Difference between Z-test, F-test, and T-test

Posted on: December 5, 2010

A z-test is used for testing the mean of a population versus a standard, or comparing the means of two populations, with large (n ≥ 30) samples whether you know the population standard deviation or not. It is also used for testing the proportion of some characteristic versus a standard proportion, or comparing the proportions of two populations.
Example:Comparing the average engineering salaries of men versus women.
Example: Comparing the fraction defectives from 2 production lines.

A t-test is used for testing the mean of one population against a standard or comparing the means of two populations if you do not know the populations’ standard deviation and when you have a limited sample (n < 30). If you know the populations’ standard deviation, you may use a z-test.
Example:Measuring the average diameter of shafts from a certain machine when you have a small sample.

An F-test is used to compare 2 populations’ variances. The samples can be any size. It is the basis of ANOVA.
Example: Comparing the variability of bolt diameters from two machines.

Matched pair test is used to compare the means before and after something is done to the samples. A t-test is often used because the samples are often small. However, a z-test is used when the samples are large. The variable is the difference between the before and after measurements.
Example: The average weight of subjects before and after following a diet for 6 weeks

27 Responses to "Difference between Z-test, F-test, and T-test"

thank buddy

thank you. this seems a clear description of the question


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Good explanation , request you add some more blogs like this , Simple and to the point explanation.

good explanation. Thank you very much

very easy and simple to understand. Thank you and keep the good works going on.

at last a good and and clear explanation !!! thanks

Hi , thanks for this explanation . It helped , but i still have one doubt. Can Z test be still used for comparing proportion of two samples when sample size is less than 30 ? for example i need to compare the conversion rate of two campaigns for 15 days . can i use Z test here ?


When comparing the average engineering salaries of men versus women, why would we use a z-test—as opposed to just comparing the averages for men versus women?

Direct comparison of two averages doen’t account for the variance of the individual data. One group could have a very small distribution of incomes and the other much larger. Then it is possible that the average of the small variance group lies within the distribution of the large variance group and that the difference between the averages isn’t actually meaningful.

the information was simple and easy to understand
thank you for your efforts

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OMG why couldn’t my professor have just said this. Or maybe he did but I didn’t realize it b/c is English is so crappy.

very easy way expressed .thanks

thank you very much,dear/

[…] in statistics in my life, and almost every time I do one, I have to go double-check to make sure which is which; about half the time, I’m wrong. I just don’t do them often enough that the information […]

clear and basic

Even tha slow learners easily understand this. Thenks n keep it up

very xlear and easy to understand , not that complicated as other information i read. thanks alot
very easy and reliable explanation it helped me much ,thanks alot

I thank you very much for this work. I must confess the work is nice.

thsnk u so much . the concept is to be to me know

thanks for well done job

Short, clear and much helpful 🙂
Thank buddy 🙂


Somewhere I’ve read that Anova is used instead of t-test to test whether the means of several groups (more than two) are equal.
So, is it used to compare means or variances?

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