ZTest Vs TTests
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 This topic has 5 replies, 5 voices, and was last updated 15 years, 4 months ago by Jim Shelor.

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August 3, 2007 at 5:30 pm #47736
Dear Friends.
I have a question…i’ll be obliges in the forum can provide me with some answers to these…
When do we use 1 sample Ztest, especially when we say that a sample drawn may not follow a normal distribution and generally found to follow a tdistributions.
Also like there are 2 sample ttests and paired ttests how come there is no 2 sample Ztest or paired Ztest.0August 3, 2007 at 5:31 pm #159533
Quality is lifeParticipant@Qualityislife Include @Qualityislife in your post and this person will
be notified via email.Hi,
z test is used when the sample size is more than 30 while t test is used for smaple size less than 30.0August 3, 2007 at 5:43 pm #159536Hi,
But in some situations even with samples more than 30 the data may be nonnormal, in that case how can one use Ztest. I am sceptical of such thumb rules. One can not generalise all processe this way.
If all we work with are samples(which are supposed to follow tdistributions) and never populations then wy this ZTest at all???
An what about 2 sample Ztest???
0August 3, 2007 at 6:20 pm #159540DD:The Ttest was designed to handle sample sizes less than 30 (google Gosset). It is also very robust to deviations from normality. There are no circumstances where I would advise someone to use the Ztest over the Ttest.Strictly speaking, the Ztest is a test for populations rather than samples. For example, if you look at the formulae you will see entries for sd(population) that are estimated by sd(hat).Cheers, BTDT
0August 3, 2007 at 7:46 pm #159548Wrong
0August 3, 2007 at 8:59 pm #159553
Jim ShelorParticipant@JimShelor Include @JimShelor in your post and this person will
be notified via email.DD,
When using Variable Data, testing one sample mean against a standard:Variance known One mean Ztest
Variance unknown One mean Ttest.
When using Variable Data, testing two sample means against each other:Variance known Two mean Ztest
Variance unknown:Variances assumed equal Two sample pooled Ttest.
Variances assumed unequal Two sample Ttest.
Paired Data Paired Ttest
There is a two sample Ztest (see above).
There is no paired data Ztest because there is no need for one.
I hope this helps.
Regards,
Jim Shelor0 
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