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Is a ttest used in nonnormal data analysis?
As Homogeneity of Varirance( Mintab) can test normal and nonnormal data for variance.
My question is does t test can do it? if not, how we can compare two nonnormal data mean value? thanks

5th February 2006, 11:42 AM


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Quote:
In Reply to Parent Post by jackylpt
As Homogeneity of Varirance( Mintab) can test normal and nonnormal data for variance.
My question is does t test can do it? if not, how we can compare two nonnormal data mean value? thanks

Yes, the ttest 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 ttest is at avoiding false alarms and avoiding failure to detects.
5. Shift to nonParametric tests.
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5th February 2006, 02:11 PM


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Homogenity of variance tests like the ttest assume normality. If your homogenity test shows no statistical difference between the two variances, the using a ttest 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 WilksShapiro or KolmogorovSmirnov.
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10th March 2011, 01:21 PM


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Re: Is a ttest used in nonnormal data analysis?
Statistica steven:
Why not to use Anderson test instead of Kolmogorov?
thanks

10th March 2011, 07:14 PM


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Re: Is a ttest used in nonnormal data analysis?
These tests are sensitive to departures from normality in different areas.
The AndersonDarling is sensitive to departures from normality in the tail areas.
WilksShapiro and KolmogorovSmirnov are sensitive to departures from normality in the center.
You should select the test that is most appropriate for your specific situation.
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11th March 2011, 10:23 AM


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Re: Is a ttest used in nonnormal data analysis?
Quote:
In Reply to Parent Post by Miner
These tests are sensitive to departures from normality in different areas.
The AndersonDarling is sensitive to departures from normality in the tail areas.
WilksShapiro and KolmogorovSmirnov 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 WS) to avoid the "shopping" for a good pvalue. Having said that, if you know that you might have a long tail, AndersonDarling is perferred.
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11th March 2011, 10:51 AM


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Re: Is a ttest used in nonnormal 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 AD 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 nonparametric 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 ttest might not be what you choose. Make sure you have continuous or interval data, not just numbers.
Cheers,
Adam

11th March 2011, 12:55 PM


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Re: Is a ttest used in nonnormal 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 TukeyDuckworth 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 ttest 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.
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