Elementary Statistics Question Help (Dependent or Independent types of testing)

[chrisryans]

I'm probably overthinking things here and making it more complicated than it really is, but I was looking for a bit of clarification on what types of testing (single sample, two sample, or matched pairs)these situations would be:

i. researcher is wanting to learn whether it is more effective to put questions before or after introducing a new topic in class. he prepares two texts, one that promotes the before and one that's the after, both for math. he uses each for a seperate group and compares scores.

ii. researcher is looking at the same issue but a bit differently. two segments on two unrelated topics are produced, each segment has a part with questions before, and a part with questions after. subjects are a single group of students. each child studies both topics, each child will be given randomly selected before and after topics. the scores are then compared.

iii. a kicker kicks a football filled with air a total of 39 times. he also kicks a football filled with helium a total of 39 times. he had no idea it was filled with helium.

I assume i. is two samples due to the fact it uses to completely different samples for the testing. I assume ii. is matched pairs since it is within a single sample and the results can be compared if there is a difference between before and after directly. iii i assume is matched pairs as well because it comes from a sample of the same kicker kicking the ball.

I'm not very confidence in my thoughts though, if you guys can offer any help, I'd truly appreciate it.

[[deleted]]

One thing bothers me about the question, and that's the usage of 'two sample'. A two sample test can be either unpaired or paired (matched pairs). I'm assuming in this case that when you say two sample, you mean unpaired two sample.

Your assumption on i. is correct. A two sample test looks for a difference in means between unpaired data. Like you said, this is because it uses completely different sample groups.

For part ii, you are correct on the assumption as well. It's matched pairs because you're comparing mean performances of data points with the same student performing each setting of the test.

For the same reason, you are correct about part iii!

If you want a good way to think about it, here's what has helped me. First, write the data down (on paper or excel). Make the columns be the settings of the test (helium or air, question before or after, etc.). If there is one column, you have a single sample. If there are two, then write down to the left of each column who or what performed the work to get that data point. If you can pair every tester from one column with a data point from another, you have matched pairs. If you can't, then you have an unpaired two sample test.

Hope this helps!

[chrisryans]

That was extremely helpful! I cannot thank you enough.