# Pair T-test

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• #37176

ROSS
Member

Hi:
Anybody can explain Pair T-test with a very simply work? Tks!

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#108907

ROSS
Member

Hi, Can sombody help me?

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#108908

Chris Seider
Participant

Get a copy of Box Hunter and Hunter’s “Statistics for Experimenters” and read the section titled “Randomized Paired Comparison Design:  Boys’ Shoes Example”.  This gives a clear example of when you can and should use paired comparison.

Hope it helps.

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#108909

mjones
Participant

First, Tony, I think you are asking about the “Paired-t test.” Next, look at the definitions on this site. You must understand them or you will make incorrect assumptions and do incorrect analyses.
To expand on the definitions, the difference in a 2-sample t and a paired-t is:
For a 2-sample t you assume you have two groups or samples and you are looking for differences in their mean (and the std dev is estimated from the sample). The test looks at the two distributions and compares them. There is no relationship between the sample groups, e.g., item #1 of the first sample has no relevance or relationship to item #1 of the second sample. This would be like comparing a sample of 10 units made last week to 10 units made this week.
For a paired-t you must have specific dependency and relevance of each sample observation. Example, test of hardness before and after heat treat for ten samples that are specifically identified so you are comparing the change from the heat treat for each of the specific samples. (Other examples: tests of specific students before and after training; test of strength of specific samples before and after aging, etc.)
NOTE: There MUST be a 1:1 relationship of the sample data. Specifically, item #1 in the first group is the same item #1 in the second; #2 is #2, etc., so the t-test test is actually done on the difference, or delta, of the two sets of observations on the same units tested. This is mathematically equivalent to a one-sample t-test of the deltas.
You can set the hypothesis to note a specific amount of change. For instance, you may want to see a certain amount of change in hardness or strength, or your hypothesis my be that “delta = 0”, i.e., there is no difference.

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#108911

mjones
Participant

C Seider suggests an excellent example. And in case you don’t have a copy of BHH…
Suppose you want to test shoe sole materials for wear resistance for boys shoes.
Alternative 1: Make 10 pairs of shoes with material A; 10 pairs with material B. Find 20 boys and randomly assign the shoes to them. Test the two groups to compare wear. There is no relationship between the two groups. Must use 2-sample t.
Alternative 2: Make 10 pairs of shoes with material A, 10 with B, but this time, have each boy wear a shoe with each type of material, i.e., boy #1 wears one shoe of material A and one of material B. Now the boys are the constant and you can simply compare wear of A vs. B for each boy. This is a paired-t. Obviously, a much more powerful test you are only concerned about comparable wear rates.

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#108914

Ken Feldman
Participant

The danger in the paired test is the possible influence of an additional factor, namely the boys.  That is why the test is really a one sample t where you compare the differences between the two and test against zero.  This blocks out the impact of the boys.  In Minitab, the differences are calculated and the test is done, all transparent to you.  If you ever wanted to see what is really going on, you merely have to take the differences between the two columns of data and then do the one sample t test with the column of differences and compare to zero.

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