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

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

Hope this is useful, thank you!

## 34 thoughts on “Difference between Z-test, F-test, and T-test”

1. aku

thank buddy

2. uday

thank you. this seems a clear description of the question

3. TIMOTHY

4. thanks buddy

5. Your style is really unique compared to other people I’ve read stuff from. Thanks for posting when you have the opportunity, Guess I’ll just bookmark this blog.

6. C k

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

7. Mai Thanh Luan

good explanation. Thank you very much

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

9. toubab95

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

10. karishma

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 ?

11. Hello.

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?

1. LAW

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.

12. ravi

the information was simple and easy to understand

13. Appreciating the persistence you put into your blog and in depth information you present.
It’s great to come across a blog every once in a while that isn’t the same out

14. 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.

15. wudi

very easy way expressed .thanks

16. subramaniabharathi

thank you very much,dear/

17. Vanlalrema Kuki

clear and basic

18. kristin

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

19. 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

20. Suoton Ekine

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

21. shaina verma

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

22. mathew

24/mathew
thanks for well done job

23. Lahiru Chamara

Short, clear and much helpful 🙂
Thank buddy 🙂

24. ampar

Hello.

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?

25. Christophe

Thanks from France… Clear and easy to understand, even if it’s not my mother tongue.

26. Mithilesh Mishra

I am confused, I have one query: if I have the samples I can anyway calculate standard deviation so I will always have the standard deviation of the population. If that is not the case, if you counter that the sd of samples is not called sd of population, in that case I will never havd sd of population. so either I can always use z-test or never use it or I may base my decision on number of samples being more or less than 30. Please elaborate.

27. Finally we have some clarity. Thanks for this!

28. Mahrukh

What is the diference between these all distribution ie t dist .z dist .f dist and chisquare so that we become able to solve these question because they are soo much confusiong .? Plz tell the answer

29. wisal

major diffrences between z and t test is what plz give me ans

30. GoOd BUddY

31. Hi, say I want to test on pre and post period, must the year be equally same (i.e 4 years pre and 4 years post) or it doesn’t matter. Appreciate your help.