Robustness - Independent samples t-test vs. One-Way ANOVA

Question

I am trying to compare the means of two groups (male/female) for different attitudes. Since my data sometimes violate the assumptions of normality and heteroscedasticity, I was planning to do a Mann-Whitney U Test. However, my professor insisted that I still use a parametric test and told me that a One-way ANOVA is more robust to such violations that a regular t-test. Now, my questions are:

• Is a One-way ANOVA more robust than an independent samples t-test?
• Can I report differences in means for just two groups, using ANOVA?

I have a copy of the SPSS guide by A. Field and would like to make such a statement: "On average, participants experienced greater anxiety to real spiders (M = 47.00, SE = 3.18) than to pictures of spiders (M = 40.00, SE = 2.68). This difference was not significant t(22) = −1.68, p > .05."

It is from the chapter on t-tests (which makes sense!), but now I am confused whether or not I can make a similar statement based on an ANOVA (for two groups only). Thanks!

Answer 1

For two samples, the standard (two-sided) two-sample t-test and an ANOVA are equivalent (unless the t-test is run with a correction for unequal variances). ANOVA is not more robust in any way. (One can easily show that $F=t^2$ where $F$ is the ANOVA test statistic and $t$ is the one of the two-sample t-test.)

There is no reason to prefer ANOVA for two groups. Note that the two-sample t-test can be run without issues in a one-sided way (for example testing $\mu=0$ against $\mu>0$) whereas the ANOVA F-test cannot (because due to $F=t^2$ it doesn't differentiate between whether $t$ is larger or smaller than 0).