<\/span><\/h2>\nThe expected ratio for a chi-squared value can be obtained by following a straightforward calculation based on the observed data. The formula is as follows:<\/p>\n
Expected Ratio = (Row Total * Column Total) \/ Grand Total<\/strong><\/p>\nTo apply this formula, you need to have a contingency table containing the observed values for the variables being analyzed. The row and column totals represent the sum of frequencies for each variable, while the grand total represents the sum of all frequencies in the table.<\/p>\n
Once you have these values, plug them into the formula and calculate the expected ratio for each cell in the contingency table. These expected ratios represent the values that would be anticipated if there were no association between the variables, assuming the null hypothesis is true.<\/p>\n
To better illustrate this process, let’s consider an example. Suppose we want to examine the relationship between gender (male\/female) and smoking status (smoker\/non-smoker). We collect data from a sample of 200 individuals and create a contingency table:<\/p>\n
“`
\n—————————————-
\n | Smoker | Non-Smoker | Total |
\n—————————————-
\n Male | 40 | 50 | 90 |
\n—————————————-
\n Female | 60 | 50 | 110 |
\n—————————————-
\n Total | 100 | 100 | 200 |
\n—————————————-
\n“`
\nUsing this contingency table, we can calculate the expected ratios to determine if there is any association between gender and smoking status.<\/p>\n
The expected ratio for the cell in the first row and first column (for male smokers) can be calculated as:<\/p>\n
“`
\nExpected Ratio = (90 * 100) \/ 200 = 45
\n“`<\/p>\n
By applying the same formula to the rest of the cells in the contingency table, we obtain the complete set of expected ratios.<\/p>\n