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# Z-test

Explanations > Social ResearchAnalysis > Z-test

## Description

The Z-test compares sample and population means to determine if there is a significant difference.

It requires a simple random sample from a population with a Normal distribution and where where the mean is known.

### Calculation

The z measure is calculated as:

z = (x - m) / SE

where x is the mean sample to be standardized, m (mu) is the population mean and SE is the standard error of the mean.

SE = s / SQRT(n)

where s is the population standard deviation and n is the sample size.

The z value is then looked up in a z-table. A negative z value means it is below the population mean (the sign is ignored in the lookup table).

## Discussion

The Z-test is typically with standardized tests, checking whether the scores from a particular sample are within or outside the standard test performance.

The z value indicates the number of standard deviation units of the sample from the population mean.

Note that the z-test is not the same as the z-score, although they are closely related.

Z-score

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