What Composite hypothesis is
Composite hypothesis is a type of statistical hypothesis test that combines two or more simple hypotheses into a single test. It is used to test the overall effect of a set of variables on a response variable.
The steps for performing a composite hypothesis test are as follows:
- State the null and alternative hypotheses:
The null hypothesis states that there is no overall effect of the set of variables on the response variable. The alternative hypothesis states that there is an overall effect of the set of variables on the response variable.
- Specify the test statistic:
The test statistic used for a composite hypothesis test is a test statistic that measures the overall effect of the set of variables on the response variable.
- Specify the distribution of the test statistic:
The distribution of the test statistic depends on the type of composite hypothesis test being performed. For example, if the composite hypothesis test is a t-test, then the distribution of the test statistic is a t-distribution.
- Calculate the test statistic:
The test statistic is calculated by applying the appropriate formula to the data.
- Compare the test statistic to the critical value:
The critical value is determined by looking up the appropriate critical value in a table or by using software. The test statistic is then compared to the critical value to determine if the null hypothesis should be rejected or not.
- Make a decision:
If the test statistic is greater than the critical value, then the null hypothesis is rejected and the alternative hypothesis is accepted. If the test statistic is less than the critical value, then the null hypothesis is not rejected and the alternative hypothesis is not accepted.
Examples
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An example of a composite hypothesis in statistics is a hypothesis which states that two or more distributions have the same mean.
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Another example of a composite hypothesis in statistics is a hypothesis which states that two or more groups of data have the same variance.
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A third example of a composite hypothesis in statistics is a hypothesis which states that two or more populations have the same correlation.