Question

Compare and contrast t-test and ANOVA:

1. what do they test for?

2. How do they do it?

3. When would you use them?

Answer 1

(1)

Both t test and ANOVA test for significance of difference between means of groups. Both of them are parametric statistical techniques used to the test the hypothesis of significance of difference between group means.

(2)

(i)

t test is used to compare the means of two populations.

In t - test, the test statistic is given by:

where

= sample mean

= population mean

s = sample SD

n = sample size.

For Degrees of freedom = n - 1 and given Significance level = , critical values of t are taken from Table.

If the calculated value of t is less than critical value of t, Fail to reject the null hypothesis. We conclude that there is no significant difference between means of the two populations.

If the calculated value of t is greater than the critical value of t, Reject the null hypothesis. We conclude that there is significant difference between means of the two populations.

(ii)

ANOVA is used to compare the means of more than two popations.

In ANOVA test statistic is:

F = Between Sample Variance/ Within Sample Variance.

For Degrees of Freedom of numerator = n1 - 1 and Degrees of Freedom of denominator = n2 -1 and given significance level , critical value of F is taken from Table.

If the calculated value of F is less than critical value of F, Fail to reject the null hypothesis. We conclude that the there is no signicant difference between population means.

If the calculated value of F is greater than critical value of F, Reject the null hypothesis. We conclude that there is significant difference between population means.

(3) t test is used when we have to compare the means of two populations.

ANOVA is used when we have to compare the means of more than two populations.