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Test Statistic

A test statistic is one that is used in the process of statistical hypothesis testing. A hypothesis test is generally specified with respect to a test statistic and is considered as a numerical summary of a set that produces the data to a singular value that can be used for performing the said hypothesis test.

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It is defined or selected in such a way that it can be used to quantify behaviors within observed data that will make the alternate hypothesis distinguishable from the null hypothesis. A very important property of such a statistic is that the sampling distribution under the null hypothesis needs to be calculated either approximately or exactly. This helps the p-values to be calculated.  specifically intent

Some of the common test statistics are given below:

  • One-sample tests are used when a sample is compared to the population from a hypothesis. The population characteristics are decided from theory or calculated from the population.
  • Two-sample tests are used when comparing two samples, generally control and experimental samples from a controlled experiment.
  • Paired tests are used to compare samples when it is impossible to control vital variables. Instead of comparing two sets, they are paired between samples so that the difference between the members becomes the sample. Generally, the mean of the differences is then equated to zero. This is generally used when a single set of test subjects has something applied to them and the test is expected to check for an effect.
  • Z-tests are done to compare entities under stringent conditions with respect to normality and a known standard deviation.
  • A t-test is used for comparing means under relaxed conditions.

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