levels of explanation, proximate (how) explanations and ultimate (why) explanations (Mayr 1961, cf. Laland et al. 2011). As you know, our mechanism for identifying cause and effect is application of the Scientific Method (Chapter 2.5). Discussions of how to detect cause and effect are provided throughout this book, but emphasized in a few sections (Chapter 16.2 and 16.3).

Good experiments.

The principles of good experiments include many steps beyond simply choosing treatments and controls. In Chapter 5 we’ll go into more depth, but I wished to list for you some of the key principles of good experimental design. With respect to human-subject research, the researcher needs to protect against many sources of potential bias.

• Randomization of subjects assigned to treatment groups controls for individual differences.
• Controls (eg, Placebos) are a means to establish controls in a study so that effects may be attributed to the active treatment.
• Single-blind implies that the subject does not know what treatment was given. 
  • Double-blind implies that not only is the subject unaware of the treatment received, but, crucially, neither does the researcher.
• The double-blind design — neither the patient-subject nor the researchers know who received the placebo or the treatment — controls for subtle biases.

The experimenter may influence the outcome of the experiment if knowledge about who received the placebo or the new drug; the subject may respond differently with knowledge that they received the placebo and not the new drug. The key intent in this experimental design is to avoid systematic error, errors in studies that may occur because of our conscious and unconscious beliefs and biases. Placebos are used as treatments because people (and animals!) sometimes get better (or worse) with or without treatment; thus, to be effective, subjects receiving a new drug must get better more frequently than do subjects on placebo. Importantly, the well-designed placebo allows the researcher to gain insight into the mechanism of action by the new drug.

A case to consider: Comparing migraine treatments.

.

Consider the following experiment (Diener et al 2006; see also Liu et al 2018): subjects who had several migraines per month were treated with acupuncture, sham-acupuncture, or standard treatments including beta blockers, calcium channel blockers, or antiepileptic drugs. After 26 weeks the reductions in reported migraines was compared. The authors reported that there was no difference in numbers of migraines among patients who received the different therapy treatments. The authors conclude that because acupuncture lacks side-effects that may occur with standard therapies acupuncture may be a good choice for patients seeking relief from migraine. This is a classic experiment — subjects were assigned to treatments by the researchers. At least in principle, if one treatment group showed better outcomes, the improvement could be attributed to the treatment. 

Another case to consider: When the cause isn’t clear.

.

Consider the following example. My dad was diagnosed with lung cancer in his late 70s; his left lung showed many spots when imaged and biopsy confirmed. Surgeons removed half of the lung and after several years he was considered cancer free. Why did he develop cancer in the first place? If you immediately think, “He’s a smoker,” that’s not a good explanation — and shame on you, you’re first instinct was to blame the patient (see discussion in Huff 2013). Dad last smoked tobacco in his early thirties (latency smoking-lung cancer link about 20 years, Lipfert et al 2019).

Tobacco smoking is not the only environmental trigger for lung cancer. Cancer of the lung in non-smokers is the seventh leading cause of cancer mortality worldwide (Field and Withers 2012). Long term exposure to radon gas, a naturally occurring, radioactive noble gas has been linked to lung cancer (EPA). I grew up on Vashon Island, Washington, in a non-smoking home environment. Radon levels on Vashon Island and other areas around Puget Sound are low (source: Washington State Department of Health). Radon is out as an explanation.

What other environmental sources may be linked to cancer? Vashon Island is rural, but, as it turned out, within range of effluent from a copper smelter located in nearby Ruston, Pierce County (Fig 1; my home was 17 km distance from the smelter). 

Figure 1. Left: ASARCO smelter, Ruston, Washington, image from Department of Ecology, State of Washington. Direction of smoke from the stack is north, toward Vashon Island. Right: Voronoi map of arsenic and lead affected areas. image from kingcounty.gov. Darker regions correspond to heavier arsenic and lead contamination of soils.

The smelter was last in operation in 1986 and was torn down in 1993 (EPA publication number 910R94001). The smelter stack rose more than 500 feet dispersing smoke laden with heavy metals, notably inorganic arsenic and lead, into the air (Bromenshenk et al. 1985). Over the smelter’s 68 years of service, winds carried away the smoke to my island and to other areas known now as the “Ruston-Vashon Island Exposure Pathway” (Kalman et al 1990). The former smelter site was among the first listed Superfund sites (1983) in the United States by the EPA. Thus, tens of thousands of people were (and continue to be) exposed to the heavy metals deposited into the soils, forming a distinct exposure group (Milham & Strong 1974; Kalman et al 1990; EPA 2000). Arsenic exposure can be via inhalation, skin, or in drinking water — areas of Vashon-Maury island continue to have high levels of arsenic in both the soil and in  any domestic water wells (PublicationNo. 14-09-044, Department of Ecology State of Washington).

Is arsenic exposure by inhalation a plausible mechanism for my Dad’s lung cancer? As shown in Fig 1, the soils on Vashon near my home were heavily impacted by the smelter. Exposure could have come about from exposure during routine yard work — I have memories of clouds of dust kicked up by the lawn mower during spring and summers. Thus, an exposure route is possible. What evidence can we come up with?

Figure 2A shows negative association between lung and bronchial cancer incidence rates per 100L persons, adjusted for age, for several Washington state counties between 2000 and 2020 and distance from the smelter in Ruston. For comparison, Figure 2B shows no association between bladder cancer incidence rates per 100K for the same counties and time period and distance from the smelter. Workers exposed to arsenic have higher rates of lung cancer (Sullivan 2007, Wei et al 2019; see Enterline et al 1987 for a study a study based on cancer of workers at the smelter). Cultured lung cells exposed to arsenic associated with changes in gene expression (Clancy et al 2012). Coincidently, two of the family dogs developed and died of cancer as did one female goat. Perhaps my dad’s lung cancer was attributed to long exposure to arsenic (a decade after the cancer, and long after he stopped with yard work, his blood readings for arsenic were in the range of a modest 11 μg/L).  

Figure 2. County cancer rates (A, lung and bronchial; B, bladder) from 2000 – 2020 vs distance in kilometers from ASARCO smelter, Ruston, WA. Data compiled from Washington Tracking Network (WTN). The counties were King (55 km), Kitsap (39.28 km), Pierce (38.48 km), San Juan ( 141.43 km), Snohomish (100.73 km), and Spokane (385.34 km).

If this scenario seems plausible, I hope you immediately recognize it as a case of confirmation bias (see Chapter 2.6). Putting aside for a moment the different arsenic species, each with different LD₅₀ (the lethal dose needed to kill half the population — see Chapter 20.10), the difficulty ascribing arsenic as a causal agent for my Dad’s cancer is that many other exposures happened simultaneously. For example, indoor carpets are a primary source of several volatile organic compounds (Haines et al 2020). Prior to 1980 carpets may have included formaldehyde and other known carcinogenic agents. Dad commuted by car between work and home — with a ferry ride between — for decades (until the early 1990s), routinely traveling heavily congested roadways, this during the years prior to and the early years of the Clean Air Act of Environmental Protection Agency of the United States (it wasn’t until 1981 that new cars met EPA emission standards: Clean Air Act timeline here). Thus, all commuters including my Dad were exposed to gasoline combustion emissions, many known to be carcinogenic (Parent et al 2007). Moreover, a limited study by Public Health of Seattle and King County (2001) found rates of cancer on Vashon between 1980 and 1988 were similar to other areas in King County.

Summary.

It’s easy to fall into the trap that experiments — and by extension meta-analysis and systematic reviews — are the best tools offered by science for developing knowledge about the world, and other approaches suffer by comparison. But after even a bit of reflection, we should recognize that it can’t be that simple. While we now “know” tobacco cigarette smoking increases lung cancer risk, and many experiments with animal models convincingly show the link (eg, Hutt et al 2005), no human experiment in the strict sense, ie, prospective, randomized control trial, has ever been conducted (hint: it would be unethical, see discussion in Allmark and Tod 2016). Instead, the accumulated evidence from observational studies on exposures of different populations over the years overwhelmingly points to smoking as a leading risk factor (cause) of lung and other cancers — an example of Hill’s guidelines of causality.  We end with a quote:

RCTs can play a role in building scientific knowledge and useful predictions but they can only do so as part of a cumulative program, combining with other methods, including conceptual and theoretical development, to discover not ‘what works’, but ‘why things work’ (p 2, Deaton and Cartwright 2017).

Questions.

.

1. Write up three learning outcomes for this page. Hint: Point your favorite generative AI to this page and ask for help.
2. Was my Dad’s lung cancer attributable to his 40 years plus exposure to soil arsenic (he’s a non-smoker)? How should we approach this question?
3. In Diener et al (2006), the authors concluded that because acupuncture lacks side-effects that may occur with standard therapies acupuncture may be a good choice for patients seeking relief from migraine. Do you agree with the authors?
4. Ethical standards evolve with time. An ongoing debate in research is whether and how placebos are to be used in human subjects research. Placebos are a means to establish controls in a study so that effects may be attributed to the active treatment. The “gold standard” of clinical trials is considered to be the randomized double-blind design — neither the patient-subject nor the researchers know who receives the placebo or the treatment. Following review of the WHO report on Use of Placebos in Vaccine Trials, pick one study and evaluate whether or not the decision to use placebos was warranted in your opinion.
5. I searched PUBMED for “double-blind” by decade and found the following results (August 2018) (Table 1). Open R and/or R Commander and create two variables, then generate a scatter plot. Describe the shape of the relationship between number of publications citing “double-blind” and time (eg, 1950 – 1959, 1960 – 1969, and so on).

5. Here’s one way to enter this data into R. At the R prompt (or in the R Script window of R Commander), create two variables, Decade and Pubs Decade <- c(seq(1950, 2020, by=10)) Pubs <- c(59,995,7161,24728,39670,54011,57043) Make an XY scatter plot plot(Decade,Pubs)
6. Repeat the PUBMED search as above but search for “placebo”. Make a table like the one above and provide a scatterplot of your results.
7. Is the concept of a placebo relevant if the subjects in your experiment are yeast cells, not humans?
   • Similarly, if your subjects are yeast cells, how does the concept of performing experiments “blind” apply?
8. Ethical standards change with time. An ongoing debate in research is whether and how placebos are to be used in human subjects research.
   • If placebos are so important, why is their use a concern in clinical trials?
   • Following review of the WHO report on Use of Placebos in Vaccine Trials (see Readings below), pick one study and evaluate whether or not the decision to use placebos was warranted in your opinion.

