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I have done regression but residuals not normal ... When I take out outlier residual are normal. But the outlier is important data so I leave it in ... In order to use my regression result do I reduce my p value confidence levels from 0.5 to 0.1 or 0.001 ... My results are between the range 0.0003 to 0.0017 and the 0.0017 is the most important result I what to show ... I my sample size is 50 so on the cusp of reasonably large enough sample to invoke theory if numbers but confidence level has me concerned ... The residuals are approximately normal

kjetil b halvorsen
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Inajawaace
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    "In order to use my regression result do I reduce my p value confidence levels from 0.5 to 0.1 or 0.001. .My results are between the range 0.0003 to 0.0017 and the 0.0017 is the most important result I what to show." This is exactly how not to do statistics. You shouldn't be wanting to show anything and manipulating your methodology accordingly. You should be setting your levels of significance and methodology a priori and discovering what the data show - not what you are hoping/torturing the data to show. – StatsStudent Jan 23 '19 at 00:08
  • Thank you....The reason that I asked was in some research it stated that you should use 0.001 when using small samples less than 500 and I also found another saying use 0.01....So I am confused with my sample size of 50 I was happy to use 0.5 but the articles made me doubt my original thoughts....So can I ask if I stick with 0.5 and invoke CLT there is enough justification for to use my p values instead of trying to worry about non normality – Inajawaace Jan 23 '19 at 00:15
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    I'm not familiar with any serious research that suggests altering significance levels based sample size. The level of significance should be selected in such a way that it considers real-world ramifications of making a Type I error. It would be extremely unusual to select a 0.5 confidence level since that would imply a 50/50 chance of rejecting the null hypothesis when the null hypothesis is true. Your choice of significance level shouldn't really depend on distributional assumptions of your data but on how much you are willing to tolerate being wrong about your null hypothesis. – StatsStudent Jan 23 '19 at 00:37
  • Sorry my original msg wanted wrong I meant 0.05 and 0.01 and 0.001...But thank you for your response I will stick with my original confidence of 0.05..And thank you for taking the time to enlighten my knowledge – Inajawaace Jan 23 '19 at 01:01
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    @Inajawaace: Can you please correct the errors in the original post (OP) by editing it? Few people read comments. – kjetil b halvorsen Jan 24 '19 at 09:01
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    You could look into robust regression. And yes, if the outlier alone really changes results, you should check carefully its correctness. – kjetil b halvorsen Jan 24 '19 at 09:02
  • Could you edit the question and [show us the distribution of residuals](https://stats.stackexchange.com/questions/58141/interpreting-plot-lm/65864#65864)? – Tim Jan 24 '19 at 09:12

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