# T-test and Analysis of Variance (ANOVA)

### From psychmethods

# Using jamovi

t-tests are covered as the second part of an introductory lecture on uni- and bivariate statistics. Building upon that, another lecture covers multivariate analyses. It first 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). Then, the Analysis of Variance (ANOVA) is introduced starting with some background information and how to do a simple ANOVA manually (in Excel), followed by more extensive background information (such as typical designs, contrasts). Finally, it will be described how several kinds of the ANOVA can be carried out in jamovi, starting with a simple One-Way ANOVA, extending it into a factorial ANOVA, adding continuous covariates (ANCOVA) and ending with a repeated-measures ANOVA.

For an introduction from another perspective, you can head to chapter 13 and chapter 14 of “learning statistics with jamovi” or to a video introduction by Barton Poulson from datalab.cc.

# Using SPSS

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 Analysis of Variance (ANOVA) is introduced starting with some background information and how to do a simple ANOVA manually (in Excel), followed 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 PC-exercise deals with the practical aspects of carrying out Analyses of Variance in SPSS. The exercise begins with a brief introduction on the preparation of one's data (e.g., file organization, hot to treat missing values, etc.), then demonstrates the equivalence of a t-test with a 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 two further ZIP-files accompanying it: The first contains the data files required in the exercise and the assignment, the other contains SPSS syntax (with comments) and SPSS output files for the analyses described in the lecture slides as well as for the additional assignments.

# More in-depth on the theoretical background

Both lecture slides include 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.

The slides on SPSS further contain 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).