R notes for question 5:

• <- is an assignment operator (assignOP); everything to the right of <- is assigned to the object named to the left of the <- operator. You can instead use = in place of <- , but because = is also used in other contexts besides assignment, a quick look at blogs by data scientists will find a preference to use <- for clarity and consistency.
• c() “combines” arguments into a vector.
• seq() is used to generate a sequence of numbers between a lower and an upper limit; if by = n is included, the sequence will be increased by the value n. If omitted, then the sequence is increased by 1.

Quiz Chapter 2.4

Experimental Design and rise of statistics in medical research

Start Quiz

Question

✕

✓

Your answer:

Correct answer:

Next

Please wait..

↺

You got {{SCORE_CORRECT}} out of {{SCORE_TOTAL}}

Your Answers

Chapter 2 contents.

.

• Introduction
• Why biostatistics?
• Why do we use R Software?
• A brief history of (bio)statistics
• Experimental Design and rise of statistics in medical research
• Scientific method and where statistics fits
• Statistical reasoning
• Chapter 2 – References and suggested reading

2.3 – A brief history of (bio)statistics

Foundations of biostatistics: key definitions.

.

Before discussing history and landmark moments in biostatistics, let’s start with basic definitions.

Bioinformatics is loosely defined as a discipline of biology primarily concerned with work involving large data sets (eg, databases), but a bioinformatician would not primarily be a statistician necessarily. Rather, a bioinformatician in addition to foundation in statistical and mathematical training would likely be fluent in at least one programming language and confident in use and design of databases.

Biostatistics, or biometry, then, refers to use of statistics in biology. Biostatistics encompasses application of statistical approaches to design, analyze, and interpret biological data collected through observation of use of experimentation. In turn, there are many broad disciplines or fields of specialty that trained biostatisticians may work.

Chance, the likelihood that a particular event will occur.

Data scientist, a very general label, is a person likely to work on “big data.” Big data may be loosely and inconsistently identified as access to large detailed and unstructured data sets such as visits and behavior within websites of tens of millions of Internet “hits” to a website like Amazon® or Google®. The data scientist would then be involved in extracting meaning from volumes of this data in a process called data mining. In the context of biology web sites like allele frequency aggregator at NCBI, which houses allele frequency information collected on human populations, the 1000 genome project, or any of the databases accessible at National Center for Biotechnology Information would constitute sources of big data for biological researchers.

Epidemiology refers to the statistics of patterns of and risk of disease in populations, particularly of humans and thus, an epidemiologist would also be considered to be a biostatistician. The statistics of epidemiology include all of the materials we will cover in this course, but perhaps if any particular analytical approach characterizes epidemiology, it would be survival analysis (review in Clark et al 2003) — in competition with compartment models to predict spread of communicable disease in populations (Brauer 2017).

Event, an outcome to which a probability is assigned.

Likelihood, the probable chance of occurrence of an event that has already occurred. Likelihood assesses how well a particular model or set of parameters explains observed data.

Probability, the chance that an event will occur in the future, given a known model or set of parameters.

Random or random chance. This is a good place to share a warning about vocabulary; statistics, like most of science, uses familiar words, but with refined and sometimes different meanings than our everyday usage. Consider our everyday use of random: “without definite aim, direction, rule, or method – subjects chosen at random” (Merriam-Webster online dictionary). In statistics, however, random refers to “an assignment of a numerical value to each possible outcome of an event” (Wikipedia, Eagle 2021). Thus, in statistics, random dictates a method of determining how likely a subject is to be included: If represents the size of the population, then random sampling implies that each individual had chance of being selected. Thus, if , then each individual has a 1% () chance of selection. This is quite different from Merriam-Webster’s definition, in which no method is assumed. To a statistician, then, random as used in everyday conversation would imply haphazard sampling or convenience sampling from a population.

Statistics may be defined as the science of collecting, organizing, and interpreting data. Statistics is a branch of applied mathematics. Note that the word statistic is also used, but refers to a calculated quantity like the mean or standard deviation. A little confusing, but the context in which statistics or statistic is appropriate is usually not a major issue.

From dice games to data science: A brief history of statistics.

.

Figure 1. Soldiers playing dice, painting by Michiel Sweerts (1618–1664). Public domain image, https://commons.wikimedia.org/

The concepts of chance and probability, so crucial to statistical reasoning — because it allows us to interpret data when outcomes are inconsistent — were realized rather late in the history of mathematics. While people have been writing about applied and theoretical math for thousands of years, probability as a topic of interest by (Western) scholars seems to date only back to the late 17th century, beginning with letters written between Pierre de Fermat (1601-1665) and Blaise Pascal (1623 – 1662) and the substantial work on probability by Pierre-Simon Laplace (1749-1827). Often, research on probability developed under the watchful eyes of rich patrons more interested in gaming (sensu Fig 1), than to scientific applications. Work on permutations and combinations, essential for an understanding of probability, trace to India prior to Pascal’s work (Raju 2011).

The history of statistics goes back further if you allow for the dual use of the term statistics, both as a descriptor of the act of collecting data and as a systematic approach to the analysis of data. Prior to the 1700s, statistics was used in the sense of collection of data for use by the governments. It is not until the latter part of the 19th century that we see scholarship on statistical analytical techniques. Many of the statistical approaches we teach and use today were developed in the decades between 1880s and the 1930s. Work by Francis Galton (1822-1911), Karl Pearson (1857-1936), RA Fisher (1890-1962), Sewall Wright (1889-1988), Jerzy Neyman (1894-1981), Egon Pearson (1895-1980, Karl Pearson’s son), George EP Box (1919-2013) remains highly influential today.

Development of randomized controlled (clinical) trials, RCT, the “gold standard,” by the 1950s provides the strongest study design to evaluate the effectiveness of clinical or other kinds of interventions. The general features of RCT are (1) comparison among groups, with at least one control group, (2) randomization, and (3) blinding, where treatment options are concealed from the subjects (single-blind) and from those charged to assess the outcomes (double-blind). Sir Austin Bradford Hill (1887-1991) is generally credited with developing the RCT (Collier 2009, Matthews 2016), but we owe RA Fisher for randomization in experimental design. Hill (1965) is also known for Hill’s criteria of causality — nine principles that can be used to establish causal relationship between epidemiological (observational) evidence and disease. Chief among these nine principles are strength of the association (effect size) and consistent association (reproducibility), elements we return to often in our introduction to biostatistics.  

Since the 1950s, there has been an explosion of developments in statistics, particularly as related to power of computer. These include use of resampling, simulation, and Monte Carlo methods (Harris 2010). Resampling — the creation of new samples based on a set of observed data — is a key innovation in statistics. Its use led to a number of innovative ways to estimate the precision of an estimate (see Chapter 3.4 and Chapter 19). Monte Carlo methods, or MCM, which involves resampling from a probability distribution, is used to repeat (simulate) an experiment over and over again (Kroese et al 2014). Computers have so influenced statistics that some now define statistics as “…the study of algorithms for data analysis” (p 175, Beran 2003). So much so, the role of computers and coding to process and model data, we now have the discipline of Data Science. For more on the history of statistics, see Anderson (1992), Fienberg (1992), and Freedman 1999; for excellent, conversational books read Salsburg (2002) and McGrayne (2011). For influential women in early development of statisticians, see Anderson (1992).

Numbers and prejudice: A hidden history of statistics.

.

Many statistical methods in use today, including regression and analysis of variance methods, can trace their origins to the late 1800’s and early 1900’s (Kevles 1998). Many of these early statisticians developed statistical methods to, at least in part, further their interests in understanding differences between racial groups of humans. Sir Francis Galton, who developed regression and correlation concepts (the details and extensions of which were the works of Karl Pearson), coined the term Eugenics, the “science” of improving humans through selective breeding. In an editorial, the journal Nature recently published an apology for it’s complicity providing “a platform to [eugenicists] views” (p 875, Nature 2022). Sir RA Fisher is rightfully remembered as the inventor of analysis of variance and maximum likelihood techniques (Rao 1992; Bodmer et al 2021), and perhaps more important, developed the concepts of sampling from populations, degrees of freedom, among other contributions. Moreover, work of Fisher, Wright, and others led to the realization that populations of the same species differed at many locations in the genome, thus completely refuting any notion of “racial purity” (Bodmer et al 2021). However, Fisher was an active promoter of eugenics (Bodmer et al 2021), and an award given by The Society for the Study of Evolution in his honor, the RA Fisher Prize, was renamed in 2020.

Eugenics is still with us (Liscum and Garcia 2022; see also Legacies of Eugenics: An Introduction Los Angeles Review of Books; Veit et al 2021), but the era of “Three generations of imbeciles are enough” (Buck v. Bell), and the forced sterilization eugenic programs of the Nazi (Kelves 1999), were thoroughly discredited on scientific grounds many times (click here for Eugenics Archive website). Do keep in mind that the times were different, and elements of eugenics thinking remains with us (cf discussion in Veil et al 2021 and references therein), it is interesting nevertheless to learn about the murky history of statistics and the objectives of some of the very bright people responsible for many of the statistical analyses we use today (see Stephen J. Gould’s “The Mismeasure of Man“). Several books tackle aspects of scientific racism, including 2017 Is science racist? by Jonathan Marks and 2019 Superior: The return of of race science, by Angela Saini, Cathy O’Neil’s 2017 accessible book Weapons of math destruction: How big data increases inequality and threatens democracy, and a host of articles and books listed at Wikipedia.

