How does ANOVA compare to other statistical tests like the t-test?

ANOVA compares means across multiple groups, while the t-test compares means between two groups. ANOVA is useful when comparing three or more groups, while the t-test is suitable for comparing two groups. ANOVA assesses overall group differences, while the t-test evaluates differences between specific pairs of groups. Both tests examine variability in data, but ANOVA considers both within-group and between-group variability, providing a more comprehensive analysis.

Analysis of Variance (ANOVA) is one of the first tests that you are introduced to in an introductory statistics class. Simply put, an ANOVA allows you to compare the variance within and between multiple (three plus) groups (with the variance here referring to the spread of values in data). This can be quite helpful when comparing average scores between test groups. Let's say we are testing the average amount of water that three containers can hold. We can use an ANOVA to put these groups against each other. However, if we want to figure out which containers differ from each other we need to perform a post-hoc test (I prefer Welch). While similar to an ANOVA, the T-Test strictly compares the means between two groups.

What is an ANOVA? An ANOVA is a statistical test for comparing more than two groups or levels. Consider groups A B and C, if I wanted to see whether there was an effect, I would have to compare: A vs B A vs C and B vs C The fact that I run three t-tests would incur an error rate of ~15% not the conventional 1 in 20 5% rate. The ANOVA or F test is an omnibus test which compares the evaluates the group means against the grand mean or overall sample population mean. There are still parametric assumptions that must be met for the test to be valid: homogeneity of variance normally distributed residuals independence of results

The Analysis of variance is one of the parametric tests and a statistical method commonly used to compare more than two population means and it is assumed that the samples are drawn from normally distributed populations with equal population variances.

The T-test is also a parametric test as a statistical analysis determining whether the means of two samples significantly differ and we utilize the t-distribution when the standard deviation is unknown and the sample size is small and it determines if two samples are drawn from the same population.

ANOVA and t-tests are statistical methods used to compare means but they differ in several ways as T-tests only compare means between two groups while ANOVA can compare means among three or more groups. ANOVA incorporates post hoc tests (Tukey test, Bonferroni correction) to handle multiple comparisons and control the overall error rate

The assumptions of T-tests and ANOVA are similar as we assume that the data are normally distributed and that the two groups being compared are equal (equal variance assumption), be sure that your dependent variable is quantitative while your independent variable is categorical.

When you want to study if there is a significant difference in the mean age of respondents across their Body mass index level ( with more than three groups), so the One-Way ANOVA is the right statistical test to use as we have one dependent variable related to Age while the independent variable is the BMI