Non-parametric tests for pairs
The total length of the videos in this section is approximately 30 minutes, but you will also spend time answering short questions while completing this section.
You can also view all the videos in this section at the YouTube playlist linked here.
Sign test
NPTestsForPairs.1.SignTest1.mp4Question 1: For which of the following would we choose a paired test? Check all that apply.
We take a simple random sample of Wellesley students and a simple random sample of MIT students to compare their assessments of their campuses' mental health resources.
We ask 30 balding men to apply a cream to the left sides of their heads so we can see whether cream is more effective than no cream for hair regrowth.
On Monday and Tuesday, 10 rats eat a regular rat diet. On Wednesday, we weigh them. On Thursday, we start the 10 rats on a new diet. On Saturday, we weigh them again, to see whether the new diet is associated with weight gain.
A set of deans plans to visit first year students in each the dorm during the first semester. The deans are interested in whether first year students' experiences depend on how long they have been at college. During first year student orientation, they talk to students from one dorm. In October, they talk to students from a different dorm.
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The second and third options only. The MIT and Wellesley students are not paired - the fact that we survey a particular Wellesley student does not tell us anything about whether a particular MIT student is included. However, the two halves of the balding mens' heads are paired - we can compare the left v. right side of each man's head. This paired structure takes advantage of our knowledge that some men might lose more hair overall than other men. For the rats, we are taking before and after measurements for each rat, so we want to take advantage of that paired structure: if some rats are heavier overall or lighter overall, we take that into account by focusing on the change in weight for each rat. The first year students are not paired, because the students in each dorm are different people, and there's no obvious pairing between each of the students in one dorm and a student in the other dorm.
Conducting a sign test
NPTestsForPairs.2.SignTest2.mp4Question 2: Why is the sign test known as a "back of an envelope" test?
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Typically, it should only appear on the back of an envelope, not in a published paper. Using the sign test means that you lose a lot of information, making it suitable to do on the back of an envelope to quickly see if you have a difference but should not typically be used in a paper because there are other tests that use more of the information that is available to you.
Conducting a signed rank test
NPTestsForPairs.3.Signed Rank Test Part 1.mp4NPTestsForPairs.4.Signed Rank Test Part 2.mp4Question 3: Under what circumstances will the signed rank statistic S be large?
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S will be large when there are many positive differences and when the differences that are positive are large in magnitude.
NPTestsForPairs.5.Signed Rank Test Part 3.mp4Question 4: Which of the following test statistics that could be used in randomization or permutation tests are only appropriate for paired data? Choose all that apply.
difference in means
ratio of medians
rank sum
sign statistic
signed rank statistic
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Sign statistic and signed rank statistic. The difference in mean could be used for paired or unpaired data. The ratio of medians and the rank sum are meant for two independent groups rather than paired data.
(Technically, there is also a single-sample sign test and a single-sample signed rank test. So, if you chose those options, you aren't technically wrong. However, those tests are rare. In this question, my goal was to distinguish between test statistics that can be used to compare two groups that are paired, versus test statistics that can be used to compare two groups that are independent.)
That's it!
During this tutorial you learned:
About paired data
About the sign test and signed rank test, which are examples of a randomization/permutation test for paired data
Why is the sign test known as a back-of-an-envelope test
The steps to perform a sign test or signed rank test
The reference distribution for a sign statistic is a binomial distribution
The pros and cons of the signed rank test
What leads to a large test statistic in a signed rank test
Terms and concepts:
sign test, signed rank test, paired data, back-of-an-envelope test, binomial distribution