Keep in mind also that geneticists and statisticians were instrumental in showing why Eugenics was unscientific, at best. See partial listing in Bodmer et al (2021). Also, see  2021 review by Rebecca Sear, Demography and the rise, apparent fall, and resurgence of eugenics, in Population studies: A journal of demography. While the algorithms of statistics should be unbiased — and we often believe that they are — clearly, humans, and the interpretations of data may be biased (Celiktutan et al 2024). Statistical reasoning absolutely requires considering sources of bias and their impacts on our conclusions.

Landmark epidemiology studies.

.

John Snow (1813-1858) is credited by some as the “Father of Epidemiology”(Ramsay 2006). During a London outbreak — the sudden increase of disease events — of cholera in 1854, Snow conducted work to establish cholera mortality with source and quality of drinking water. At the time, the prevailing explanation for cholera was that it was an airborne infection. Snow’s map of cholera mortality in the Golden Square district of London in relation to a water pump on Broad Street is shown in Fig 2, Snow’s theory of contaminated water was not accepted as an explanation for cholera until after his death.

Original map by John Snow showing the clusters of cholera cases in the London epidemic of 1854, drawn and lithographed by Charles Cheffins.

Figure 2. Original map by John Snow showing the clusters of cholera cases in the London epidemic of 1854, drawn and lithographed by Charles Cheffins. Image Public Domain, from Wikipedia.

Snow’s work and dataset can be viewed and thanks to Paul Lindman and others, the work can be expanded: for example, define areas around pumps by walking distance (Fig 3). The R package is cholera. Figure 2 shows a plot like Snow’s annotated map.cholera.

Figure 3. Plot of Snow’s London using R cholera package. Triangles marked with p1-p13 represent public water pumps. Red dots represent cholera cases.

R code to make the plot was

snowMap()

Snow’s ideas about cholera were not accepted in his time and you should recognize that by itself, a cluster map supports both the airborne and waterborne theories. The cholera package contains additional data to help visualize the area, including setting regions by walking distance (Fig 4).

Figure 4. Plot of Snow’s London with walking areas drawn about the 13 water pumps. R cholera package.

R code to make the plot was

plot(neighborhoodWalking(case.set = "expected"), "area.polygons")

Epidemiology of cancer.

.

This is an undeveloped section in my book. For now, I’ve listed a number of key landmark studies — a selective and incomplete list — in the history of epidemiology and cancer risk — these would serve well as case studies:

• Tobacco as a carcinogen
  • Doll R, Hill AB. Smoking and carcinoma of the lung; preliminary report. Br Med J 1950; 2: 739–748
  • Fontham ET, Correa P, Wu-Williams A, Reynolds P, Greenberg RS, Buffler PA, Chen VW, Boyd P, Alterman T, Austin DF, Liff J, Greenberg SD. Lung cancer in non-smoking women: a multicenter case-control study. Cancer Epidemiol Biomarkers Prev 1991;1:35-43
• Diet and cancer risk
  • Kolonel LN, Hankin JH, Lee J, Chu SY, Nomura AM, Hinds MW. Nutrient intakes in relation to cancer incidence in Hawaii. Br J Cancer 1981;44:332-339.
• Obesity, exercise, and cancer risk
  • Calle EE, Rodriguez C, Walker-Thurmond K, Thun MJ. Overweight, Obesity, and Mortality from Cancer in a Prospectively Studied Cohort of U.S. Adults. N Engl J Med 2003;348:1625-1638.
• Hormones and cancer risk
  • Marchbanks PA, McDonald JA, Wilson HG, Folger SG, Mandel MG, Daling JR, Bernstein L, Malone KE, Ursin G, Strom BL, Norman SA, Wingo PA, Burkman RT, Berlin JA, Simon MS, Spirtas R, Weiss LK. Oral contraceptives and the risk of breast cancer. New Engl J Med 2002;346(26):2025-2032.
• Cancer risk and occupations
  • absence of cervical cancer but high incidence of breast cancer in nuns (Ramazzini, 1713)
  • cancer of the scrotums among chimney sweeps of London (Pott, 1775)
  • Silverman DT, Hoover RN, Mason TJ, Swanson GM. Motor exhaust-related occupations and bladder cancer. Cancer Res 1986;46:2113-2116.

Please see review by Greenwald and Dunn (2009).

Questions

1. Write up three learning outcomes for this page. Hint: Point your favorite generative AI to this page and ask for help.
2. Expand my example of landmark studies (also called pivotal or seminal studies) in epidemiology of cancer to a subject of your own interest. For example, vaccination and communicable diseases like polio.

.

Quiz Chapter 2.3

A history of (bio)statistics

Start Quiz

Question

✕

✓

Your answer:

Correct answer:

Next

Please wait..

↺

You got {{SCORE_CORRECT}} out of {{SCORE_TOTAL}}

Your Answers

Chapter 2 contents

.

• Introduction
• Why biostatistics?
• Why do we use R Software?
• A brief history of (bio)statistics
• Experimental Design and rise of statistics in medical research
• Scientific method and where statistics fits
• Statistical reasoning
• Chapter 2 – References and suggested reading

2.2 – Why do we use R Software?

If this page is TL;DR, and you’re in a rush, then instructions to install R onto your macOS or Windows PC are provided in Install R.  To run in the cloud only, see Use R in the cloud.

Why R? The case for using R in biostatistics education.

.

Why do we use R Software? Or put another way: DrD, Why are you making me use R?

Truth? You can use just about any acceptable statistical application to get the work done and achieve the learning objectives we have for beginning biostatistics. However, we will use the R statistical language as our primary statistical software in this course. Part of the justification is that all statistical software applications come with a learning curve, so you’d start at zero regardless of which application I used for the course.

In selecting software for statistics I have several criteria. The software should be:

• if not exactly easy, the software should have a reasonable learning curve
• widely accessible and compatible with all most personal computers
• well-respected and widely used by professionals
• free software
• open source
• well-supported for the purposes of data analysis and data processing
• really good for making graphics, from the basics to advanced
• capable to handle diverse kinds of statistical tests

R meets all of these criteria. R history began back in 1993 and has always been available as free software under the terms of the Free Software Foundation’s GNU General Public License in source code form. R compiles and runs on a wide variety of UNIX platforms and similar systems, including GNU/LINUX, FreeBSD, and various Linux distros like the popular Ubuntu^®, in addition to their more famous Microsoft Windows^® and Apple macOS^® distributions. To facilitate access to the software, numerous mirror sites are available from sites around the world, with cloud.r-project.org supported by RStudio perhaps the most widely used. From January 2024 to December 2024, more than 8.5 million downloads of base R were made from the RStudio CRAN mirror site (CRAN stands for Comprehensive R Archive Network.

install.packages("cranlogs")
library(cranlogs)
# How many downloads of base R around start of Fall semester?
 out <- cran_downloads("R", from = "2025-08-01", to = "2025-08-31")
sum(out$count)

[1] 582524

R is straightforward to use once you learn how to work with the language, but has a steep learning curve; after all, it’s a programming language. I recommend installing the program onto your computer, but ready to go R is also available at multiple cloud services, including Google CoLab and Posit Cloud. The remainder of this page is directed at users who choose to install R to their computer, although much of the discussion holds regardless of the R environment choice, local or Cloud.

For local installs of R, I also recommend use of the GUI R Commander.  Use of R Commander helps with the learning curve, and eventually, your use of code will become second nature. We don’t use RStudio, but as your skills improve, I recommend transitioning to the IDE RStudio; after the initial growing pains are behind you, RStudio likely will be a better solution over R Commander.

This discussion implies learning R programming. However, while we need statistical software to do statistics, students in my BI311 course must keep in mind that learning objectives for a biostatistics course is about the concepts and interpretation of statistics, not just use of the software. In other words, learning how to use R is not the focus of BI311 nor will you likely achieve R programming competency by the end of the semester. I certainly encourage students to strive for competency and I give frequent bonus opportunities to demonstrate coding skills during the semester.

Why R and not some other statistics software?

Thus, you might ask if the purpose of the course isn’t to learn R, why work with R instead of a more familiar app or software, eg, Microsoft Excel^® (hereafter simply referred to as Excel), or Google Sheets, or even my favorite open-source office alternative, LibreOffice Calc? Or, perhaps even just one of the many online calculators, if the course learning objective is to “just” learn about statistics?

First, I believe that real data derived from real biology or biomedical problems are essential elements to a first course in biostatistics. That’s not a particularly unique perspective although I don’t have survey results of other statistics instructors to back up the claim. Real problems involve observations on multiple subjects, many variables — large data sets; this alone precludes use of hand calculations and calculators. As a corollary, we will not spend a great deal of time learning the in’s and out’s of the algorithms that form particular statistical tests. Now, do understand that there is a tremendous benefit to understanding statistics by working through the equations, by looking at the algorithms, and there’s no escaping the need for understanding that probability provides the foundation of statistics inference (Chapter 8). Thus, for most of us, the statistical software available to us provides an appropriate framework for applying correct statistical tests to our projects. Therefore, the decision is about which statistical package we should use.

Second, R is perhaps the choice in academia for statistical software. A PUBMED search found more than 1500 citations of R. Visit Robert A. Muenchen’s web page (The popularity of data analysis software, r4stats.com) to see updated statistics on statistical software use. Those of you continuing on to graduate school or to professional schools will find that many of your statistically literate colleagues use R and not one of the commercial programs. While there are many excellent commercial packages (Table 1), and in some cases you can make spreadsheet programs do statistics (typically add-ins are required), all statistical software come with steep learning curves. Thus, part of my selling point to you is that learning to use R is at the cutting-edge in your field and, given that all of the software you could use can have have their challenges, it is best to work with something that will be around and is in wide use, without the burden of a financial investment.

Table 1. A selective list of statistical software.

see Wikipedia for list of additional software

Third, what about online sites like plot.ly where, for free, you can plot and, in some cases, calculate statistics? What about the web application at Brightstat, which claims to provide an SPSS-like experience online (Stricker 2008)? While it is true that there are many wonderful websites that can perform many of the statistical tests we will use this semester, these sites are not suitable for more than occasional use.

How to get started with R.

.

