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As explained in Vol. 21, a chi-square test is used to examine the relationship between the age groups of the population and effectiveness/ineffectiveness.
In turn, we explain the chi-square test.
Summarize the data into a cross-tabulation table
Table 1 is a cross-tabulation table summarizing the results of the study on the effectiveness of the new drug X in young, middle-aged, and older age groups.
[Table 1] Number/percentage of valid and invalid of new drugs
Find the expected frequency
Which of the cases in Table 1 show no association between age and validity or invalidity? As shown in Table 2, all age groups show the same overall percentage (total).
[Table 2]
The expected frequency is the number that says, “If there was no relationship, this would have happened.” The original number of people is called the measured frequency.
The number of people with the ratios listed in Table 2 was obtained from the total number of people in each stratum. (Table 3)
Expected frequency = vertical total × horizontal total ÷ total number of people
[Table 3] Calculation of the expected frequency
The percentage of expected frequencies by age group was the same for valid and invalid frequencies. (Table 4)
[Table 4] Expected frequencies by age group
Calculation of chi -square value
If the actual frequency is close to the expected frequency, the relationship is weak; if it is far from the expected frequency, the relationship is strong.
[Table 5] Comparison of the actual and expected frequencies
To determine the degree of agreement, we calculate each individual cell.
(Actual frequency–expected frequency)2 ÷expected frequency
[Table 6] Calculation of chi-square value
The total value for each cell is 13.19. This value is called the “chi-square value.”
The larger this value, the greater the difference between the expected frequency and the original data. In other words, if the chi-square value is large, it can be considered that “there is likely a relationship between age group and effectiveness/ineffectiveness.”
Significance judgment by p-value
The criteria for how much the chi -square value can be judged to be “large” will be compared with the critical value determined by statistics. As the degrees of freedom differ depending on the number of categories in the cross-tabulation table, the critical values are also different criteria. We can now easily calculate the p-value, which, in this case, was 0.0014.
The result was p<0.05; therefore, it can be said that there is a relationship between age group and effectiveness/ineffectiveness in the population.
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