# Statistics

How do I report a 1-way between subjects ANOVA in APA style? Three or four things to report You will be reporting three or four things, depending on whether you find a significant result for your 1-Way Betwee Subjects ANOVA 1.

Introduction. Welcome to the Handbook of Biological Statistics!

This online textbook evolved from a set of notes for my Biological Data Analysis class at the University of Delaware. My main goal in that class is to teach biology students how to choose the appropriate statistical test for a particular experiment, then apply that test and interpret the results. I spend relatively little time on the mathematical basis of the tests; for most biologists, statistics is just a useful tool, like a microscope, and knowing the detailed mathematical basis of a statistical test is as unimportant to most biologists as knowing which kinds of glass were used to make a microscope lens.

Statistics Glossary: L. Lack of Fit.

For certain designs with replicates at the levels of the predictor variables, the residual sum of squares can be further partitioned into meaningful parts which are relevant for testing hypotheses. Specifically, the residual sums of squares can be partitioned into lack-of-fit and pure-error components. This involves determining the part of the residual sum of squares that can be predicted by including additional terms for the predictor variables in the model (for example, higher-order polynomial or interaction terms), and the part of the residual sum of squares that cannot be predicted by any additional terms (i.e., the sum of squares for pure error).

Data transformations. Many biological variables do not meet the assumptions of parametric statistical tests: they are not normally distributed, the variances are not homogeneous, or both.

Using a parametric statistical test (such as an anova or linear regression) on such data may give a misleading result. In some cases, transforming the data will make it fit the assumptions better. To transform data, you perform a mathematical operation on each observation, then use these transformed numbers in your statistical test. For example, as shown in the first graph above, the abundance of the fish species Umbra pygmaea (Eastern mudminnow) in Maryland streams is non-normally distributed; there are a lot of streams with a small density of mudminnows, and a few streams with lots of them. Applying the log transformation makes the data more normal, as shown in the second graph.