Final answer:
The minimum expected cell size for crosstabs is at least five when conducting a Chi-square test of independence to ensure the validity of the results. To calculate the expected frequency, multiply the row total by the column total and divide by the total surveyed. If expected frequencies are less than five, categories may need to be combined.
Step-by-step explanation:
The minimum expected cell size for crosstabs, when conducting a Chi-square test of independence, is at least five. This requirement is essential to ensure the validity of the test's results. When the expected frequency in any cell of a contingency table is less than five, the Chi-square test may not be the appropriate test to use, as it can lead to inaccurate results.
To calculate the expected frequency for a particular cell in a contingency table, use the formula:
(row total) × (column total) / total number surveyed. If the expected frequencies are too low, combining categories may be necessary to achieve the minimum expected value. For instance, suppose we are looking at a contingency table with a row total of 255 and a column total of 298 within a survey of 839 individuals. The expected frequency for that cell would be:
Expected frequency = (255 × 298) / 839
In some cases, such as with a sample of cell phone customers, you may round the answer to the next higher value to achieve the needed minimum cell count.
Remember that the bottom line is: the expected value of each cell must be at least five to conduct a reliable Chi-square test. If the expected frequencies are below this threshold, you may need to consider an alternative statistical method or data transformation.