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# If the two populations are not normally distributed , then the inference procedures for the difference between two means can still be valid ,...

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If the two populations are not normally distributed , then the inference procedures for the difference between twomeans can still be valid , provided the sample sizes are large.The sampling distribution of* - *, is approximately normal , provided the independent sampling distributions of* , and * , are themselves approximately normal .The results obtained from the pooled - variance I procedure Versus the Welch procedure , when applied to the samedata set , will always be significantly different .One problem with taking observations on the same experimental unit , as in a paired difference test , is that it canincrease the variability in the experiment .The paired difference procedure is less susceptible to the populations being non - normal , since taking the difference*between two non - normal populations will result in a normal distribution .