# Should I use an independent samples t-test or ANOVA?

Posted July 13, 2020

Those new to statistical analysis sometimes wonder if they should use an independent samples t-test or a one-way ANOVA.  Let’s start at the beginning.  Both of these tests assess differences in a scale level variable by categorical, nominal variable.  For example, is there a difference in GPA by gender.

### Assumptions

Both the t-test and the ANOVA have the same assumptions: normality and homogeneity of variance.  The normality assumptions can be assessed with a Shapiro Wilks test or by a Q-Q scatterplot.  The homogeneity of variance test can be assessed with the Levene’s test.  In the Shapiro and Levene’s test, a non-significant result indicates that the assumptions of the independent sample t-test or one-way ANOVA are met.

So which one is better?

For a test of difference in a scale variable by a dichotomous, categorical independent variable, both tests’ results are exactly the same.  In fact, if you squared the resulting t-value, it would equal the F-value.  The probability is exactly the same too.  If the probability is 0.05 or less, we conclude that the means are different, then look to see which mean is larger or smaller.

Caveat

If your independent variable has three or more categories, then you must use the ANOVA.  The t-test only permits independent variables with only two levels.

If you want to see for yourself, you can go to www.IntellectusStatistics.com, try it for a week for free, download an example dataset, and run both the independent samples t-test and the one-way ANOVA.

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