# Z-Test Vs T-Tests

Six Sigma – iSixSigma Forums Old Forums General Z-Test Vs T-Tests

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• #47736

DD
Participant

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 Z-test, especially when we say that a sample drawn may not follow a normal distribution and generally found to follow a t-distributions.
Also like there are 2 sample t-tests and paired t-tests how come there is no 2 sample Z-test or paired Z-test.

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#159533

Quality is life
Participant

Hi,
z test is used when the sample size is more than 30 while t test is used for smaple size less than 30.

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#159536

DD
Participant

Hi,
But in some situations even with samples more than 30 the data may be non-normal, in that case how can one use Z-test. 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 t-distributions) and never populations then wy this Z-Test at all???
An what about 2 sample Z-test???

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#159540

BTDT
Participant

DD:The T-test 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 Z-test over the T-test.Strictly speaking, the Z-test 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

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#159548

Mikel
Member

Wrong

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#159553

Jim Shelor
Participant

DD,

When using Variable Data, testing one sample mean against a standard:

Variance known  One mean Z-test
Variance unknown  One mean T-test.

When using Variable Data, testing two sample means against each other:

Variance known  Two mean Z-test
Variance unknown:

Variances assumed equal  Two sample pooled T-test.
Variances assumed unequal  Two sample T-test.
Paired Data  Paired T-test

There is a two sample Z-test (see above).

There is no paired data Z-test because there is no need for one.

I hope this helps.

Regards,

Jim Shelor

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