A few words about my approach to the software in my biostatistics course. I note to students during the semester that our course is not a programming course, but rather, programming skills are acquired along the way. Our focus is how to do statistical analysis, how to design experiments, etc. Coding skills without understanding of the why we’re doing it is not unlike learning to cook by following a great recipe as opposed to learning about the art and science of flavor (NPR Science Friday, March 15, 2024) — the homework is solved but the why we can support our conclusions may be obscure.

We set aside the first couple of class meetings simply to setup student’s Windows PC or Apple macOS computers to do data science; for students with access to Chromebooks or iPad tablets, we need to set them up to run R in the Cloud (eg., Google Colaboratory) — in other words, there’s a lot of pre-work that can present barriers to actual doing statistics in R (or other software). Once we have the environment set up for the students, we utilize a “tell-show-do” approach to learning how to code. The “tell” part includes sharing script; the “do” part is mostly done by students outside of class as part of completing homework.

First work with the language can be frustrating, so I also encourage a “five minute” rule — if it ain’t working, stop. So, by all means when Run through a troubleshooting checklist, but please don’t continue to struggle — the gap is between the instructions and where the student is with the material — it’s a me-as-instructor problem, not a student must work harder problem! 

All statistics work follows a similar workflow.

The basic workflow for a data project, using R as the primary statistical programming tool, looks like that illustrated in Figure 1.

Figure 1. A basic workflow with R.

The workflow begins with the assumption that a data set already exists. Getting the data into an R session depends on the source of the data, for example stored in spreadsheet file or from a table on a webpage. Data cleaning and processing of the data may be in order — for small and modest-sized data sets, my own preference is to do most of the data cleaning in my spreadsheet app, but R has full capabilities to handle or “wrangle” data. Next, the raw data should be stored in R session in a data frame object. Once the data frame object is available, exploratory data analysis, including summary statistics and data visualization can proceed. Higher order analytics, including statistical inference and modeling, can then begin.

The R statistical language, accompanied by additional packages to extend its capabilities beyond basic math and statistical functions, provided a complete statistical environment. R is best viewed as a programming language for statistics (data analysis), and data processing. Power users of R learn how to write scripts that do t-tests, ANOVA, regression, etc. The scripts are just lines of code that R understands and it provides the user tremendous control over analysis and inference of data sets. Because of this flexibility and power, however, R can be intimidating at first. So, we’ll start slowly with scripts, introducing just what we need to get started and build from there. We’ll be addressing R issues in more depth over the next several weeks, but for the first week, our goal(s) should be to make sure each of you knows how to start/exit R, how to create and utilize a working directory, and how to use R as a calculator. You obtain your copy of R from the R Project for Statistical Computing, available at https://www.r-project.org. Instructions to install R are provided in Install R.  A ten-part tutorial to get started using R is provided in Mike’s Workbook for Biostatistics.

 /Users/username/Desktop/BI311

Why R Commander, why not RStudio?

.

We utilize an R package that provides a menu-driven context to much of the typical statistics one needs to do biostatistics. The package is called R Commander (Rcmdr), which provides a graphic user interface or GUI. Rcmdr therefore significantly eases the learning curve for doing statistics with R. We use a package called R Commander, which provides drop down menus for most of the typical kinds of analyses. Rcmdr is in use in many courses across the world (more than 17K downloads in August 2025), and among the other GUI available for R, Rcmdr is among the best supported GUI available for R. R Commander function is extended by plug-ins; as of August 2025, there were 31 plugins that extend Rcmdr’s capabilities. Instructions to install R Commander are provided in Install R Commander. 

Wait! Why don’t we use Excel? My instructor in {insert course here} used Excel…

.

A very reasonable question for you to ask — why don’t we use Microsoft Excel or Google Sheets for statistics? Moreover, it is highly likely that you have gained at least some introduction to descriptive statistics and graphing with spreadsheets in former courses — shouldn’t we learn statistics within a software framework you are already familiar?

After all, “Can’t Microsoft Excel do statistics?” Mostly the answer is, no, not really (Fig 2).

Figure 2. “Spreadsheets,” xkcd.com no. 2180.

MS Excel, Google Sheets, Apple Numbers, and for that matter, Calc, the spreadsheet application in my favorite office app LibreOffice (LibreOffice is a free, open-source alternative to Microsoft Office), can be used to calculate many descriptive statistics. With some effort, these applications can be extended by use of either Analysis ToolPak or Solver Add-ins to do more complicated statistics like regression and analysis of variance, and curve fitting.

However, use of MS Excel for statistical analysis involves learning a number of commands, syntax, and developing workflows that are neither intuitive nor standard. Some publishers have provided add-ins that are reportedly designed to simplify this process (eg, XLStat, UNISTAT, Real Statistics using Excel). None of these options are free and none are in use in any major way by scientists (see Robert Muenchen’s The popularity of data analysis software). The free add-ins of Analysis ToolPak and Solver may work for you if you own a Windows PC, but only Solver is included for the Mac versions of Excel. MacOS users may download and install StatPlus:MacLE, which is a limited, but free alternative to the Analysis ToolPak add-in; for a complete package a Pro version is available (licenses started at $89, web site: www.analystsoft.com/en/products/statplusmacle/).

An additional caution: you should be aware that there have been reports over the years that algorithms selected by Microsoft for Excel have not always been to industry standards (eg, McCullogh and Wilson 2005). In short, the fit of Excel and other spreadsheet apps for use in statistics is not a simple one. To do the kinds of statistics we will use routinely in class, Excel would need to be modified with add-ins, and the add-ins would be the result of programming by someone. And you would still need to learn how to write the code.

What about graphics? You may like Microsoft Excel’s ability to do graphics. Indeed, Excel, Google Sheets, and LibreOffice Calc can be used to generate many typical kinds of statistical plots. But again, in comparison to R, spreadsheet app graphics are limited and require a deal of effort to generate acceptable plots. I think you’ll be surprised at how straight-forward R is. Here’s an example, first rendered in Microsoft Excel, then in base R. And importantly, the kinds of plots Excel does well at are not necessarily the plots suitable for research publication. For example, Excel allows you to make bar charts easily, but cannot do box plots. Box plots are preferred over bar (column) charts for ratio scale data.

Statistics comparisons between R and MS Excel.

.

About that learning curve. Let’s compare R and MS Excel for basic functions common in data analysis. Similar conclusions hold for comparisons to Google Sheets and LibreOffice Calcs.

Table 2 lists the observations we can use to conduct comparisons of the applications.

A simple data set

One of the first steps in data analysis is to produce what are called descriptive statistics. Common descriptive statistics are the mean and the sample standard deviation. Let’s compare Excel and R for retrieving these two statistics.

With Excel, to calculate the arithmetic mean of 24 numbers, enter the values into a single column of 24 rows, then enter “=average(A2:A25)“, without the quotes, into a new cell of the spreadsheet. “A2:A25” refers to where data would be contained in column A rows 2 through 25. Typically the first row in a worksheet would contain the name of the variable, eg, “A.” Depending on the significant figures set, the estimate returned by Excel for the mean of A is 59.58333333.

Similarly, to obtain the standard deviation, type =stdev(A2:A25), into a new cell of the spreadsheet. Again, depending on the significant figures set, Excel returns a value of 37.05215674 for the standard deviation of A.

In contrast, to obtain the mean and standard deviation for a variable in an R data set, all you would type at the R prompt (>), or in the script window

and then submit the code is:

myA <- c(12, 14, 20, 25, 28, 29, 32, 34, 35, 39, 47, 47, 50, 53, 54, 71, 79, 87, 89, 96, 105, 122, 130, 132)

where the “c” is a function to combine arguments into a vector and saved to the object myA, followed at the new line by

mean(myA)

Hit enter after entering the command) and R returns

[1] 59.58333

For the standard deviation, write the R base function sd()

sd(myA)

Hit enter after entering the command and R returns

[1] 37.05216

It’s not much of a difference, but note that to get the mean (arithmetic average) I typed seven characters in R, but 16 characters in Excel; similarly, for the standard deviation I typed in 5 characters in R, but 13 characters in Excel. That’s a savings of 56% and 62%, respectively. Excel tries to help by using AutoComplete to anticipate what you want to enter, but AutoComplete doesn’t always work properly (eg, see gene name errors generated by use of default Microsoft Excel settings, Ziemann et al 2016).

In conclusion, R is quicker for descriptive statistics.

Graphics comparison between R and MS Excel.

.

MS Excel is often cited for its graphics capabilities (Camões 2016). We can make the familiar scatter plots, bar charts, and pie charts in Excel. These plots and more are easily obtained in R. I won’t elaborate here about graphics, we talk at some length about graphics in Chapter 4. But here’s one example in R.

Let’s plot myB vs myA. We already provided the data for variable A, here’s the data for variable B.

17, 21, 21, 26, 27, 32, 28, 42, 40, 30, 71, 53, 56, 61, 55, 89, 82, 63, 116, 162, 116, 154, 137, 149

Don’t recall how to assign a set of numbers to an object, B, in R? See above and look again at how we assigned the numbers to object myA.

To get a simple scatter plot (Fig 3), I may write at the R prompt.

plot(myA,myB)

Figure 3. Basic scatter plot made in R, plot(myA,myB).

And here’s the comparable default plot (Fig 4) from Microsoft Excel, Office 365

Figure 4. Basic scatterplot made in Microsoft Excel.

Now, both graphs need some work, and to be fair, these are just the defaults. With some effort, you can make an Excel graph look pretty good. But note — the defaults in Excel don’t generate axis labels, while R default plot does. Excel adds a useless title and legend; both need to be removed. Excel also adds grid lines where typically one would not include these in a scientific plot; for example, in the case of scatterplots, grid lines can distract the viewer from the data points and reduce the data-to-ink ratio Tufte 1984).

Count the steps to generate an acceptable scatter plot (Table 3). I’ve also added R Commander (Rcmdr) steps for comparisons (Rcmdr lets you use drop-down menus like Excel or Google Sheets or LibreOffice Calcs).

Table 3. Steps needed to make a simple scatterplot in R, R Commander, or Microsoft Excel.

