# Paired t test or 2 sample t test?

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• #52334

Lim BT
Participant

May i know what is the difference between Paired t test and 2 sample t test? I did some study and its mentioned that Paired t test is for dependent sample and 2 sample t test is for independent sample. But i dont really understand what is mean? Can anyone enlighten me? Got any example to share? Thanks

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#184016

Gutierrez
Participant

Let me take a stab at answering this for you with a specific example. Lets say you have a bread making process and you want to know what is the statistical increase in height of a loaf when going from before baking to after baking. If I take a sample of 50 loaves and measure the height before baking and then take another sample of 50 DIFFERENT loaves after baking – I can use the 2-sample t test to see what the statistical difference is between the two sample mean heights. If however, I am able to measure the exact same loaf before and after baking, I can use the paired t test because I’m measuring the average difference between before and after baking on the SAME loaf of bread. Minitab will calculate the confidence interval of this average difference for the entire sample. If the confidence interval is different than zero, there is a statistical difference.  In this particular case the paired t test is a much more powerful test than simply a 2 sample t. Did I confuse you more or did this help???

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#184018

Lim BT
Participant

Hi Alex, thanks for the reply. So the statistical difference is based on the confidence interval instead of the p value?

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#184020

Craig
Participant

the null hypothesis would be mu = 0
if p is low (less than .05) you reject the null.
If you reject the null, you should also see that the 95% confidence interval for the mean-difference does not include zero.

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#184023

MBBinWI
Participant

Lim:  Perhaps the bread baking example is not clear enough.  Here is another example that I think is easier to understand.
We are interested in evaluating the difference in wear characteristics between two materials used for athletic shoes.  We could do this a couple of different ways – 1) subject samples of each of the materials to exactly the same wear situations and then compare the measured wear between samples of A and B, this would be a 2 sample-t.  2) make shoes with one sole of material A and one of material B (swapping sides for different sample pairs) and have these “pairs” of shoes worn by different people, comparing the difference in wear between samples of A and B, this would be a paired t-test (the pairing would be through the individual who wore a pair of shoes with each material).
Pairing means that there is a relationship between the two items being evaluated, thus they are dependant.  It has nothing to do with the p value or confidence interval (although the pairings provide a different and direct relationship between the items that must be factored in).

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#184025

Cone
Participant

BHH100

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#184028

annon
Participant

As a practical aside, once you have your data collected, you can crank it through both the paired and 2 sample t and see if the two tests offer different “opinions”.  If you accept/fail to accept the null in both tests,  you have what you need…and dont forget to run your power and sample size test (especially if the test “fails”) to quantify its ability to detect a meaningful difference should it occur (ie power).  Good luck.

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#184034

MBBinWI
Participant

OK, I’ll bite – ???

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#184037

Cone
Participant

Box, Hunter, and Hunter page 100.It is the “classic” shoe example you eluded to in your post. Explained
well with examples of the right and wrong analysis.

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#184038

Sloan
Participant

So, is that like the classic joke where the old comedians sit around and just say punch-lines and everyone laughs because they all know all of the jokes?
“… a pig like that, you don’t eat all at once!”

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