# I What is unpaired t-test?

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1. Feb 28, 2017

### Tyto alba

I was reading a book that said:

Unpaired t-test is applied to unpaired data of independent observations made on individuals of two different groups (of a single sample) or samples drawn from two populations.

Now what wiki says is that they are not unpaired the e.g. given is one with 50 and 50 individuals. Besides they do not mention the groups coming from a single sample. (wiki)

Is the definition mentioned by my book correct?

2. Feb 28, 2017

### Stephen Tashi

The wikipedia article you linked does not say that the measurements in that example are "not unpaired". It says the measurements are unpaired.

The fact that there are two groups of 50 in the example, does not imply the measurements are paired. It is possible to have two groups of unpaired measurements that are equal in size.

Did you mean to say "from a single population"? You are correct that example in the wikipedia does not specify the population from which the 100 students are selected.

The definition in your book defines an "unpaired t-test" and it is a correct definition. You did not quote a definition that shows how your book defines the concept of "unpaired".

Consider an example where we selecting 100 students at random from student population of , say, the students enrolled at Cal Tech. If we do a study where 50 of the students eat a normal diet and 50 eat a special diet, then to judge whether weight gain or loss after 6 months is affected by the special diet, we would use an unpaired t-test. If student Zed Smith is in the group that eats the normal diet, we have no reason to pair his results with those of any other student - unless he happened to have a twin brother!

However, suppose each of the 100 students eats a normal diet for 6 months and then eats a special diet for 6 months. Then to judge whether weight gain or loss after 6 months is affected by the special diet, we could use a paired t-test. In this situation we have data like: Zed Smith's weight after 6 months of normal diet vs Zed Smith's weight after 6 months on the special diet.