Conclusion? R is quicker for routine statistical plots like a scatter plot. And I didn’t even count the steps needed to change MS Excel’s dreadful diamond icon points.

That’s one step in R, four steps in Rcmdr, but eight steps for Microsoft Excel. LibreOffice Calc is a little better at only four steps, but like MS Excel, you’d need to change several components to the graph (Fig 5).

Figure 5. Basic scatterplot made in LibreOffice Calc.

plot(myA,myB, pch = 22)

So, you’re telling me I don’t need a spreadsheet application?

.

No, not at all. We use spreadsheets, and more generally, databases, to store data. Spreadsheets apps are designed to make data entry and data management approachable and efficient. They remain an important tool for researchers (Browman and Woo 2017).

R is not that great of a spreadsheet; packages are available to seamlessly tie your spreadsheet and database data to R via ODBC. We will routinely enter and manipulate data in MS Excel, then import the data into R for analysis.

Spreadsheet apps like MS Excel and Google Sheets (see also LibreOffice Calc) are great at being a spreadsheet program, R is great at being a statistical software program. You should take advantage of what the tools do best.

Still not convinced?

.

R is in use all over the world, by students and professionals alike and if one is going to spend the time to learn how to use a statistics software program, you should learn a standard program, like R.

And it’s not just me. Read about R in this 2009 New York Times piece, “Data analysts captivated by R’s power.” Look who purchased (April 2015) Revolution Analytics, a major player in the development of the R programming language.

Why install R on your computer?

.

Convenience. Control. Offline.

At the Biology department of Chaminade University, we have installed and maintain R, Rcmdr, and RStudio along with all required packages on our Macbook Pro® Lab computers for your use during class and during optional, proctored biostatistics work sessions. Since 2018, R is increasingly available “in the cloud” (eg, RStudio Cloud), which would mean you could run R in your browser and avoid installation on your computer. You can run significant analysis with R in the cloud via the free Google Colaboratory and CoCalc are now available: I encourage you to look into these platforms. Unfortunately, these services are not quite ready for the classroom. For example, RStudio in the Cloud is free to use on a limited basis, but quickly requires a significant subscription cost with increasing use. Google Colab and GoCalcs require use of Jupyter notebooks, which add yet another layer to the learning curve without focusing on learning statistics. Second, although access to their servers is easy, running simultaneous connections via Chaminade’s single public IP address is likely to lead to problems for us. Third, I want you to use R Commander (Rcmdr) to assist in the learning curve — Rcmdr cannot be run in the Cloud (ie, RStudio in the Cloud, Google Colaboratory, or CoCalc).

Therefore, you are encouraged to install R, Rcmdr, and even RStudio, onto your own computers, in part because of the convenience, but also because R is not generally available to students on campus, ie, only the Biology department’s computers have the up-to-date R software installed.

To get started, go to your Canvas website and view How to install R on your own computer.

An additional benefit to installing a version of R on your computer, you’ll understand more about the software if you take the time to install and if need be, troubleshoot your installation of the software. Moreover, there’s a considerable amount of help out there for R. For example, a simple Google search(keywords: tutorial “install R”), returns more than 700K hits, and more than 40K January 2023 alone (add “after:2023-01-01” to Google search box). In fact, there’s so much out there that you’ll want to sample from several sites and select the voice that works best for you.  

Questions

1. Write up three learning outcomes for this page. Hint: Point your favorite generative AI to this page and ask for help.
2. I listed several spreadsheet apps: Microsoft Excel, Google Sheets, Apple Numbers, LibreOffice Calc. Which of these are free to download and install to your computer? Which are freely available via the Cloud?
3. What level of confidence do you have to this statement: I am confident in my ability to use spreadsheet apps for my BI-311 work this semester. Response options: 
   1. Strongly disagree.
   2. Disagree.
   3. Agree.
   4. Strongly agree.
4. What level of confidence do you have to this statement: I am confident in my ability to use the R programming software for my BI-311 work this semester. Response options: 
   1. Strongly disagree.
   2. Disagree.
   3. Agree.
   4. Strongly agree.

.

Quiz Chapter 2.2

Why do we use R software?

Start Quiz

Question

✕

✓

Your answer:

Correct answer:

Next

Please wait..

↺

You got {{SCORE_CORRECT}} out of {{SCORE_TOTAL}}

Your Answers

Chapter 2 contents

.

• Introduction
• Why biostatistics?
• Why do we use R Software?
• A brief history of (bio)statistics
• Experimental Design and rise of statistics in medical research
• Scientific method and where statistics fits
• Statistical reasoning
• Chapter 2 – References and suggested reading

1.1 – A quick look at R and R Commander

A first look at R.

R is a programming language for statistical computing (Venables et al 2009). R is an interpreted language — when you run (execute) an R program — the R interpreter intercepts and runs the code immediately through its command-line interface, one line at time. Python is another popular interpreted language common in data science. Interpreted languages are in contrast to compiled languages, like C++ and Rust, where program code is sent to a compiler to a machine language application. R is free to use and available via many platforms, from local installations on a person’s laptop to running on cloud servers (Fig 1).

Figure 1. Choose how you will interact with R: on your computer (Blue box) or in the cloud (Red box). Users of Linux, macOS, and WinPC can either install R to their computer or choose to access R in the cloud (and/or, black arrow).

Before you begin, you have a choice: how do you want to work with R (Fig 1)? In part, the choice depends on your computing device. If you have a desktop or laptop computer, running Linux, Apple macOS, or Microsoft Windows, then R can be installed onto your computer (blue box, Fig 1). If, however, you have a ChromeBook, Apple iPad or iPhone, or any Android Tablet or Smartphone, you would go with the second option (red box, Fig 1).

For those going with installing R to their computer, the second choice is to pick the environment for creating and running scripts and managing file input and output during a session. Working environments for R in the cloud include RStudio and Jupyter Notebooks (eg, Google CoLab) (red box, Fig 1 — see Note 2 below). For installed R, two suggested environments are R Commander and RStudio, an Integrated Development Environment or IDE, RStudio (Fig 1). The choice depends on your needs — an IDE is helpful when you plan to write a lot of code, it’s a comprehensive programming environment, which includes many tools that support writing code from scratch.

For our course at Chaminade University, I recommend R Commander because of the drop-down menu approach to accessing statistical functions in R; R Commander is not a comprehensive environment, but it provides the necessary scripting window along with access to markdown editing. R Commander, Rcmdr, is an R package that provide a graphical user interface or GUI for R. It is based on the tcltk package. R must be installed first before installing the R Commander package. R Commander provides familiar menu functions, like many commercial statistical software. R Commander, like the IDE RStudio, is not necessary for R programming or conducting statistical analysis or even generating reports via markdown. R Commander, however, shrinks the learning curve with R programming basics so that students can focus on learning statistics, which is the chief objective of the Biostatistics course at Chaminade.

The following steps user through use of R and R Commander, from installation to writing and running commands. Mike’s Workbook for Biostatistics has a ten-part tutorial, A quick look at R and R Commander, which I recommend.

Install R.

.

Full installation instructions are available at Install R, and for the R Commander package, at Install R Commander. Here, we provide a brief overview of the installation process.

Download a copy of the R installation file appropriate for your computer from one of the Comprehensive R Archive Network (CRAN) mirror site of the r-project.org. For Hawaii, the most convenient mirror site is provided by the folks at RStudio (https://cloud.r-project.org/. In brief, Windows 11 users download and install the base distribution. MacOS users must first download and install XQuartz (https://Xquartz.org), which provides the X Window System needed by R’s GUI (graphic user interface). Once XQuartz is installed, proceed to install R to your computer. MacOS users — don’t forget to drag the R.app to your Applications folder!

Start R.

.

The following is a minimal look at how to use R and R Commander. Please refer to tutorials at  Mike’s Workbook for Biostatistics (R work, part 1 – 10) to learn use of R and R Commander.  

We’re just getting started, so the next thing to learn is how to set your working environment for your R sessions. Although we’ll discuss the R environment more as we proceed, it’s a good idea to start with a best practice action common in data science — always create and work from a working folder. This can be a local folder on your computer or pointed to a folder in your cloud storage. On my mac I usually create a folder on the desktop, example BI-311, and point to that as my working folder for a project. Now, we need to point R to use the working folder — we do this at start of each R session (or modify some code R needs during start up to always point to the folder — for now, we leave that for a later exercise). 

Once R is installed on your computer, start R as you would any program on your computer. For example, the icon for the R.app as it appears in the dock on a MacBook is shown in Figure 2.

Figure 2. R.app icon shown on a MacBook dock.

To point R to our working folder, there are several options. For now, we’ll go with writing and submitting a simple function in R. Recall that R has a command-line. The R prompt appears on the command line in the RGUI as the greater-than typographical symbol “>” at the beginning of a line (Fig 2). The prompt is returned by R to indicate the interpreter is ready to accept the next line of code.

First, discover where R is pointing to by submitting (type the command exactly as written then select keyboard shortcuts on Windows enter, or on macOS return key) the function getwd() at the prompt.

Ready to

On my MacBook, R returns

> getwd()
[1] "/Users/[username]/Documents"

To point to my working folder, I submit setwd("/Users/[username]/Desktop/BI311". When I run getwd() again, R returns the update

> getwd()
[1] "/Users/[username]/Desktop/BI311"

Ready to do some work?

R coding practices in this book and in the companion workbook roughly follow guidance outlined in a September 2018 R-Bloggers post, “R Code — Best practices,” by The R Trader. Of note, naming conventions: variables are nouns, variable names are written in lowerCamelCase; functions are verbs, function names are period separated, eg, my.function; script file names all end with .R and are written snake_case.R. Comments, preceded by #  and a single space, eg, # A brief comment, are sparingly included in code, but reserved for explanatory sentences in the text. We use <- and not = for assignment statements.

Where discussion requires reference to instructions on use of the R programming language, R code (instructions) the user needs to enter at the R prompt are shown in code blocks.

Courier New font within a “code block.”

