What is the difference between a t-test for 2 independent samples vs. a paired t-test? Give...

What is the difference between a t-test for 2 independent samples vs. a paired t-test?

Give an example of when a Chi-squared test would be used. How would you find the degrees of freedom (df) for one of these tests?

Expert Solution

2 independent samples t test is used to test 2 groups which are independent of each other, that is, not related in any way. So, participants of one group are not related to the participants of the other group.

Paired samples t test is used to test 2 groups which are related in some way or the other. This means that (i) participants of the two groups may be totally same, or (ii) participants of the 2 groups are genetically related, or (iii) participants of one group can be matched with the participants of the other group by some attribute.

We use the chi-square test to test the association between 2 variables. For example, testing whether gender (Man or Woman) is associated with preferred holiday type (Beach or Mountains).

For degrees of freedom calculation, we first consider the levels of the 2 variables. For gender, it is = 2 = r (say). For preferred holiday type, it is also = 2 = c.
Hence, df = (r - 1)(c - 1) = 1 * 1 =1.

orchestra answered 2 years ago

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