# T-test and Analysis of Variance (ANOVA)

# Theoretical introduction

The lecture briefly introduces how different variable types determine which statistical methods can be used, what assumptions determine when parametric statistical tests can be used (and which procedures can be used to test these assumptions). The the Analysis of Variance (ANOVA) is introduced starting with some background information and how to do a simple ANOVA manually (in Excel), followd by more extensive background information (such as typical designs, contrasts). Finally, more complex ANOVA models are introduced, starting with Analysis of Covariance (ANCOVA) over the multivariate forms (MANOVA and MANCOVA) to an application of these multivariate forms in profile analysis (e.g., for tracing development over time or distinguishing between subtests within a larger test battery).

The lecture includes practical examples for calculation: A LibreOffice/Excel-file with a demonstration how a very simple ANOVA (with one three-step factor; example from Field (2018), Ch. 12) is calculated by hand, as well as a ZIP file to run a several ANOVA models (ANCOVA, MANOVA and a profile analysis) in MATLAB / Octave (from Tabachnik & Fidell (2013), Ch. 6, 7, 8).

# Practical exercises using SPSS

The PC-exercise deals with the practical aspects of carrying out Analyses of Variance in SPSS. The exercise begins with an brief introduction on the preparation of ones data (e.g., file organization, hot to treat missing values, etc.), then demonstrates the equivalence of a t-test with an univariate ANOVA (if there is only one predictor with two steps), how multiple predictors / factors can be included in the ANOVA (incl. continuous predictors in an ANCOVA) and how multivariate dependent variables can modelled (MANOVA) to the use of the MANOVA within repeated-measures ANOVA and Profile analysis. This is followed by an assignment to test the acquired knowledge practically.

In addition, there is a file with additional assignments and the solutions to it.

Finally, there are two ZIP-files: One with the data files required in the exercise and the assignment, another another containing SPSS syntax (with comments) and SPSS output files for the analyses described in the lecture slides as well as for the additional assignments.