Question

Question:
Please indicate if the following are independent or paired samples of t-tests:
a) Attitudes of 8th graders toward art before and after visiting a museum on a field trip
b) Differences in political opinions of father and sons
c) Differences in rates of attendance at Rutgers football games for students raised in New Jersey and those raised in  Pennsylvania
d) Differences between freshman and sophomores in the class on time spent studying
e) A comparison between education levels of the youngest and the oldest children in a family


Here's what I think the answers are:
a) Paired - Repeated Measures
b) Paired- Natural
c) Independent
d) Independent
e) Paired- Natural

I know how to calculate the t value for independent and dependent variables, but I'm terrible at discerning if a two-sample t test is an independent or a paired sample to begin with (unless it is stated in the problem).
I keep going over the definitions for each type, but I am still confused. I know that in an independent sample the groups do not relate to each other and there's no logical pairing for x and y. While in paired samples the groups are dependent/related to each other. There are 3 main types of paired samples those being natural pairs, matched pairs, and repeated measures.
~Natural Pairs- the two groups are naturally related ex) parents & children, identical twins
~Matched Pairs- individuals are paired by the researcher before the experiment ex) a control group & a treatment group,  
~ Repeated Measures- measurements are taken at two different times ex) pre-test & post test, before & after

I would appreciate any help to understand the difference between independent and paired samples for real world examples, thank you.

Answer 1

Yes, the definitions of independent and paired t-test are correct.

The two-sample t-test is an independent t-test since both the samples are used. In paired t-test, the difference is used.

a, b, c and d are correct but the last e is not the example of paired t-test. Because of the youngest and oldest children, education levels may differ. Both have their own choice, so they do not depend on each other. That's why they are not considered as paired samples. Youngest and oldest both are different objects. So it is the example of independent test.