I'm trying to do a correlation test between two categorical variables. The independent variable is nominal (Item Type: A, B, C) and dependent is ordinal (High, Medium, Low). When I try to apply the Chi-square test I noticed that some of the expected values are less than 5. Can someone suggest a suitable correlation test/methodology find a correlation between the variables in such a case?
At the outset, Chi-square test is for testing the significant of association between categorical variables. It is not correlation. The term correlation can be used when both the variables are having orders (low-high). The expected count is different from the observed count. The observed count is the count that your data has in each cell of the cross tabulation. The expected count is the count calculated based on the ratios of each cell counts by rows and columns. If the number of cells having the expected count less than 5 is less than 20% of the total number of cells, there is no problem. Chi-square test requires at least 80% of the cells to have the expected count more than 5.
One option is to merge the two categories. You can merge the category having the counts less than 5 with the nearest category by row or by column (merging two categories in first variable or in second variable) and perform the Chi-square test.