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

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!

• Your professor told you incorrect information.
– Dave
Sep 21 at 21:39
• One way ANOVA on two groups is equivalent to the corresponding two-sided t-test. You should get the same p-value every time. Sep 22 at 3:00
• The exceptions would be if there is a Welch test performed (default behavior in R) or if the calculation winds up doing a paired test.
– Dave
Sep 22 at 3:05

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).