statistical calculations to prove normal distribution

Statistical calculations to prove normal distribution how to#

I performed a t-test on these two observations (1000 data points each) with unequal variances, because they are very different (0.95 and 12.11). The mean of X and Y were 4.2 and 15.8 (which were the same as population +- 0.15) and the variance was 0.95 and 12.11. The plot was very much normally distributed. So, I decided to do this on both X and Y, 1000 times, and obtained samples, and I assigned a random variable to the mean of each sample. And, the mean of this random variables will be a good estimate of the population mean. Is this right?įrom central limit theorem, I understand that if you perform sampling (with/without repetition depending on your population size) multiple times and compute the average of the samples each time, then it will be approximately normally distributed. But then I am about to perform a two-SAMPLE t-test. My confusion is that, I consider them to be two populations and that's why I checked for normal distribution. I plotted histograms of both X and Y and they were not normally distributed, one of the assumptions of a two-sample t-test. If the assumptions are satisfied, is it relevant to use a parametric two-sample t-test here? I ask this because from my understanding its usually applied when the size is small? I would like to know if the means of these two observations are equal. Suppose I have two groups/observations, X and Y, with size $N_x=215$ and $N_y=40$.

If the data (or my explanation) isn't clear enough, I'll try to explain better by editing.

Statistical calculations to prove normal distribution how to#

I would like to know if its right, and if not, how to proceed.

I'll eliminate all the biological details and experiments and quote just the problem at hand and what I have done statistically.