ANOVA is a statistical method for analysing differences in group means in a sample. Can the data from the Washington Post assist me in determining whether there are any significant differences in the ages of people shot across different races?

Null Hypothesis (H0): There is no significant difference in age means across races.
(In the frequentist interpretation, a small p-value indicates that the observed data is unlikely to have occurred by chance, leading to the rejection of the null hypothesis. It is called a ‘frequentist’ theory because it views probabilities as the frequency of events occurring over repeated experiments. It contrasts with the Bayesian approach, in which probabilities can also represent degrees of uncertainty.)

Alternative Hypothesis (H1): Significant difference in the means of age across different races.

Let’s do the Shapiro-Wilk test for normality and Levene’s test for Homogeneity of Variances.

The lack of variance homogeneity and the absence of normality in any major group raises concerns about the robustness of the ANOVA results. Out of curiosity, I continued with ANOVA and obtained the following results.

Given the assumptions violations, I must interpret these results with caution. While the results indicate significant differences, the reliability is questionable, despite the fact that I intuitively believe them after looking at the data for a long time.

I’m thinking about doing more analyses, like Welch’s ANOVA or non-parametric tests, to see if the results are consistent across methods.