Question

What kind of data lend themselves to perform an analysis of variance and/or an independent-samples t test? Given your answer above, why should you use analysis of variance instead of just using an independent-samples t test?

Answer 1

T-test tests for differences between means of two independent groups. ANOVA tests for differences between means for 2 or more groups. ANOVA test for variation between the means and within each mean. That is, ANOVA uses a different calculation. Its value is in looking at variation between and within the means. It not only compare the means (like the t-test) but examines the variation in calculating the means. Excessive variation in calculating a mean reduces the chance of determining a significant difference. The ANOVA test is robust to the assumption of normality.

T test vs ANOVA.

There is a very thin line of separation between t-test and ANOVA, i.e. when the population means of only two groups is to be compared, the t-test is used, but when means of more than two groups are to be compared, ANOVA is used.

When we are comparing the two or more groups using t test then there may be the chance of type 1 error occure. So thats why when we are comparing the two or more groups we used ANOVA instead of indepedent t test.

Three separate t-tests would affect the stated or desired level of significance. You would increase the risk of committing a Type 1 error.