ANOVA (f-test)

ANOVA (‬
‭ F-tests)‬
‭

‭T-Test Limitations‬
‭➔‬‭t-tests may be fun (😀) but they have a few‬‭limitations‬‭,‬‭3 to be exact‬
‭◆‬ ‭can only compare‬‭two group means‬‭at a time‬
‭◆‬ ‭can only analyze‬‭one independent variable‬‭at a time‬
‭◆‬ ‭conducting too many tests‬‭increases the Type 1‬‭error‬‭rate‬
‭➔‬‭to combat these limitations, we conduct‬‭ANOVA‬‭s‬
‭◆‬ ‭the‬‭analysis of variance‬
‭◆‬ ‭essentially a t-test that’s been expanded to hold more than 2 groups of variables at a time‬

‭What Can ANOVA Do?‬
‭➔‬‭compare‬‭two or more groups‬‭at a time‬
‭➔‬‭analyze‬‭one or more independent variables‬‭simultaneously‬
‭➔‬‭test for‬‭interactions‬‭between independent variables‬
‭➔‬‭controls for type 1 error rate‬


‭➔‬‭the ANOVA uses the‬‭f statistic‬
‭◆‬ ‭F = t‬‭2‬

‭Assumptions‬
‭➔‬‭same as the ones used for independent samples t-tests as they’re equivalent tests‬
‭➔‬‭the data/observations are‬‭independent‬
‭➔‬‭assume the‬‭DV is normally distributed‬‭for‬‭all groups‬
‭➔‬‭assume that the‬‭variances are homogenous‬‭across‬‭all‬‭groups‬
‭➔‬‭no outliers‬‭beyond +/- 4sd in all groups‬

‭Logic of Using ANOVA‬
‭➔‬‭the‬‭purpose‬‭of collecting samples is to‬‭estimate the‬‭populations parameters from sample‬
‭statistics‬
‭➔‬‭two ways of estimating population variance‬
‭◆‬ ‭error estimate‬‭(σ‬‭2‬‭e‭)‬ -‬‭within group variance‬
‭●‬ ‭the variance found within samples‬
‭◆‬ ‭treatment estimate‬‭(σ‬‭2‬‭t‭)‬ -‬‭between group variance‬