Exam 7: Nonparametric Measures of Association

Correct Answer:

Verified

$$\begin{array} { l } E _ { 1 } = n - \text { modal category } = 121 - 45 = 76 \\E _ { 2 } = ( 42 - 31 ) + ( 56 - 32 ) + ( 23 - 17 ) = 11 + 24 + 6 = 41 \\\\\lambda _ { \mathrm { PRE } } = \frac { E _ { 1 } - E _ { 2 } } { E _ { 1 } } = \frac { 76 - 41 } { 76 } = 0.4605\end{array}$$
Lambda is an asymmetric measure of association.

Correct Answer:

Verified

$$\begin{array} { c } E _ { 1 } = n - \text { modal category } = 320 - 178 = 142 \\E _ { 2 } = ( 166 - 109 ) + ( 154 - 121 ) = 57 + 33 = 90 \\\text { PRE } = \frac { E _ { 1 } - E _ { 2 } } { E _ { 1 } } = \frac { 142 - 90 } { 142 } = 0.3662\end{array}$$
The error in predicting favor for gun control is with knowledge of Democrats/Republicans opinion reduced by 36.62%.

Correct Answer:

Verified

It is appropriate to utilize tau b as a measure of association because the number of rows and columns in the table are equal.
N_s = 3,043 (value from problem 7)
N_d = 348 (value from problem 7)
T_y = 1,475 (value from problem 9)
T_x for cell A = (31) × (8 + 3) = 341
T_x for cell B = (12) × (32 + 12) = 528
T_x for cell C = (2) × (4 + 17) = 42
T_x for cell D = (8) × (3) = 24
T_x for cell E = (32) × (12) = 384
T_x for cell F = (4) × (14) = 56
Total T_x = 1,375
$$\begin{array} { c } b = \frac { N _ { s } - N _ { d } } { \sqrt { \left( N _ { s } + N _ { d } + T _ { y } \right) \left( N _ { s } + N _ { d } + T _ { x } \right) } } = \frac { 6043 - 348 } { \sqrt { ( 3043 + 348 + 1475 ) ( 3043 + 348 + 1375 ) } } \\= \frac { 2695 } { \sqrt { 4866 \times 4766 } } = \frac { 2695 } { 4815.74 } = 0.5596\end{array}$$
Utilizing tau b, you find that the relationship between level of officer/population ratio and the level of overall job satisfaction is moderate (similar to the value you got utilizing Somer's d, but significantly lower than the value you got utilizing gamma).