Welch’s ANOVA is an alternative to conventional ANOVA that does not require equal variances. It may be more resilient when there is variable variance.

Welch’s ANOVA is designed to be resilient when the premise of equal variances is violated. It achieves this robustness by modifying the conventional F-statistic to account for unequal variances. The Welch F-statistic, which accounts for various group variances, is computed using the mean squares ratio.

The Levene’s test revealed significant differences in variances between ethnic groups in my earlier ANOVA analysis, casting doubt on the fundamental premise of equal variances in conventional ANOVA. I chose Welch’s ANOVA as a replacement because I understood how its distinct design addressed different variances by varying the F-statistic and degrees of freedom for greater precision. The Shapiro-Wilk tests, however, revealed that the age distribution was not normal in the majority of racial groups. I recognise that large deviations from normalcy can have an impact on results, even though Welch’s ANOVA can handle minor deviations. The severity of these violations, as well as the specifics of my dataset, will determine whether I use Welch’s ANOVA or investigate other options. In some cases, I might consider using non-parametric tests  when there is extreme non-normality or small sample numbers.