# Paired t-test p value

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• #30776

CT
Participant

Think I have a wrong concept of the Paired t-test, so I would appreciate some help here:
In column X1, 4 data points: 1.0, 5.0, 10.0, 20.0
In column X2, 4 corresponding data: 1.1, 5.0, 10.0, 20.2
Performing a paired t on them yielded: T = -1.57, P = 0.215

But if I swap the numbers in column X2: 20.2, 5.0, 10.0, 20.2
Performing a paired t on them yielded: T = -0.01, P = 0.993

My questions are:
1.  Why is P value so low in the first paired t-test?
2.  Why did P value increase after I swapped the data? Shouldn’t it get worse, seeing that it’s paired?
CT.

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#80633

rams
Participant

When performing this test, maintain the order of the data because they are “paired” (not independent). Else, you are performing a 2-sample test where the assumption is that the 2 population are independent. Paired t-test is like performing a one sample test on the difference of each paired data. Your null hypothesis is Ho : difference = 0.
Hope this helps
rams

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#80634

CT
Participant

Hi rams,
Thanks for the reply.  Actually, that is precisely what I’m asking – why is it that when I jumble up the order, I do not get the result that I expected.
If you punch the data in Minitab or Excel, you’ll see what I mean.  Why didn’t it tell me in the first test that my means are very very close?  Why did it tell me after I mess the order up that my means are equal?
Thanks!
CT.

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#80645

rams
Participant

CT,
When you jumble the arrangement, you don’t get the same difference of each pair. In this way, result will be different.
If you use 2-sample t-test (2 independent) samples, you’ll get the same result.

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#80646

CT
Participant

Hi rams,
No offence but I think you still do not understand my question.  I do know the difference between a paired and a 2-sample t.
It’s the paired t’s P value that’s puzzling me.  Why does it go up towards 1.0 only AFTER I mess up the data??
CT

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#80656

Ron
Member

If you unmatch the pairs you have a new problem.
A paired T is as stated it matches the 1st experience to its second experience. When you jumble up the order you no longer maintain the chain of experience.

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#80661

Jamie
Participant

The difference is because a paired t-test tests the difference between the pairs of data. It basically takes the difference between each “pair” and tests whether this difference is significantly different then 0. You can do a paired t also by taking the difference yourself and do a one sample t vs the differences against 0. You’ll get the same result. So if you rearrange the pairs the differences between the pairs will also be different. Paired tests are only done when it “doesn’t make sense” to be able to rearrange the data. If you subjected 10 parts to a chemical and wanted to test the difference before and after exposure, its important that the before measurment for part 1 is matched with the after measurment from part 1. Its not proper to match the before from part 1 with the after of say part 7 (ie rearrange the data). If it makes sense that the data doesn’t have one and only one matching “pair” you probably should not be using a paired t-test.
Hope this helps,
Jamie

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#80663

Dillon
Participant

You got a relatively low p-value for the first set because 2 of the 4 samples showed a shift in the same direction and 2 showed no shift at all, therefore, there is some likelihood that condition X2 is causing a shift up in your output.
You got a high p-value for the second set because sample 1 shifted way up (1.0 to 20.2), sample 4 shifted way down (20.0 to 1.1), and the other 2 did not change at all.  It cannot be determined with any certainty whether condition X2 causes output to go up or down.

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#80726

CT
Participant

Thanks to all for your posts.
Thanks Doug, you answered my questions.  I am one of those guilty of using statistical tests without fully understanding the derivation of formulae!

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