Until you write your own functions, the general idea is, you enter one set of commands at a time, one line at a time. For example, to create a new variable, curryPoints, containing points scored by the NBA’s Steph Curry during the 2016 playoffs, type the following code at the R prompt (displayed as >, the “greater than” sign)

curryPoints <- c(24,6,40,29,26,28,24,19,31,31,11,18,19)

.

and to obtain the mean, or arithmetic average, for curryPoints at the R prompt type and enter

.

mean(curryPoints)

.

Output from R function mean will look like the following

.

[1] 24.42857

.

Functions in R, or any other data science programming language, are intended to automate a task.

df.curryPoints <- data.frame(curryPoints)

The R prompt appears in the RGUI as the greater-than typographical symbol “>” at the beginning of a line (Fig 3). The prompt is returned by R to indicate the interpreter is ready to accept the next line of code.

Figure 3. The R GUI on a macOS system; red arrow points to the R prompt.

Everything that exists is an object.

.

A brief programmer’s note — John M. Chambers, creator of the S programming language and a member of the R-project team, once wrote that sub-header phrase about R and objects. What that means for us: programming objects can be a combination of variables, functions, and data structures. During an R session the user creates and uses objects. The ls() function is a useful R command to list objects in memory. If you have been following along with your own installed R app, then how many objects are currently available in your session of R? Answer by submitting ls(). Hint: the answer should be one object.

A routine task during analysis is to calculate an estimate then use the result in subsequent work. For example, instead of simply printing the result of mean(curryPoints), we can assign the result to an object. 

myResult <- mean(curryPoints)

.

To confirm the new object was created, try ls() again. And, of course, there’s no particular reason to use the object name, myResult, I provided! Like any programming language, creating good object names will make your code easier to understand.

When you submit the above code, R returns the prompt, and the result of the function call is not displayed. View the result by submitting the object’s name at the R prompt, in this case, myResult. Alternatively, a simple trick is to string commands on the same line by adding ; (semicolon) at the end of the first command. For example,

myResult <- mean(curryRoints); myResult

.

Objects created during an R session, like curryPoints, are stored in memory within the Global Environment. To remove an object, use the command rm(myVariable). Why remove objects during an R session? If you are attempting multiple tasks in a homework assignment, removing unneeded objects helps maintain a clean and organized workspace, improving code readability and reducing the chance of accidental errors. 

Write your code as script.

.

While it is possible to submit code one line at a time, a much better approach is to create and manage code in a script file. A script file is just a text file with one command per line, but potentially containing many lines of code. Script files help automate R sessions. Once the code is ready, the user submits code to R from the script file.

Figure 4 shows how to create a new script file via the RGUI menu: File → New script.

Figure 4. Screenshot of drop down menu RGUI, create new script, Windows 11.

The default text editor opens (Fig 5).

Figure 5. Screenshot of portion of R Script editor, Windows 11. A simple R command is visible.

Submit code by placing cursor at start of the code or, if code consists of multiple lines, select all of the code, then hit keyboard keys Ctrl + R (Windows 11) or for macOS, Cmd + Enter.

I recommend starting with a clean environment, by using rm(list = ls()) at the beginning of a script.

By default, save R script files for reuse with the file extension .R, eg, my_script.R. Because the scripts are just text files you can use other editors that may make coding more enjoyable (see RStudio in particular, but there are many alternatives, some free to use. A good alternative is ESS).

Install R Commander package.

.

By now, you have installed the base package of the R statistical programming language (see for detailed instructions). The base package contains all of the components you would need to create and run data analysis and statistics on sets of data. However, you would quickly run into the need to develop functions, to write your own programs to facilitate your work. One of the great things about R is that a large community of programmers have written and contributed their own code; chances are high that someone has already written a function you would need. These functions are submitted in the form of packages. Throughout the semester we will install several R packages to extend R capabilities. R packages discussed in this book are listed at R packages of the Appendix.

Our first package to install is R Commander, Rcmdr for short. R Commander is a package that adds function to R; it provides a familiar point-and-click interface to R, which allows the user to access functions via a drop-down menu system (Fox 2017). Thus, instead of writing code to run a statistical test, Rcmdr provides a simple menu driven approach to help students select and apply the correct statistical test. R Commander also provides access to Rmarkdown and a menu approach to rendering reports.

install.packages("Rcmdr")

.

In addition, download and install the plugin 

install.packages("RcmdrMisc")

See Install R Commander for detailed installation instructions.

Start R Commander.

.

After installing Rcmdr, to start R Commander, type library(Rcmdr) at the R prompt and enter to load the library

library(Rcmdr)

.

On first run of R Commander you may see instructions for installing additional packages needed by R Commander. Accept the defaults and proceed to complete the installation of R Commander. Next time you start R commander the start up will be much faster since the additional packages needed by R Commander will already be present on your computer.

Note that you don’t type the R prompt and, indeed, in R Commander Script window you won’t see the prompt (Fig 6). Instead, you enter code in the R Script window, then click “Submit” button (or Win11: Ctrl+R or for macOS: Cmd+Enter), to send the command to the R interpreter. Results are sent to Output window (Fig 6). 

Figure 6. The windows of R Commander, macOS. From bottom to top: Messages, Output, Script (tab, Markdown) Rcmdr ver. 2.4-4.

Figure 6 shows how the R Commander GUI looks on a macOS computer. The look is similar on Microsoft Windows 11 machines (Fig 7).

Figure 7. The windows of R Commander, Win11. From bottom to top: Messages, Output, Script (tab, R Markdown) Rcmdr ver. 2.5-1.

We use R Commander because it gives us access to code from drop-down menus, which at least initially, helps learn R (Fox 2005, Fox 2016). Later, you’ll want to write the code yourself, and RStudio provides a nice environment to accomplish your data analysis.

Improve Rcmdr experience.

Windows users: R Commander works best in Windows if SDI option is set. This can be accomplished during R installation (“Startup options” popup, change from default “No” to “Yes” to customize), but you can also change after installing R. Win11 users should change from MDI to SDI — from one big window to separate windows — (see Do explore settings, WinPC see Fig 9; macOS see Fig 10). The downside of SDI is that while multiple Windows may appear during an R session, one or more windows may be hidden by an open window. For example, plots will popup in a new window and may be obscured by the Rcmdr window if full screen. A simple trick to view active windows on Win11 is to use the keyboard shortcut s Alt + Tab to view and cycle between windows. What about SDI and RStudio? RStudio experience will be similar whether MDI (default) or SDI was selected.

macOS users: To improve R Commander performance, turn off Apple’s app nap (see Do explore settings, Figures 6), which should improve a Mac user’s experience with R Commander and other X Window applications.

Complete R setup by installing LaTeX and pandoc for Markdown.

.

LaTeX is a system for document preparation. pandoc is a document converter system. Markdown is a language used to create formatted writing from simple text code.  Once these supporting apps are installed, sophisticated reports can be generated from R sessions, by-passing copy and paste methods one might employ. See Install R Commander for instructions to add these apps.

R Markdown.

.

Markdown is a syntax for plain text formatting and is really helpful for generating clean html (web) files.  R Commander also helps us with our reporting. R Markdown is provided as a tab (Fig 6, Fig 7). Provided you have also installed pandoc on your computer, you can also convert or “render” the work into other formats including pdf and epub. Unsure if your computer has pandoc installed? If you are unsure than most likely it is not installed. 😁 Rcmdr provides a quick check — go to Tools and if you see Install auxiliary software, then click on it and a link to pandoc website to find and download installation file.  You can also confirm install of pandoc by opening a terminal on your computer (eg, search “terminal” on macOS or “cmd” on Win11), then enter pandoc –version at the shell prompt. Figure 8 shows version pandoc is installed on my Win11 HP laptop.

Figure 8.  Screenshot of terminal window (cmd) on win11 computer, checking for installed pandoc on a win10 pc.

Enter your R code in the script window, submit your code, and your results (code, output, graphs) are neatly formatted for you by Markdown. Once the Markdown file is created in R Commander, you can then export to an html file for a a web browser, an MS Word document, or other modes.

Do explore settings!

.

After installation, R and R Commander are ready to go. However, students are advised that a few settings may need to be changed to improve performance. For example, on Win11 PCs, R Commander recommends changing from the default MDI (Multiple Document Interface) to SDI (Single Document Interface).  Check the SDI button via Edit menu, select GUI preferences menu.  Click save, which will make changes to .RProfile, then exit and restart R. Check to make sure the changes have been made (Fig 9). 

Figure 9. Screenshot of GUI preferences settings after changing from default MDI to SDI, win10

For macOS users, both R and Rcmdr will run better if you turn off Apple’s power saving feature called nap. From Rcmdr go to Tools and select Manage Mac OS X app nap for R.app… (Fig 10).

Figure 10. Screenshot Rcmdr Tools popup menu, macOS 10.15.6

A dialog box appears; select off to turn off app nap (Fig 11).

Figure 11. Screenshot Rcmdr Set app nap dialog box, macOS 10.15.6

Exit R Commander.

.

Click on Rcmdr: File → Exit, then choose to exit from just R Commander, or both R Commander and R.

If you exit just R Commander or both R and R Commander, you’ll receive a pop-up request to confirm you want to quit R Commander (click yes), and a second prompt asking if you want to save your script. In general, select yes and then you’ll be able to take up where you left off. Similarly, if asked to save your workspace, choose no. If you save workspace, this creates an .RProfile text file with settings for how R and R Commander will behave the next time you start R. The file will be saved to your current working folder, which R will use the next time R starts. At least while you are getting started, you should avoid creating these .RProfile files.

As long as the current session of R is active, then the library for Rcmdr, as well as any other library loaded during the R session, is in memory. To start R Commander again while R is running,  at the R prompt, type and submit

Commander()

Questions.

1. Biostatistics students should work through my ten R lessons, A quick look t R and R Commander, available in Mike’s Workbook for Biostatistics.
2. Students should also search Internet for R tutorials and R Commander tutorials. Find recent tutorials and work through several of them. We get better when we practice.

Quiz Chapter 1.1

A quick look at R and R Commander

Start Quiz

Question

✕

✓

Your answer:

Correct answer:

Next

Please wait..

