Can I use parametric statistics for a large sample (150) that doesn’t have a normal distribution?

Question by merisorrr: Can I use parametric statistics for a large sample (150) that doesn’t have a normal distribution?
I gave a test to 150 students and it turned out to be too easy, so the distribution of their scores is skewed. I ran a Kolmogorov-Smirnov test which confirmed that the distribution is not normal. But one statistics book seems to say that if the sample is greater than 100, then I can use parametric statistics anyway. Is that true?

Best answer:

Answer by steppenwolf
The short answer is no. Sometimes, the probabilities are distributed in a decidedly different fashion than the standard normal distribution. When you plot the histogram, you may observe multiple modes i.e., peaks for the distribution or you may have tails that are much heavier than a typical normal distribution. I am not sure what you want to use the data for? If you want to use it for hypothesis testing or testing for outliers, a normal distribution may still be useful in some cases if the deviation from normal is not too large. If you really want to try fitting a different distribution to the data, you can try the skew-normal distribution. But you will need a statistical package which will fit this distribution and allow you to interpret the results/calculate event probabilities.

http://en.wikipedia.org/wiki/Skew_normal_distribution

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