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
13 Responses to "Difference between Z-test, F-test, and T-test"
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October 7, 2012 at 8:05 pm
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November 28, 2012 at 1:53 pm
very easy and simple to understand. Thank you and keep the good works going on.
February 20, 2013 at 9:12 am
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 ?
April 17, 2013 at 8:32 pm
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?
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November 16, 2011 at 8:25 pm
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