# Test statistic

### Test statistic

A random variable used in hypothesis testing to determine whether to support or reject the null hypothesis.

A hypothesis test will use a distribution (normal distribution, t-distribution, etc) with a known area to calculate a p-value that your results are due to chance. The p-value is the used in combination with the test statistic to draw your conclusions, if there is a large enough test statistic and small enough p-value you may be able to reject the null hypothesis.

### Estimated Standard Error

For some hypothesis tests, it is necessary to calculate the Estimated Standard Error (ESE) first as part of the test statistic calculation. There are various ways of estimating the standard error dependent on which test you’ve selected. ### Test statistic for sign tests

If the hypothesis was testing an assumed median we could use a sign test and we’d need to calculate how many observations are above and below that assumed median. The test statistic is the smaller of the number of values lying below or the number lying above the assumed median.

### Test statistic for one-sample z-tests

Where ‘A’ is the hypothesised mean, this is the formula for the test statistic for a one-sample z-test (NB: the ESE has been merged into this formula): 