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If I am wrong, please correct me.
My understanding is that 95% Confidence Limits for LSMean(i)-LSMean(j) in proc glm is that there are 95% confidence (not probability) of minus of group(i) population mean and group(j) population mean located on the rang. P value is probability of result you get or more extreme result if null hypothesis is true. In this case, if goup(i) mean=group(j) mean(H0), both groups are t distribution, test statistic (t) is calculated, then checked the t table ( which is got by theoretical t distribution) and freedom of degree, p value is got, if 0.05 is set as significant level, and if p value is less then 0.05, the H0 is refused and H1 accepted. All conclusions are based on ideal model, but actually the research design, sample size, bias, ect. could affect the conclusions.
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