# central limit theorem

can I do my statistics work based on the central limit theorem? I need to perform a t-test, ANOVA and multiple regression. my outcome variable is highly not normally distributed (Highly positively skewed) and my sample size N=115. I'd like to keep the non-parametric tests as a last option for me.

• Please search for the extensive discussions about this on the site. Why do you want nonparametric to not be the first option? Why are results from $n \rightarrow \infty$ of interest to you? – Frank Harrell Mar 7 '14 at 22:27
• Indeed nonparametric and semiparametric statistics are of interest to most statistician. Though theoretical statements, like normality and equal variance, for t-test and ANOVA promise an upper hand over nonparametric test. In practice parametric statistic faces a lot of problems. – Chamberlain Foncha Mar 7 '14 at 23:05
• I see, I already used a lot of non-parametric tests in my work. but I need to perform multiple regression and that is why the assumption of normality made a problem for me. so can I consider the central limit theorem to assume normality? – Mahmoud Ismael Mar 7 '14 at 23:18
• Why don't you perform the regression and see just how much the residuals depart from normality? Then you can provide us much more specific and focused information to help you choose appropriate procedures. – whuber Mar 7 '14 at 23:45
• PLEASE INDICATE WHETHER YOU HAVE WORKED OUT THE FREQUENCY POLYGON OR YOU HAVE CONTINUOUS DATA? Moreover specify that you have outcome values in terms negative or positive or both. – Subhash C. Davar Mar 9 '14 at 9:59

(1) The CLT is a result in the limit as $n\to\infty$. There's no particular n that's certain to be large enough. e.g. see here which gives a method which works for constructing cases which require larger sample sizes than any $n$ you can nominate.