↺

You got {{SCORE_CORRECT}} out of {{SCORE_TOTAL}}

Your Answers

Chapter 1 contents

.

• Getting started
• A quick look at R and R Commander
• Chapter 1 – References

4 – How to report statistics

Introduction: Reporting your results.

While you are thinking about exploring data sets and descriptive statistics, please review our overview of data analysis (Chapter 2.4 and 2.5). While the scientific hypotheses come first, how experiments are designed should allow for straight-forward analysis: in other words, statistics can’t rescue poorly designed experiments, nor can it reveal new insight after the fact.

Once the experiments are completed, all projects will go through a similar process:

• Description: Describe and summarize the results.
• Check assumptions.
• Inference: conduct tests of hypotheses.
• Develop and evaluate statistical models.

Clearly this is a simplification, but there’s an expectation your readers will have about a project. Basic questions like how many subjects got better on the treatment? Is there an association between Body Mass Index (BMI) and the primary outcome? Did male and female subjects differ for response to the treatment? Undoubtedly these and related questions form the essence of the inferences, but providing graphs to show patterns may be as important to a reader as any p-value — a number which describes how likely it is that your data would have occurred by chance — eg, from an Analysis of variance.

Each project is unique — sorry, what a breathtakingly obvious statement — but what elements must be included in a results section?

Data visualization.

We describe data in three ways: graphs, tables, and in sentences. In this page we present the basics of when to choose a graph over presenting data in a table or as a series of sentences (ie, text). In the rest of this chapter we introduce the various graphics we will encounter in the course. Chapter 4 covers eight different graphics, but is by no means an exhaustive list of kinds of graphs. Phylogenetic network graphs are presented in Chapter 20.11. Although an important element of presentation in journal articles, we don’t discuss figure legends or table titles; guidelines are typically available by the journal of choice (eg, PLOS ONE journals guidelines).

A quick note about terminology. Data visualization encompasses charts, graphs and plots. Of the three terms, chart is the more generic. Graphs are used to display a function or mapping between two variables; plots are kinds of graphs for a finite set of points. There is a difference among the terms, but I confess, I won’t be consistent. Instead, I will refer to each type of data visualization by its descriptive name: bar chart, box plots, histograms, scatter plot, etc. Note that technically, a scatter plot can refer to a graph, eg, a line drawn to reflect a linear association between the two variables, whereas bar charts and box plots would not be a graph because no function is implied.

Why display data?

Do we just to show a graph to break the monotony of page after page of text or do we attempt to do more with graphs? After all, isn’t “a picture’s worth a thousand words?” In many cases, yes! Graphics allow us to see patterns. Data visualization is a key part of exploratory data analysis (Tukey 1977), or data mining in the parlance of big data (Keim 2001). Data visualization is also a crucial tool in the public health arena, and finding effective graphics to communicate, at times, complex data and information to both public and professional audiences can be challenging (see discussion in Meloncon and Warner 2017). 

Graphics are complicated — all the interplay among pixels etc and rendering process — and expensive to do well. Text is much cheaper to publish, even in digital form. But the ability to visualize concepts, that is, to connect ideas to data through our eyes (see Wikipedia), seems to be more the cognitive goal of graphics. Lofty purpose, desirable goal. Yes, it is true that graphics can communicate concepts to the reader, but with some caution. Images distort, and default options in graphics programs are seldom acceptable for conveying messages without bias (Glazer 2011). 

Here’s some tips from a book on graphical display (Tufte 1983; see also Camões 2016).

Your goal is to communicate complex ideas with clarity, precision, and efficiency. Graphical displays should:

• show the data
• avoid distorting the data
• present numbers in a small space
• help the viewer’s eye to compare different pieces of data
• serve a clear purpose (description, exploration, tabulation, decoration)
• be closely integrated with statistical and verbal descriptions of a data set.

We accomplish these tasks by following general principles involving scale and a commitment to avoiding bias in our presentation.

Importantly, graphs can show patterns not immediately evident in tables of numbers. See Table 1 for an example of a dataset, “Anscombe’s quartet,” (Anscombe 1973), where a picture is clearly helpful.

Anscombe’s quartet

The Anscombe dataset is also available in R packages data(Anscombe, package="carData"), or you can copy/paste from Table 1 into a spreadsheet or text file, then load the data file into R (eg, Rcmdr → Load data set). Note that the data set does not include the column summary statistics shown in the last row of the table.

Before proceeding, look again at the table — See any patterns in the table?

Maybe.… Need to be careful as we humans are really good at perceiving patterns, even when no pattern exists.

Now, look just at the last row in the table, the row containing the descriptive statistics (the means and standard deviations). Any patterns?

The means and standard deviations are the same, so nothing really jumps out at you — does that mean that there are no differences among the columns then?

But let’s see what the scatter plots look like before we conclude that the columns of Y ’s are the same (Fig. 1). I’ll also introduce the R package clipr, which is useful for working with your computer’s clipboard.

Figure 1. Scatter plot graphs of Anscombe’s quartet (Table 1)

#R code for Figure 1.

require(clipr)
#Copy from the Table and paste into spreadsheet (exclude last row). Highlight and copy data in spreadsheet
myTemp <- read_clip_tbl(read_clip(), header=TRUE, sep = "\t")
#Check that the data have been loaded correctly
head(myTemp)
#attach the data frame, so don't have to refer to variables as myTemp\$variable name
attach(myTemp)
#set the plot area for 4 graphs in 2X2 frame
par(mfrow=c(2,2))
plot(X, Y1, pch=19, col="red", cex=1.2)
plot(X, Y2, pch=19, col="orange",cex=1.2)
plot(X, Y3, pch=19, col="yellow",cex=1.2)
plot(X, Y4, pch=19, col="blue",cex=1.2)

And now we can see that the Y ‘s have different stories to tell. While the summary (descriptive) statistics are the same, the patterns of the association between Y values and the X variable are qualitatively different: Y1 is linear, but diffuse; Y2 is nonlinearly associated with X; Y3, like Y1, is linearly related to X, but one data point seems to be an outlier; and for Y4 we see a diffuse nonlinear trend and an outlier.

So, that’s the big picture here. In working with data, you must look at both ways to “see” data — you need to make graphs and you also need to calculate basic descriptive statistics.

And as to the reporting of these results, sometimes Tables are best (i.e., so others can try different statistical tests), but patterns can be quickly displayed with carefully designed graphs. Clearly, in this case, the graphs were very helpful to reveal trends in the data.

When to report numbers in a sentence? In a table? In a graph?

The choice depends on the message. Usually you want to make a comparison (or series of comparisons). If you are reporting one or two numbers in a comparison, a sentence is fine. “The two feral goat populations had similar mean numbers (120 vs. 125) of kids each breeding period.” If you have only a few comparisons to make, the text table is useful:

Table 2. Data from Kipahoehoe Natural Area Reserve, SW slope of Mauna Loa.

To conclude, tables are the best way to show exact numbers and tables are preferred over graphs when many comparisons need to be made. 

Couldn’t I use a pie chart for this?

Yes, but I will try and persuade you to not. Pie charts are used to show part-whole relationships. If there are just a few groups, and if we don’t care about precise comparisons, pie charts may be effective. Some good examples are Figure 1 O’Neill et al 2020, 

Sometimes, people use pie charts for very small data sets (comparing two populations, or three categories, for example). These work well, but as we increase the number of categories, the graphic likely requires additional labels and remarks to clarify the message. The problem with pie charts is that they require interpretation of the angles that define the wedges, so we can’t be very precise about that. Bar charts are much better than pie charts — but can also suffer when many categories are used (Chapter 4.1). 

To illustrate the problem, here’s a couple of pie charts from Microsoft Excel (a similar chart can be made with LibreOffice Calc) for our goat data set; compare this graph to the table and to the bar chart below (Fig 2).

Figure 2. Excel pie chart of Table 2 data set.

A bar chart of the same data (Fig 3).

Figure 3. Bar chart of Table 2 data set

The bar chart (Fig 3) is easier to get the message across; more goat kids were found outside the fenced area then inside the fenced in areas. We can also see that more goat kids were found in the “other” areas compared to the kipuka. The pie chart (Fig 2) in my opinion fails to communicate these simple comparisons, conclusions about patterns in the data that clearly would be the take-home message from this project. Aesthetically the bar chart could be improved — a mosaic plot would work well to show the associations in the project results (See Ch 4.4 Mosaic plots). Furthermore, a strong case can be made that the bar chart is over kill — after all, there’s only the four points to show.

But we are not done with this argument, to use graphics or text to report results. Neither the bar chart (mosaic plot) or the pie chart really work. The reader has to interpret the graphics by extrapolating to the axes to get the numbers. While it may be boring — 1.5 million hits Google search “data tables” boring — tables can be used for comparisons and make the patterns more clear and informative to the reader. Here’s a different version of the table to emphasize the influence of fencing on the goat population.

Table 3. Revised Table 2 to emphasize comparisons between inside and outside the fence line on feral goat population on Mauna Loa.

Table 3 would be my choice — over a sentence and over a graph. At a glance I can see that more goat kids were found outside of the fenced area, regardless of whether it was in a kipuka or some other area on the mountain side. Table 3 is an improvement over Table 2 because it presents the comparisons in a 2 X 2 format — especially useful when we have a conditional set.

For example, it’s useful to show the breakdown of voting results in tables (numbers of votes for different candidates by voters party affiliation, home district, sex, economic status, etc.). Interested readers can then scan through the table to identify the comparison they are most interested in. But often, a graph is the best choice to display information. One final point, by judiciously combining words, numbers, and images, you should be able to convey even the most complex information in a clear manner! We will not spend a lot of time on these issues, but you will want to pay some attention to these points as you work on your own projects.

Some final comments about how to present data.

What your graph looks like is up to you, lots of people have advice (eg, Klass 2012). But we all know poor graphs when we see them in talks or in papers; we know them when we struggle to make sense of the take-home message. We know them when we feel like we’re missing the take-home message.

