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To determine the relationship between employees’ scores on the manual dexterity test and their performance ratings, we take employees’ scores on the manual dexterity test as x and performance rating as y. then we will determine slope M using the equation: Y = Mx + C.
Where C is a constant, determined by a change in y coordinate divided by a change in x coordinate. The change in y coordinate is given by subtracting the minimum value of y from the maximum value given by: Change in y = max value of y – minimum value of y = 95 -70 = 25.
Similarly, Change in x = maximum value of x- minimum value of x = 52 -32 = 20.
Then slope (M) = change in y/ change in x = 25/20 = 1.25.
This implies that Y = 1.25x + C.
This implies that for every one unit of employee’s performance rate, there is a 1.25 unit of employees scores on the manual dexterity test. This means that an increase in employees' scores on the manual dexterity test by one unit implies that the performance rate increases by 1.25 units.
For the second question, if the regression equation is: Job performance = 32.465 + (1.25 * manual dexterity test score).
Then if the manual dexterity test is 44, the candidate's predicted job performance is: 32.465 + (1.234* 44) = 86.761.
This means that if the candidate's score on the manual dexterity test is 44, then the predicted job performance is 86.761.
If we assume that candidates with scores above 43 on the manual dexterity test were hired, this means that these candidates have a predicted performance of 85. Looking at the sex issue, we see that the number of males hired is seven (7) and the number of females hired is 13, all of them above the cutoff of 43. Similarly, on race six (6) Hispanics, eight (8) whites, and six (6) blacks were hired. Calculating in terms of percentages indicates that 81.25% females and 50% males were employed. The percentage of Spanish employed is 66.67%, blacks and whites hired were 66.67% and 81.25% respectively. Thus, the use of this test has adverse effects on sex in that the number of females hired was higher than the number of males hired. The use of this test discriminated against males and favored females.
Out of the total number of Hispanic candidates, six of them were hired translating to 66.67%. 6/10 blacks were hired which is equivalent to 60%. 8/11 whites hired which is 72.73%. Therefore, the use of this test led to the employment of more whites than Hispanics and blacks.
Given the validity of the results, I would recommend the use of this kind of test because it is quick, easy to use, and economical to administer measures of manual dexterity. Sub-tests require no scoring keys and are quick to score (Thomas et al. 2014).
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