What kinds of questions can you answer with an ANOVA (one or two-way), a t-test, and a Chi-squared analysis?

A T-test is used to compare two samples or two population means, where both sets of data have normal distributions. A T-test can be used to see whether or not men and women spend different amounts of money on shoes per year, or whether two different apple orchards produce the same amount of apples per tree.

A Chi-squared test is used to see if there's a difference between expected frequencies and observed frequencies. It's often used in population studies relating to genetics, for example, when determining the frequency of genes in a population vs. the observed genetics or phenotypes in that population.

An analysis of variance (ANOVA) is used when comparing the differences between groups and among groups, an assessment that's not possible in a T-test that compares two groups. We cannot conduct multiple T-tests between and among groups because statistical power will be lost. For example, if we're comparing the growth and reproduction rates between animals that are fed three different types of food, we'd use an ANOVA to compare the variance among the groups.