When to use advanced statistical tests
Dr. Harvey Motulsky, President GraphPad Software
GraphPad Insight Issue Number 14, Spring 1998
All contents are copyright © 1995-1998 by GraphPad Software, Inc. All rights reserved.
GraphPad Software focuses on helping laboratory and clinical scientists perform basic data analysis. In controlled laboratory experiments, you generally change one variable and observe the effect on another. GraphPad programs make it very easy to perform the statistical tests you need to analyze these kinds of data. But sometimes you need more advanced tests, and this article introduces you to the kinds of tests available.
The most common situation where you need an advanced statistical test is when you have more than one independent variable. The outcome variable is called the dependent variable. Variables that affect the dependent variable are called independent variables. Multiple regression, and related tests, fit a model to best predict the dependent variable from two or more independent variables. These tests are sometimes used when you manipulate several independent variables at once, perhaps dose and time. They are also used when you manipulate only one independent variable (treatment), but you want to correct (adjust) the results for differences in other variables such as age or disease severity.
Multiple regression is used when the dependent variable is a continuous measurement such as blood pressure or enzyme activity. Standard multiple regression fits to a simple model:
Y = ß0 + ß1X1 + ß2X2 + ß3X3 …
The independent (X) variables can be continuous (i.e. age or weight) or categorical (i.e. gender coded as 0=male; 1=female). The results of multiple regression tell you which of the X variables make a significant contribution to predicting Y and the best-fit results of the coefficients. You can read more about the theory and interpretation of multiple regression in the InStat Guide to Choosing and Interpreting Statistical Tests.
An entire family of statistical tests is related to multiple regression. Stepwise variable selection procedures figure out which subset of X variable(s) contributes the most towards predicting Y. Cox proportional hazards regression fits a multiple regression model where the outcome is survival time. Logistic regression is used when the outcome is a categorical variable with two possible outcomes (i.e. male/female, success/failure). Multiple nonlinear regression allows for nonlinear relationships between the outcome Y and the various independent X variables; i.e. fitting a response as a function of both dose and time.
When the independent variables are categories (treatment, gender, strain) rather than measurements (blood pressure, weight), factorial ANOVA is the appropriate test. The simplest form is two-way ANOVA to simultaneously test for the effects of two grouping variables. For example you might want to test the effects of several different drugs (factor 1) on two strains of animals (factor 2). Extensions of ANOVA account for repeated measurements in the same subject, posttests between treatments, and analyzing more than two factors at once.
InStat and Prism are primarily designed to analyze data from experiments with straightforward designs. The tests discussed above are not performed by any GraphPad program, with the exception of multiple regression (performed by InStat, but without any stepwise procedures) and two-way ANOVA (performed by Prism, but without posttests or repeated measures). You’ll need more advanced programs (or a statistician) to analyze more complex experiments or studies. To learn more, link to recommended books and programs from the recommendation section of the GraphPad Data Analysis Resource Center on our home page.