# T-test vs. Permutation test on (not surely) normal data

This question follows my previous one. I will now provide my data in order to help you help me :)

As previously said, I have N=42 from a controlled experiment. People made a questionnaire assessing their mood and then played a videogame. They obtained a score from the game.

According to the questionnaire score, they may either be considered as "negative", "neutral" or "positive", respectively represented by the colors red, grey and green.

The following is the plot of the untouched data.

I would like to do some hypothesis testing on score means, like Mean(positive people) > Mean(neutral people).

As I learned from the previous question, if the data is approximately Normal, I can use the T-test. Because histogram does not show interesting facts, I bootstrapped the score mean.

What follow are the results of the bootstrap

Call:
boot(data = Tol\$Tol.Score, statistic = mean.fun, R = 1500, sim = "ordinary")

Bootstrap Statistics :
original   bias    std. error
t1* 2817.702 4.079778    91.06932


How much am I safe to perform the tests using the T-test? Shall I use a permutation test instead? Other thoughts?

Extra question: there is one subject that I consider as an outlier. He/she obtained a score < 5. What should I do with it? From what I learned, me shall never remove the outliers. But, since N is 42, it particularly affects the mean of its class (i.e., neutral)

Thank you again for your help.

Context: experiment that will be part of my MSc thesis and maybe a scientific paper.

Update: the dotted colored lines are the mean of scores the three groups

• Why are you grouping instead of, e.g., running a regression? – jbowman Feb 12 '12 at 15:09
• They are grouped because of previously defined parameters. That is, those with mood < k are negative, those between k and j are neutral and those > j are positive). Honestly, I am not really prepared for the "regression" subject but, from what I studied, I can still use t-tests or permutation tests for mean comparisons. Keep in mind that I really am a newbie with Statistics :) – user8438 Feb 12 '12 at 15:14
• On a not very related point, you should know that ~10% of men are red-green colorblind. Many people will not be able to read your figure at all. If you were to send your paper out for review w/ 3 white male reviewers, there is a 1/4 chance that >=1 couldn't read it. I would strongly advise you to use different colors. Some additional info can be found here: stats.stackexchange.com/questions/16631/… Best of luck with your project. – gung - Reinstate Monica Feb 12 '12 at 16:49
• Cheers @gung for your advice, I will change the colors of course! – user8438 Feb 12 '12 at 16:54