I wanted to see how close is a stochastic variable to one. For this purpose I bootstrapped the data 100,000 times. This resulted a non-Normal distribution. If it was normal, I used t-test to understand how close is its mean to one, but now I don't know how to check this.
It makes no sense to test the difference of a bootstrapped sample, no matter what the sampling distribution is (the p-value will will evetually be only a function of the bootstrap size!). What you can do is to interpret the "confidence interval" of the statistic you bootstrapped (for the 95% CI this is usually the range between the 0.025- and the 0.975-quantile of your bootstraped values).
Hi , since your data not normally distributed , I would suggest using ANOVA, and because you have too big sample size , using T-Test is fine unless sample is not skewed or one that naturally fits another distribution type, you may want to run a non parametric test. A non parametric test is one that doesn’t assume the data fits a specific distribution type. Non parametric tests include the Wilcoxon signed rank test, the Mann-Whitney U Test and the Kruskal-Wallis test.
Hi Ahmed Al Saedi
tank you for your answer. I tried non-parametric tests. The problem is that for normal distribution, one sample t-test does what I want, but for non-parametric distributions, I cannot find the equivalent Wilcoxon rank sum test.
Hi Jochen Wilhelm
Thank you very much for the explanations. Actually, I want to know how confident is my estimation. Assume I ave some data, and fitted a line to them. Te slope of this line is about 1.01. I want to compare this value with one, and report how close is this value to one. I bootstrapped the data 100,000 times, and found the slope of the fitted lines. Now< I want to compare this distribution with my desired value (one).
As I told you: the range from the 0.025-quantile to the 0.975-quantile of the bootstrapped values gives the 95% confidence interval for the slope. You can turn this around and find which quantile refers to a slope of 1.01. If this is, for instance, the 0.01-quantile, you can claim a difference to 1.01 with a (1 - 2*0.01)*100% = 98% confidence (or reject the null that the slope is 1.01 with p = 2*0.01 = 0.02.
Hi, Asieh:
If it is of interest to you to determine if the bootstrapped distribution overlaps the value 1, then compute an exact 95% (or whatever desired %) discrete confidence interval for the former and see if the CI includes the value 1. Using this methodology requires NO distributional assumptions.
https://odajournal.com/2014/10/10/discrete-95-confidence-intervals-for-oda-model-and-chance-based-classifications
https://odajournal.com/2018/11/26/comparing-exact-discrete-95-cis-for-model-vs-chance-ess-to-evaluate-statistical-significance
https://odajournal.com/2017/04/18/what-is-optimal-data-analysis
Hope this is useful!
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