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. 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 ?

  2. 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.

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  5. 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

  6. ampar


    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?

  7. 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.

  8. 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

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