Chapter 19 Summarizing and Analyzing Your Data With Statistics
You will be using a variety of statistical tests to evaluate your data. These tests quantify the probability that you have obtained your results by chance, which lets you to determine whether you should accept or reject your hypothesis.
Tables 1-3 below outline the most common statistical methods used in general biology teaching labs. Each tool or test is explained in more detail on subsequent pages of the Guide with a:
- Description of what the test is used for;
- What the statistical hypotheses should look like;
- Sample of the test applied to a small dataset; and
- Description of how to interpret and report your data.
Table 1. Descriptive and Summary Statistics
| Tool or Test | Example | How Is It Used? |
|---|---|---|
| Arithmetic Mean | 2019 mean household income in the US was $116,735. | Estimates the middle of the range of values mathematically. |
| Median | 2019 median household income in the US was $68,703 | Estimates the middle of a range of values using observed measures. Measurements are sorted in rank order; the middle measurement is the estimated middle of the distribution. |
| Standard Deviation | Normal adult blood hemoglobin averages 42.1 ± 3.28% | Estimated spread in the measurements |
Table 2. Comparisons and Hypothesis Testing
| Tool or Test | Example | How Is It Used? |
|---|---|---|
| Two-sample t-test | Comparing the mean heavy metal content of clams collected in Nova Scotia vs. New Jersey | Tests a null hypothesis that the means of a measurement variable are the same in two groups. |
| Paired t-test | Compare cholesterol level in blood of people before vs. after switching to a vegetarian diet. | Tests a null hypothesis that the means of the measurement variable are the same before vs. after a treatment. |
| ANOVA | Compare blood cholesterol levels of male vegetarian, female vegetarian, male omnivorous, and female omnivorous students. | Tests a null hypothesis that 3+ different groups have the same means for the measurement variable. |
| Chi-square goodness of fit | The number of red, pink, white flowers in a genetic cross fits an expected 1:2:1 ratio | Tests a null hypothesis that observed frequencies are not different from expected frequencies. |
| Chi-square independence | Compare the proportion of HIV patients who get worse after taking a new drug to the proportion who get worse after taking a placebo | Tests a null hypothesis that proportions are same in different groups. |
Table 3. Statistical Modeling
| Tool or Test | Example | How Is It Used? |
|---|---|---|
| Correlation | Measure salt and fat intake in different people’s diets, to see if people who eat a lot of fat also eat a lot of salt | See whether two variables are potentially related to each other. (Correlation is not the same as a causal relationship.) |
| Linear regression | Measure chirping speed in crickets at different temperatures, & test whether chirping speed varies with temperature | See if changes in an independent variable predict changes in a dependent variable. |
| " | Estimate air temperature based on chirping speed of crickets | Estimate the value of one unmeasured variable corresponding to a measured variable |
19.1 Where to Learn More
This Guide covers just a fraction of all there is to know about biostatistics. This introduction will get you started thinking about some foundation concepts and using some simple tests. When you are ready, check out these additional resources.
HHMI Data Explorer is an interactive web site that you can use to build graphs and learn how different parts go together. In the Materials box on the right side is a link to download the HHMI Statistical Analysis Selection Guide. This short reference helps you choose the right statistical test for your data.
MacDonald’s Biostatistics Handbook. This is an exceptional resource. Much of the information in this portion of the Guide is based on Dr. MacDonald’s book, which he kindly granted us permission to use. http://www.biostathandbook.com/
Motulsky H. 2013. Intuitive Biostatistics: A Non-Mathematical Guide to Statistical Thinking, 3rd edition. Oxford University Press, 576 pp.
Nuzzo R. 2014. Statistical errors: P values, the ‘gold standard’ of statistical validity, are not as reliable as many scientists assume. Nature, 506:150-152.
19.2 Instructors’ Supplement
19.2.1 Adapting Your Guide
Our introduction to biostatistics describes the statistical tests that our students use most often. If there are other statistical tests that are more appropriate for the types of analyses your students do, add new descriptions for them to the tables on this page, add new pages outlining each test, and remove any current ones that are not needed.
Alternatively, if your students have a separate statistics resource guide, the pages on biostatistics can be deleted entirely. Be sure to refer your students to the local resource.