Am I using T-Test correctly?

[zi_pota]

I am sampling small group of 11 people. I am trying to see the effect of changing one factor in the test. I sampled the 11 people before the change to get data. Then a while later, I changed a factor and retested the same individuals. I would like to do a t-test to determine the factor's effect.

Is it alright to use the same group of people?

[schlag]

I think that you first have to set up your null and alternative hypothesis, specify what kind of data you are facing and then select the test.

The t test requires that the data is normally distributed. In particular this means that any outcome between minus infinity and plus infinity is possible.

The t test can also be applied if you believe that the sample is sufficiently large. However you cannot prove that it is large, in particular there is no number that one can specify a priori.

Long story short, the t test does not seem appropriate.

Instead I would use the Wilcoxon test. Note however that this test can only determine that there was an effect. If you use the same people in both treatments you have to use the version for matched pairs.

[TheEcologist]

Long story short, the t test does not seem appropriate.

And Why exactly, based on the limited information given, would you feel that a (robust) test like a (paired) t-test is not appropriate?

[schlag]

I could have just written: "You can apply the paired t test if you believe that the data is normally distributed". However this is the wrong approach, to form beliefs in a way to make tests one knows about applicable.

Moreover, i bet that the underlying data does not have the property that it could be generated from a normal distribution as typically outcomes have exogenous bounds.

I do hope you know that the size of the paired t test is one if you make no assumptions. To be aware of this result seems to be a necessary ingredient for anyone to recommend the t test.

To assume that the sample is large enough to believe that the sample is approximately normally distributed does not make a lot of sense given there are 11 observations.

So you can help him by saying: "do what others do". Or you can help him by highlighting some of the basics, like the importance of first specifying the null and the alternative hypothesis.

To a novice this could be more difficult to understand so I tried a shorter posting. To the more advanced I do not expect this to be well accepted due to the "love" of the t test in the literature.