# T-testing

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• #29850

Daren Heiner
Participant

A question with two sample variable data testing.
When comparing two samples for statistical difference.  Do you need equal samples of both… like  60 and 60  or can you compare both populations with saples like 70 and 90 and statisticaly  conclude there is no difference.
thanks

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#77156

melvin
Participant

Daren:
When comparing the means of two samples using a t-test, you do not need to have an equal number of samples in each of the two sets being compared.
You do, however, need to use an F-test to see if the two sets of data have equal variances.  If they do, a pooled (from the two) standard deviation will be used in most statistical software packages.  If the variances are not equal and a pooled standard deviation is used, the reliability of the model can be greatly reduced.

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#77182

Sridhar
Member

Hi Daren,
You can campare two samples with different sample size also, But here you have to make an assumption about your population standard deviations. If you assume standard deviations are equal then you can calculate the pooled standard deviation.
How to do this you get here in this website
http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm
thanks
A.Sridhar

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#77341

Kaushik
Participant

Tests like the T test or ANOVA do not require the sample sizes to be equal. Your population sizes could be different. For tests like the Mood’s median test, which compares the median values of your different sets of data , your population size for both samples would have to be equal.T and ANOVA tests assumes normality of data while tests like the Mood’s median test do not.

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#77349

Georgette
Participant

Good answers from everyone.
The only thing I would add is an explanation of sample sizel.
The sample size calculation that you will do in minitab (if that is the software you use)  will identify the minimum sample size you need.  If the sample size required shows “60”,  you need at least 60 samples before,  and at least 60 after.
One more thing  – -if the variances aren’t equal,  you can still do a two-sample t-test.  Just be sure the check box next two “assume equal variances”  is NOT checked (If you use the minitab software)

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#77355

Ropp
Participant

I agree that all the answers to this thread have been ‘on the money’.
One other aspect to consider here is the situation where the sample sizes are greatly different. While 1-way Anova and post-hoc testing is still appropriate, the power of the F test will be lower under these conditions.
Also, some post-hoc tests that require equal or ‘almost equal’ sample sizes will not be appropriate (Tukey’s HSD, for example). In this case, a more robust test, such as Games-Howell may be employed.

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#173179

Viti
Participant

When doing t-testing what type of samples do you recommend?

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#173187

Robert Butler
Participant

Let’s do a re-cap:
1. A two sample t-test does not require equal number of samples.
2. A two sample t-test can be run on samples of any size equal to or greater than 2 per population.
3. A two sample t-test does not require equal variance of the sample populations but it does require the adjustments noted – if you are using a machine then you have to have the capability to tell the machine that the variances are unequal and if you are doing the calculation by hand you need to know how to compute the pooled estimate of variance as well as the synthetic degrees of freedom associated with the pooled variance – Brownlee – Statistical Theory and Methodology in Science and Engineering pp.299-303 has the details.
4. A two sample t-test is robust to non-normality. See the following post for details:
https://www.isixsigma.com/forum/showmessage.asp?messageID=110215
5. The issue of sample size for a t-test (or any other test) relates to questions concerning the power of the test result.  It has nothing to do with the mechanics of the calculation of the t statistic nor the number of samples needed to perform the t-test calculation.

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#173199

Ron
Member

Robert,
Thanks I I waswondering when someone with actual statistical knowledge was going to jump in..I was just enjoying the view from on high.

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