t test
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 This topic has 6 replies, 5 voices, and was last updated 13 years, 10 months ago by Robert Butler.

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November 26, 2008 at 9:35 pm #51407
A tvalue is actually a standard deviation score (this might give you a hint as to how it might be calculated) based on the tdistribution. The tTest is useful if you have a small number of observations and only one or two groups of observations with which to conduct your hypothesis testing. When the number of observations (in each group) exceed 30, the tdistribution starts to look like the normal distribution, and the analysis of variance (ANOVA) becomes the preferred test.
0November 26, 2008 at 10:27 pm #178129I’ll play:
The answer is “When do I use a ttest”?
I’ll take hypothesis testing for 200, Alex!0November 26, 2008 at 10:52 pm #178130
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.The ttest is used for a comparison of two samples. This can be paired samples, independent samples from two populations or samples from a single population compared to a target.
The ttest is useful anytime you have the above conditions. It was originally developed for comparisons where the sample sizes were small but sample size is not a driver as far as its use is concerned. A check of the appendix of any basic book on statistics will show ttables with values up to infinity.
“We have seen in Section 9.7 that two sample means can be compared with the twosample t test. The generalization of this problem to k means, k > 2, brings us to the body of techniques known as the analysis of variance. – Statistical Theory and Methodology in Science and Engineering – Brownlee. pp. 309.
Therefore
ttest – two means
ANOVA – more than two means.0November 27, 2008 at 12:00 am #178131
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.Hi RobertMay I pick a nit here? You can of course use ANOVA with just two means as you are no doubt aware. It’s quite interesting to do an example by both methods with people learning the ropes of hypothesis testing: Row A B
1 20.4 20.2
2 24.2 16.9
3 15.4 18.5
4 21.4 17.3
5 20.2 20.5
6 18.5
7 21.5TTest of difference = 0 (vs not =): TValue = 1.12 PValue = 0.289 DF = 10
Both use Pooled StDev = 2.3627
OneWay ANOVA
Source DF SS MS F P
Factor 1 6.99 6.99 1.25 0.289
Error 10 55.82 5.58
Total 11 62.82The Pvalues are the same for both the ttest and the ANOVA and in fact the F statistic is the square of the tstatistic. Thus the ttest is equivalent to the ANOVA Ftest in this case.Best Wishes
Bower Chiel0November 27, 2008 at 11:39 am #178141Let’s not forget the use of the ttest for regression coefficients!
0November 27, 2008 at 2:45 pm #178143
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.RobertApologies for my garbled post – what looked fine on screen appeared as a dog’s breakfast online!Sample A 20.4 24.2 15.4 21.4 20.2 18.5 21.5
Sample B 20.2 16.9 18.5 17.3 20.5A ttest of mean for Population A equals mean for Population B, versus the alternative that they differ, gives t = 1.12 and Pvalue of 0.289 (equal population variances assumed).ANOVA for the same hypotheses gives F = 1.25 and Pvalue of 0.289.The Pvalues are identical and in fact the F value is the square of the t value – the two tests are exactly equivalent.It’s also interesting to consider the ANOVA alternative to the paired ttest.Best WishesBower Chiel0November 28, 2008 at 1:47 pm #178150
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.Bower, that was a good nit to pick. You’re right, I should have included a comment concerning the ANOVA case when k = 2. Thanks for covering that situation as well as providing numbers so someone can run the test for themselves.
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