There are many different statistical test procedures. Before we look at the tests you may use, let’s do some quick reminders!
Remember that the idea with test procedures is that you have a null and alternative hypothesis, and you are examining whether your data allows you to reject the null hypothesis in favor of the alternative hypothesis. If we fail to reject the null, that does not mean that we’ve proven the null to be true because we had to assume the null was true to do all the computations for the test.
Key pieces of the output for a statistical test include the test statistic and P-value. P-values are computed based on different distributions for the different test procedures, but you don’t need to worry about this detail.
Test procedures will allow you to investigate hypotheses of interest, but remember that if you are interested more in the parameter estimates (for example, questions like: what is the difference in average claw width between female and male crabs), you can also generate confidence intervals for the parameters. Now let’s take a look at some statistical test procedures you will see in Biology classes.
Broadly speaking, hypothesis tests can be divided into two classes of tests: parametric tests and nonparametric tests. The difference between the classes relates to the conditions underlying these procedures. Parametric procedures tend to have a condition that specifies the variable of interest must have a normal distribution, or a similar sort of constraint. Nonparametric procedures have more relaxed conditions. Most of the tests you will see are probably parametric test procedures, but you should be aware that nonparametric tests exist and may see them in some applications, especially when parametric conditions do not appear to hold.
Examples of parametric tests:
Two-sample t-test– There are many different t-tests. For the test you will see, we will assess the difference in means between two independent populations. The predictor variable is categorical and response is quantitative (most often, continuous).
Chi-square of homogeneity– These related tests can be used to determine whether two categorical variables vary with respect to group. Both the predictor and response variables are categorical. Counts are compared.
Two-way ANOVA (ANalysis Of VAriance)- This test has a simpler form (a one-way ANOVA) that allows you to compare means across 3 or more independent populations (one categorical predictor and a (continuous) quantitative response). For the two-way setting, you add an additional categorical predictor variable. So, the two-way ANOVA allows you to examine differences in means across groups defined by 2 categorical predictors variables. In other words, two-way ANOVA allows you to determine whether two categorical variables can explain variability about the mean of the continuous response variable.
Simple linear regression– This procedure allows you to evaluate whether the predictor variable can predict values of the response variable based on a linear relationship between the two variables. Both the predictor and response are quantitative variables.
Based on the descriptions of tests, you can see that determining the variable types and knowing which is predictor and response is important to helping to identify an appropriate test procedure. If you aren’t sure about which test procedure to use, there are reference materials available to assist you. As the procedures you want to use become more advanced (and/or complicated, depending on your point of view) in your future professional life, you can ask a statistician (or biostatistician) for assistance!
Nonparametric Analogs:
Many parametric tests have a nonparametric analog (a nonparametric test you can often turn to if the parametric distribution conditions fail to hold). For the tests described above, the analogs are:
| Parametric Procedure | Nonparametric Procedure |
| Two-sample t-test | Mann-Whitney test or Wilcoxon Rank Sum |
| One-Way ANOVA | Kruskal-Wallis |
| Pearson Correlation in simple linear regression | Spearman correlation |
Additional non-parametric tests you may use include the Kolmogorov-Smirnov test.