<\/span><\/h2>\nThe expected value in chi-square is determined by multiplying the row total by the column total and dividing it by the grand total.<\/strong> This calculation helps us assess if the observed frequency differs significantly from the expected frequency, indicating a significant association between the variables being analyzed.<\/p>\nThe formula to calculate the expected value (E) for each cell in a chi-square table is as follows:<\/p>\n
E = (Row Total x Column Total) \/ Grand Total<\/p>\n
Let’s illustrate this with a concrete example. Consider a study investigating the relationship between gender (male\/female) and the occurrence of a medical condition (yes\/no). We have collected data from 500 participants and obtained the following contingency table:<\/p>\n
| | Medical Condition: Yes | Medical Condition: No | Total |
\n|—————-|———————–|———————–|——-|
\n| Gender: Male | 100 | 200 | 300 |
\n| Gender: Female | 150 | 50 | 200 |
\n| Total | 250 | 250 | 500 |<\/p>\n
To calculate the expected value for the cell representing males with the medical condition, we apply the formula:<\/p>\n
E = (300 x 250) \/ 500 = 150<\/p>\n
Similarly, we can calculate the expected values for the remaining cells in the contingency table.<\/p>\n
Once we have the expected values calculated, we can compare them to the observed frequencies or actual counts obtained from the study. By assessing the discrepancies, we can determine if there is a significant association between the variables.<\/p>\n