Interpret this statistic. Why was gamma applicable here? Please show your

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Interpret this statistic. Why was gamma applicable here? Please show your work.

**Part II: Ordinal-Ordinal and Ordinal-Nominal Measures of Association**

4) A researcher is interested in examining the relationship between age and health status. Importantly, they have already determined that there is likely a statistically significant relationship between these two variables in the population. Now they are interested in assessing the strength of the relationship.

Below is R output for a bivariate table cross-tabulating age (the independent variable) and health status (the dependent variable). The gamma statistic (γ) is printed below it. Interpret this statistic. Why was gamma applicable here? Please show your work.

|                  | excellent | good | fair | poor |
|------------------|-----------|------|------|------|
| 49 and younger   | 249       | 419  | 167  | 39   |
| 50 and older     | 192       | 383  | 173  | 88   |

Gamma: 0.1607286

**Explanation of Table and Statistic:**

The table displays a cross-tabulation of age groups (49 and younger vs. 50 and older) against health status categories (excellent, good, fair, poor). Each cell contains the observed count of individuals within each age and health status combination.

The gamma statistic (γ = 0.1607286) measures the strength and direction of association between two ordinal variables. It ranges from -1 (perfect negative association) to +1 (perfect positive association), with 0 indicating no association. A gamma of 0.1607286 suggests a weak positive association between age and health status, meaning that as age increases, there is a slight tendency for health status to decrease. 

Gamma is applicable here because both age and health status are ordinal variables, allowing for meaningful ranking and comparison of categories.
Transcribed Image Text:**Part II: Ordinal-Ordinal and Ordinal-Nominal Measures of Association** 4) A researcher is interested in examining the relationship between age and health status. Importantly, they have already determined that there is likely a statistically significant relationship between these two variables in the population. Now they are interested in assessing the strength of the relationship. Below is R output for a bivariate table cross-tabulating age (the independent variable) and health status (the dependent variable). The gamma statistic (γ) is printed below it. Interpret this statistic. Why was gamma applicable here? Please show your work. | | excellent | good | fair | poor | |------------------|-----------|------|------|------| | 49 and younger | 249 | 419 | 167 | 39 | | 50 and older | 192 | 383 | 173 | 88 | Gamma: 0.1607286 **Explanation of Table and Statistic:** The table displays a cross-tabulation of age groups (49 and younger vs. 50 and older) against health status categories (excellent, good, fair, poor). Each cell contains the observed count of individuals within each age and health status combination. The gamma statistic (γ = 0.1607286) measures the strength and direction of association between two ordinal variables. It ranges from -1 (perfect negative association) to +1 (perfect positive association), with 0 indicating no association. A gamma of 0.1607286 suggests a weak positive association between age and health status, meaning that as age increases, there is a slight tendency for health status to decrease. Gamma is applicable here because both age and health status are ordinal variables, allowing for meaningful ranking and comparison of categories.
Expert Solution
Step 1

 

Conditions for Gamma:

4)

Strength of Association Value of Gamma
No association 0
Weak association ±0 .01- 0.09
Moderate Association ±0 .10 –0.29
strong association ±0.30 – 0.99
Perfect association ±1.00

 

From the given output,

The gamma coefficient is 0.1607, which is lies between the range 0.10-0.29.

Hence, there exists a moderate association.

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