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Mar 16, 2017 6:44 AM
(1103 views)

Hello,

Can I get good performance in the t-test for mean comparisons, even if the normality assumption is violated ? (This in the case of comparison of two populations that have similar number of observations for each one (n = 41 and n = 42). I need some references to support this.

Thank you

Adias

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Mar 16, 2017 10:53 AM
(2037 views)

Solution

The curvature in the normal quantile plot suggests that there is some skew in the population, one of the reasons that the goodness of fit test rejects the normal distribution model. The skew is not that strong, though, so the sample means are approximately normally distributed after all and the t test should be valid.

Here is a reference for estimating the minimum sample size necessary to assure that the sum of the random variables is normally distributed:

Sugden, R. A., et al. (2002) "Cochran's Rule for Simple Random Sampling,

J of the Royal Statistical Society, Series B, Statistical Methodology. 62(4):787-793.

Learn it once, use it forever!

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Mar 16, 2017 6:52 AM
(1100 views)

If the populations are not normally distributed, the assumption that the sample means may not be violated if the sample size is large enough. The Central Limit Theorem says that the sum of N random variables is normally distributed for large N. The size N depends on the skewness of your population.

In what way and to what extent are the populations not normal?

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Mar 16, 2017 10:18 AM
(1079 views)

Thank you,

"In what way and to what extent are the populations not normal?"

By plot distribution and Shapiro-Wilk W test (alpha = 0.05). In the figure attached there is an example of the plot and test for one population.

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Mar 16, 2017 10:53 AM
(2038 views)

The curvature in the normal quantile plot suggests that there is some skew in the population, one of the reasons that the goodness of fit test rejects the normal distribution model. The skew is not that strong, though, so the sample means are approximately normally distributed after all and the t test should be valid.

Here is a reference for estimating the minimum sample size necessary to assure that the sum of the random variables is normally distributed:

Sugden, R. A., et al. (2002) "Cochran's Rule for Simple Random Sampling,

J of the Royal Statistical Society, Series B, Statistical Methodology. 62(4):787-793.

Learn it once, use it forever!

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Mar 16, 2017 12:03 PM
(1048 views)

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Mar 16, 2017 10:47 AM
(1070 views)

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Mar 16, 2017 11:11 AM
(1055 views)

You could also perform the t test with the Oneway platform (Fit Y by X) and then bootstrap the difference with JMP Pro.

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