STATISTICS FROM A TO Z<br />-- CONFUSING CONCEPTS CLARIFIED
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Statistics Tip of the Week: What's the Difference between a 2-Sample t-test and a Paired t-test?

9/22/2016

1 Comment

 
Picture
Many folks are confused about this, especially since the names for these tests themselves can be misleading. What we're calling the "2-Sample t-test" is sometimes called the "Independent Samples t-test". And what we're calling the "Paired t-test" is then called the "Dependent Samples t-test", implying that it involves more than one Sample. But that is not the case. It is more accurate -- and less confusing -- to call it the  Paired t-test.
First of all, notice that the 2-Sample test, on the left, does have 2 Samples. We see that there are two different groups of test subjects involved (note the names are different) -- the Trained and the Not Trained. The 2-Sample t-test will compare the Mean score of the people who were not trained with the Mean score of different people who were trained.

The story with the Paired Samples t-test is very different. We only have one set of test subjects, but 2 different conditions under which their scores were collected. For each person (test subject), a pair of scores -- Before and After -- was collected. (Before-and-After comparisons appear to be the most common use for the Paired test.) 

Then, for each individual, the difference between the two scores is calculated. The values of the differences are the Sample (in this case: 4, 7, 8, 3, 8 ). And the Mean of those differences is compared by the test to a Mean of zero.
1 Comment
OB link
5/7/2018 04:34:31 am

Yes Andy, this is definitely confusing, especially when in the independent t-test the pairs must be independent pairs :),
the dependency is only inside the pair, usually the same subject.
We can say the paired t-test involve two samples, but usually for the same subjects. (or other connection)
I can recommend the following online calculator that will check also the normality assumption and will check for outliers: http://www.statskingdom.com/160MeanT2pair.html

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    Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.

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  • Home
    • Why This Book Is Needed
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