Here’s my basic, very subjective take on communicating information with graphics — aka a grammar of graphics, sensu Tufte 2001, and Wilkinson 2005.

• Always include proper labeling: axes, units, legends, and captions.
• Minimize white space (for example, the scatter plots above could be improved simply by increasing the point size of the data points)
• Yes, minimize white space, but always respect the scale, particularly when comparisons are intended.
• Avoid bar charts for comparisons if you are trying to compare more than about three or four things.
• Use color sparingly and with intention: a consistent palette distinguishes groups.
• Avoid overly simple graphs with just a handful of points or bars. Just write it up!
• A graphic in a science report that is worth “a thousand words” probably is too complicated, too much information, and, very likely, whatever message you are trying to convey is better off in the text.

Clever graphics may be visually stunning and, perhaps, serve well to advertise the take home message, but likely they need to be accompanied by a sophisticated text as guide to those take home messages.

Homework to go with this topic.

Homework 2B: Graphs in Mike’s Workbook for biostatistics.

Quiz

In addition to ten general questions in quiz-form about this page contents, a total of 94 questions among the several subchapters, a mix of true or false and multiple choice question format. 

Quiz Chapter 4

How to report statistics

Start Quiz

Question

✕

✓

Your answer:

Correct answer:

Next

Please wait..

↺

You got {{SCORE_CORRECT}} out of {{SCORE_TOTAL}}

Your Answers

Chapter 4 contents

• Graphs and tables
• Bar (column) charts
• Histograms
• Box plot
• Mosaic plots
• Scatter plots
• Adding a second Y axis
• Q-Q plot
• Ternary plots
• Heat maps
• Graph software
• References and suggested readings

0.1 – Disclaimers and copyright

Disclaimers

.

Because this is a biostatistics book, many of the examples and problems come from the medical and biomedical research literature. Nothing in this eBook, or included as part of any accompanying text, web site, or supplemental material to this eBook, should be construed as an attempt to offer or render a medical opinion or otherwise engage in the practice of medicine. I may be a doctor, but I’m not that kind of doctor.

Financial and opinion disclaimers

This site is solely supported by me, Michael “Mike” Dohm, and I don’t monetize the site. Responsibility for the content rests with me, not my employer, Chaminade University of Honolulu. The opinions expressed on this website, or supplemental material to this website, are solely those of the myself and do not necessarily reflect the views of my employer. Chaminade University is not responsible for any errors or omissions in this content or any damages resulting from its use.

Trademark Notice

.

Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe or endorse. A partial listing of products mentioned or discussed in this book include the following.

Copyright of the R statistical programming language is held by the R Foundation. R and R Commander are freely available under the GNU General Public License.

Markdown is registered trademark held by John Gruber.

Posit, Rstudio, R markdown, and Shiny are registered trademarks of Posit.

pandoc is the registered trademark held by Dr John MacFarlane.

Microsoft Access, Excel, Word, Microsoft Office, OneDrive, Windows, Windows XP, Windows Vista, Windows 8, Windows 10, and Windows 11 are registered trademarks of Microsoft Corporation.

Finder, iCloud, iPad, iPhone, macOS, Mac OS X, MacBook, MacBook Pro, OS X, Pages, Quartz, QuickTime, and Safari are registered trademarks of Apple Corporation.

LibreOffice is a registered trademark of The Document Foundation.

Chrome, Chromebook, Google Sheets,Google CoLaboratory, Google Docs, Google Drive are registered trademarks of Google LLC.

I have included several cartoons (n = 10) from the wonderful xkcd.com series by Randall Munroe. Copyright clearly belongs to xkcd. 

Other products mentioned in this eBook are the trademarks of their registered owners.

No-responsibility disclaimer

.

Coding examples are provided throughout this eBook. No warranty applies; use of any code examples from this eBook and the “use at your own risk” liability disclaimer applies. The author shall not be liable for any loss of data or other direct or indirect losses that may or may not result from use of code presented herein.

More R code

R code snippets and scripts are written by me, but where noted, may be modified from code shared on line. Since Fall 2026, much of my coding is now done with AI assistance, ChatGPT and Gemini. Where generative AI was used, I declare that use (see AI-DECLARATION.md).

Fair use disclaimer

All efforts to cite and reference scholarly works as needed are included, but there may be some content that may inadvertently refer to works not authorized by the copyright holder. However, Mike’s Biostatistics Book falls under Section 107 of the Copyright Act because it is intended for educational purposes only.

Copyright

.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

How to cite this work

If you wish to use this material, please cite as Dohm, Michael R (2026) Mike’s Biostatistics Book version 3.0, biostatistics.letgen.org.

The eBook does contain my attempt at evidence-based opinion on many statistics subjects. However, as the work is not peer-reviewed, and, like most textbooks, is predominately a secondary source, I would not recommend the eBook as a sole-source reference.

Preface contents

.

Preface

0.1 – Disclaimers and copyright

1 – Getting started

What this book is about.

The primary theme of this applied statistics book is to foster statistical thinking. By developing statistical thinking approaches, biology students gain a way to understand and approach biology problems using statistical concepts and reasoning. Thus, my task in writing chapters was to focus on a problem-solving approach by using real-world data and examples, introducing and expanding on conceptual understanding, and modeling the process of statistical investigation. Our goal is to help students achieve competence in the foundations of biostatistics. Adopting a statistical thinking philosophy is crucial for professionals across medical and scientific disciplines because it provides the analytical tools needed to draw valid, evidence-based conclusions from complex biological and health data.

How to use this book.

.

This eBook is intended to accompany and support students at Chaminade University of Honolulu enrolled in BI-311 Biostatistics, a one semester introduction to biostatistics. Like all textbooks, the intent is to provide the reader with a guided and interactive presentation about the subject. However, the text should not be taken as the only voice — there are plenty of good textbooks, many free, to help you learn statistics. You are encouraged to seek additional help with the material. 

Homework and projects.

.

Mike’s Biostatistics Book is a stand alone product, but the purpose of the book is to provide content for my biostatistics course. Homework and projects designed to build confidence with the material are provided in a separate workbook, also available as a free eBook as Mike’s Workbook for Biostatistics, provides tutorials on R code and project management, homework inspired by chapter contents. The workbook also provides guidance for student-directed projects that enable students to learn biostatistics firsthand.

The websites serve the course,

.

Mike’s Biostatistics Book is hosted at biostatistics.letgen.org. Organization at the site is facilitated by the WordPress wp-gitbook theme by Tom J. Nowell at https://github.com/tomjn/wp-gitbook. Thank you, Tom!

The course, BI-311 Biostatistics, is a CANVAS CMS website is accessible through chaminade.edu. The course website helps me to organize and support the course. BI-311 is web-enhanced course, not a blended or hybrid course; that is, online materials are presented to supplement your work in class and do not replace “face-to-face” time. During — and since — the Covid-19 pandemic I produced a number of videos based on lecture materials for BI-311; many of these are still available at my YouTube channel for the course — they all lack, shall we say, a polished approach.

Students of BI-311 enrolled in CANVAS will find lecture slides, help with your computer, help with R statistical programming language and R Commander, a basic statistics GUI that works with R, and an extensive glossary covering statistics and data science terminology. BI-311 students submit their work to CANVAS course site hosted by Chaminade University. Online quizzes provide rapid feedback and suggestions for further study. 

Material on CANVAS course site  is organized to follow the table of contents from Mike’s Biostatistics book.  For a 16-week semester, the course would be divided into three parts

Part 1. Chapter 1 — 7 → Exam 1

Part 2. Chapters 8 – 14 → Exam 2

Part 3. Chapters 15 — 18 → Exam 3

In addition, students are expected to complete a self-directed student research project, typically a small meta-analysis, but can also be original research based on experiments. I typically do not permit student-led original survey work — surveys are deceptively challenging to do well, require approval from IRB (which is doable, but again, challenging given the time constraitns of the semester), and may detract from the purpose of the project, which is to support learning biostatistics.

Book conventions.

.

Chapters are divided into main subject sections. Subheadings within sections indicate that important concepts follow, concepts you will be expected to understand and demonstrate that understanding on BI-311 quizzes and exams.

Figures and tables in each chapter start with Figure 1 and Table 1. If a figure from chapter 3 is referred to in chapter 5, then the reference to that figure will be Figure 3.1, with Figure 1 referring to the first figure in Chapter 5. Additional notes about the book were provided in the Preface.

Equations were written using LaTeX; in some cases, equations are presented as images.

Each section also include questions and additional readings, particularly where there are opinions or interpretations of statistical concepts, references are provided. For example, we spend considerable time discussing what the “p value” means. Additional readings either extend the discussion or provide context to the topic.

Like any new subject, a key to your success will be to learn the language. Terms in the text requiring definitions and your attention are in bold. Take care with definitions in statistics: while the words are recognizable, their meanings are often distinctly different from common usage.

On many pages I include parenthetical notes, which are intended to provide additional information or tangential information while minimizing disruption to the reader’s attention to the main text. Parenthetical notes are enclosed in green box, like this one.

R code.

.

Throughout the text we will also include relevant R code. R code you type will appear in a sentence as a code block, like help.start(), or as a preformatted shaded text block, like so

help.start()

R code you type will be in blue; any output from R will be displayed as red type. 

Each section includes worked examples that are presented to illustrate concepts, demonstrate how R can be used, and include interpretations as appropriate. 

Questions for the reader.

.

I have added questions at the end of most book sections to emphasize important concepts or to have you explore more about a subject. Questions range from extensions of concepts introduced in the section to exercises and problems to solve. Questions in the text are generally short answer or require a numerical solution.

New as of Fall 2025. Most chapters include about 10 questions based on the readings, a total of 928 as of December. Quiz questions are multiple choice or True/False; click on a response and get immediate feedback. Questions in the book are intended to provide the student with an outline of topics likely to show up on quizzes and exams. On the other hand, the accompanying workbook, Mike’s Workbook for Biostatistics, provides students with opportunities to conduct more detailed data analysis and to learn about the R language.

Chapter 1 contents

.

• Getting started
• A quick look at R and R Commander
• Chapter 1 – References