turn on suggestions

Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.

Showing results for

- JMP User Community
- :
- Discussions
- :
- Discussions
- :
- t-test

Topic Options

- Subscribe to RSS Feed
- Mark Topic as New
- Mark Topic as Read
- Float this Topic for Current User
- Bookmark
- Subscribe
- Printer Friendly Page

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Report Inappropriate Content

Mar 16, 2017 6:44 AM
(1779 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

Solved! Go to Solution.

1 ACCEPTED SOLUTION

Accepted Solutions

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Report Inappropriate Content

Mar 16, 2017 10:53 AM
(3205 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!

6 REPLIES

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Report Inappropriate Content

Mar 16, 2017 6:52 AM
(1776 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?

Learn it once, use it forever!

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Report Inappropriate Content

Mar 16, 2017 10:18 AM
(1755 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.

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Report Inappropriate Content

Mar 16, 2017 10:53 AM
(3206 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!

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Report Inappropriate Content

Mar 16, 2017 12:03 PM
(1724 views)

Thank you Mr Markbailey for your attention!

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Report Inappropriate Content

Mar 16, 2017 10:47 AM
(1746 views)

Without an operational definition of 'good performance' it's impossible to answer your question. If all else fails I suggest any one of the non-parametric tests for testing the hypothesis for two population means. This way you don't have to come up with a definition for 'good performance' and you aren't necessarily tied to any distributional assumptions.

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Report Inappropriate Content

Mar 16, 2017 11:11 AM
(1731 views)

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

Learn it once, use it forever!