The Elsmar Cove Business Systems and Standards Discussion Forums Is a t-test used in non-normal data analysis?
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Is a t-test used in non-normal data analysis?

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Post Number #1
5th February 2006, 05:04 AM
 jackylpt Total Posts: 38
Is a t-test used in non-normal data analysis?

As Homogeneity of Varirance( Mintab) can test normal and non-normal data for variance.
My question is does t -test can do it? if not, how we can compare two non-normal data mean value? thanks

Post Number #2
5th February 2006, 12:42 PM
 Steve Prevette Total Posts: 2,515
Quote:
 In Reply to Parent Post by jackylpt As Homogeneity of Varirance( Mintab) can test normal and non-normal data for variance. My question is does t -test can do it? if not, how we can compare two non-normal data mean value? thanks
Yes, the t-test is based upon an assumption of normality. If you are concerned about the normality of your data, here are some options:

1. Assume the Central Limit Theorm will get you to "good enough". Generally if you have more than 10 samples you probably are getting close.

2. Ignore the issue. With only 5 samples (for example) it is pretty hard to prove your data are not normal anyway.

3. If you know what distribtution the data are, or theoretically "ought to be", run a mathematical transform to shift them to normality. An example is time to failure data can tend to be exponential.

4. Run your own tests using random numbers and check distributions like what you have been seeing to see how good the t-test is at avoiding false alarms and avoiding failure to detects.

5. Shift to non-Parametric tests.
Post Number #3
5th February 2006, 03:11 PM
 Statistical Steven Total Posts: 1,092
Homogenity of variance tests like the t-test assume normality. If your homogenity test shows no statistical difference between the two variances, the using a t-test to compare means is conservative. If the variances are not equal, using the Sattherwaite's approximation might help.

Again, you should first test the data for normality using Wilks-Shapiro or Kolmogorov-Smirnov.
Post Number #4
10th March 2011, 02:21 PM
 Mexicanquality Total Posts: 22
Re: Is a t-test used in non-normal data analysis?

Statistica steven:
Why not to use Anderson test instead of Kolmogorov?

thanks
Post Number #5
10th March 2011, 08:14 PM
 Miner Total Posts: 4,098
Re: Is a t-test used in non-normal data analysis?

These tests are sensitive to departures from normality in different areas.

The Anderson-Darling is sensitive to departures from normality in the tail areas.

Wilks-Shapiro and Kolmogorov-Smirnov are sensitive to departures from normality in the center.

You should select the test that is most appropriate for your specific situation.
 Thank You to Miner for your informative Post and/or Attachment!
Post Number #6
11th March 2011, 11:23 AM
 Statistical Steven Total Posts: 1,092
Re: Is a t-test used in non-normal data analysis?

Quote:
 In Reply to Parent Post by Miner These tests are sensitive to departures from normality in different areas. The Anderson-Darling is sensitive to departures from normality in the tail areas. Wilks-Shapiro and Kolmogorov-Smirnov are sensitive to departures from normality in the center. You should select the test that is most appropriate for your specific situation.
Miner, excellent point!

My general rule of thumb is to stick with a single test (I tend to use W-S) to avoid the "shopping" for a good p-value. Having said that, if you know that you might have a long tail, Anderson-Darling is perferred.
Post Number #7
11th March 2011, 11:51 AM
Re: Is a t-test used in non-normal data analysis?

One thing to keep in mind -if you're using a software package such as Minitab, is what normality test they use by default. You can use several specific normality tests within Minnie, but it defaults to the A-D test for the basic reports. Just FYI. Also - I believe some of the tests are sample size sensitive, so you might take a look at how much data you have as an input to which test you select.

You can use a non-parametric test like Mood's median to see if any differences exist without worrying about distribution though, but take a look at what the data is. If it's something like a hole diameter then you might expect that to be normally distributed. However, if you're evaluation cycle times or arrival times, you would look more toward a lognormal, so a t-test might not be what you choose. Make sure you have continuous or interval data, not just numbers.

Cheers,

Post Number #8
11th March 2011, 01:55 PM
 Bev D Total Posts: 3,530
Re: Is a t-test used in non-normal data analysis?

all of the above complications and caveats are true for statistical tests that are based on the assumption of Normality.

on the other hand in the real world most processes, experiments and data are relatively straighforward. As long as the experimental structure is correct* the only necessarry analysis is to plot the raw data and look for the differences. The Tukey-Duckworth approach is typically sufficient for a statistical sanity check.

I've solved hundreds of problems and performed thousands of analyses of various types and with the exception of screenign experiments and thsoe that were looking for really small differences - I've never used - or needed a t-test or ANOV. (although I do admit that at times I will run the test after I've completed the analysis just for those individuals who 'have to see the p value' because graphs elude them) I have used ANOM on occassion but not lately. Why get all fancy when you don't have to?

*the biggest error I've seen in experimental analyses is not an incorrect statistical test, but a poorly designed experimental structure.
 Thank You to Bev D for your informative Post and/or Attachment!

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