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For goodness of fit test using Chisquare test, Expected frequency = Total number of observations * theoretical probability specified or Expected frequency = Total number of observations / Number of categories if theoretical frequencies are not given. For contingency tables (test for independence) Expected frequency = (Row total * Column total) / Grand total for each cell
There are many chi-squared tests. You may mean the chi-square goodness-of-fit test or chi-square test for independence. Here is what they are used for.A test of goodness of fit establishes if an observed frequency differs from a theoretical distribution.A test of independence looks at whether paired observations on two variables, expressed in a contingency table, are independent of each.
It is often a "goodness of fit" test. This is a test of how well the observations match the frequencies that would have been expected on theoretical basis. The theoretical basis may simply be your hypothesis.
You first decide on a null hypothesis. Expected frequencies are calculated on the basis of the null hypothesis, that is, assuming that the null hypothesis is true.
A chi-square test is often used as a "goodness-of-fit" test. You have a null hypothesis under which you expect some results. You carry out observations and get a set of results. The expected and observed results are used to calculate the chi-square statistic. This statistic is used to test how well the observations match the values expected under the null hypothesis. In other words, how good the fit between observed and expected values is.