Interpret this statistic. Why was gamma applicable here? Please show your
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F268cba5b-26bb-4b8b-85a2-e8c814820090%2Ff6adb1f1-ede9-4663-8649-811fb51edc90%2Fr9zcy5c_processed.png&w=3840&q=75)
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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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