The chi-square “goodness of fit” tests hypotheses that the proportions from the obtained sample are a “good fit” to the proportions known to exist in the population, i.e., the expected proportions. It can also test whether proportions are occurring randomly.
Test of Correlation
Correlation analysis is used in case of two continuous variables. Let's say we want to explore the relationship between height and weight. We will use correlation to measure this relationship.
Independent Sample T-Test
One way of measuring the difference between two samples is to compare two unrelated samples. In some experimental designs, you measure two groups one time. With independent samples, you test whether the means of the samples are, not just different, but statistically significantly different.
ANOVA is used for comparing 3+ groups or 3+ variables in 1 group. For example:
One-way ANOVA can be used to compare whether children from school A, B, and C have equal mean IQ scores.
Repeated measures ANOVA can be used to compare whether the mean rating for beer A, B, and C is equal for all people.