IGNOU MST 25 2026 - A study was conducted to compare two diagnostic methods say, Method-I

Question

A study was conducted to compare two diagnostic methods say, Method-I and MethodII. The following table shows the classification of the presence of infection on 5-point Likert Scale (none, mild, moderate, severe and extreme): Method-II Method-I None Mild Moderate Severe Extreme None 89 5 16 2 4 Mild 36 3 15 6 2 Moderate 20 4 22 6 1 Severe 14 2 37 18 16 Extreme 4 1 16 23 50 Compute simple and weighted Kappa Statistic(s) to compare both methods.

14 May 2026

Answer :

Word Count : 476

To compare Method-I and Method-II for agreement on the diagnosis of infection measured on a 5-point Likert scale, Cohen’s simple Kappa and weighted Kappa statistics are computed. The observed frequency table is: [ \begin{array}{c|ccccc|c} & \text{None} & \text{Mild} & \text{Moderate} & \text{Severe} & \text{Extreme} & \text{Row Total} \ \hline \text{None} & 89 & 5 & 16 & 2 & 4 & 116 \ \text{Mild} & 36 & 3 & 15 & 6 & 2 & 62 \ \text{Moderate} & 20 & 4 & 22 & 6 & 1 & 53 \ \text{Severe} & 14 & 2 & 37 & 18 & 16 & 87 \ \text{Extreme} & 4 & 1 & 16 & 23 & 50 & 94 \ \hline \text{Column Total} & 163 & 15 & 106 & 55 & 73 & 412 \end{array} ] Total number of observations: [ N = 412 ] For simple Kappa statistic, first calculate the observed proportion of agreement: [ P_o = \frac{89+3+22+18+50}{412} ] [ P_o = \frac{182}{412} = 0.4417 ] Next compute expected agreement by chance: [ P_e = \sum \frac{(R_i \times C_i)}{N^2} ] Where (R_i) and (C_i)

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