Question
A study was conducted to compare two diagnostic methods say, Method-I and Method-II. 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.
Answer :
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Skip in 10
First, let's solve step by step manually. We have a 5×5 table comparing Method-I and Method-II with categories: None, Mild, Moderate, Severe, Extreme. Let’s denote these categories as 1, 2, 3, 4, 5 respectively. Step 1: Compute totals Row totals (Method-II): * None: 89 + 5 + 16 + 2 + 4 = 116 * Mild: 36 + 3 + 15 + 6 + 2 = 62 * Moderate: 20 + 4 + 22 + 6 + 1 = 53 * Severe: 14 + 2 + 37 + 18 + 16 = 87 * Extreme: 4 + 1 + 16 + 23 + 50 = 94 Column totals (Method-I): * None: 89 + 36 + 20 + 14 + 4 = 163 * Mild: 5 + 3 + 4 + 2 + 1 = 15 * Moderate: 16 + 15 + 22 + 37 + 16 = 106 * Severe: 2 + 6 + 6 + 18 + 23 = 55 * Extreme: 4 + 2 + 1 + 16 + 50 = 73 Grand total N = sum of all = 116 + 62 + 53 + 87 + 94 = 412 Step 2: Compute simple (unweighted) Kappa Kappa formula: [ \kappa = \frac{P_o - P_e}{1 - P_e} ] Where: * (P_o) = observed agreement = sum of diagonal / N
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