What Goodness - of - fit test is
Goodness-of-fit tests are used to compare observed data with expected data and determine how well the two match. The tests are usually performed when there is a hypothesis that the data should follow a certain distribution.
Steps for Goodness-of-fit Tests:
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Prepare the data: Collect the data that will be used in the test and organize it into a table.
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State the null and alternative hypotheses: The null hypothesis is that the data follows the expected distribution, while the alternative hypothesis is that the data does not follow the expected distribution.
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Choose a test statistic: Choose a test statistic that will be used to measure the differences between the observed and expected data.
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Calculate the test statistic: Calculate the test statistic based on the observed data and the expected data.
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Determine the critical value: Determine the critical value of the test statistic that would reject the null hypothesis.
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Compare the test statistic to the critical value: Compare the calculated test statistic to the critical value. If the test statistic is greater than the critical value, then the null hypothesis is rejected. If the test statistic is less than the critical value, then the null hypothesis is accepted.
Examples
- Goodness-of-fit tests can be used to determine if a set of data fits a specific probability distribution.
- Goodness-of-fit tests can be used to compare two or more models in order to determine which model is the best fit for a particular dataset.
- Goodness-of-fit tests can be used to check if a sample of data follows a given population distribution.
- Goodness-of-fit tests can also be used to determine if two samples come from the same population.
- Goodness-of-fit tests can be used to check for significant differences between observed and expected frequencies in contingency tables.