How to use this page
Enter observed frequencies into the table. If your research design involves a [2 x 3] table, you should enter your data in the 6 cells in the upper left portion of the data table, defined by the first two Conditions and the first three Groups. You can choose any subset of rows and columns for your data. You can also choose to leave cells corresponding to observed frequencies of zero blank. Non-integer observed frequencies are permitted.
If you are performing a test of goodness of fit, you may choose to enter your data in any single column or row. However, observed zero frequencies need to be explicitly included (i.e., you'll need to actually input "0" in those cells, otherwise it will be assumed that those cells are not part of your study design). Once you have entered your data, click on the Calculate button and expect to see output in the beige cells. If you see scientific notation for your p-value - it means that p is really small.
This tool also provides a chi-square incorporating Yates' correction for continuity. This correction is often employed to improve the accuracy of the null-condition sampling distribution of chi-square.
Use of the chi-square tests is inappropriate if any expected frequency is below 1 or if the expected frequency is less than 5 in more than 20% of your cells. The status cell at the bottom of the table will let you know if there is a problem. In the 2 x 2 case of the chi-square test of independence, expected frequencies less than 5 are usually considered acceptable if Yates' correction is employed.
When using the chi-square goodness of fit test, sometimes it is useful to be able to specify your own expected frequencies. If there is a theoretical reason for doing so, the following table will allow you to enter your own expected frequencies. Non-integer expected frequencies are allowed. Use as many cells in this table as necessary, making sure that: (a) the marginal total is the same for both observed and expected frequencies; (b) there are no expected frequencies < 1; and (c) no more than 20% of your expected frequencies are < 5. If a frequency is entered in an Observed cell, then a frequency must also be entered in the corresponding Expected cell (the opposite is also true).