Tech Notes

My notes on Statistics, Big Data, Cloud Computing, Cyber Security

t-test, z-test or Anova


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

Which t test should we use : an paired or unpaired?

A t test makes some assumptions. The first important assumption is that the distribution of the population of your sample data is normal.A t test cares about the distribution of the population, not the distribution of your samples.

Unpaired means that you simply compare the two groups. So, you will build a model for each group (calculate the mean and variance), and see whether there is a difference. Paired means that you will look at the differences between the two groups. A paired test first calculates the difference from one group to the other, and runs a one-sample t test.

Disclaimer : These are my study notes – online – instead of on paper so that others can benefit. In the process I’ve have used some pictures / content from other original authors. All sources / original content publishers are listed below and they deserve credit for their work. No copyright violation intended.

References for these notes :

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