Youareemployed asa psychometristat BanksUnitedof SouthernAfrica (BUSA).FrankHendersonandIshaMyerare your colleagues in theassessment department andarealsoregisteredpsychometrists. You directly report toJohnStevens, the HR Director and head of psychological assessment at BUSA. The assessment department specializes in psychological assessments, the development of in-house psychometric tests and the psychometric evaluation of psychometric instruments.All departmental activities are geared towards selecting the best candidates for vacant positions or promoting current employees at BUSA to higher positions within theorganisation.

One morning,Ishacontactsyou in your office.Ishais in charge of evaluating and purchasing new psychometric instruments at BUSA.

She tells you that BUSA have recently received a complaint from the Health Professions Council of South Africa (HPCSA). A candidate that was unsuccessful in applying for a managerial position in thesalesdepartment lodged a complaint with the HPCSA. The candidate is of the opinion that the psychometric properties of the measures we are using for selection purposes are unreliable and bias against African candidates since the test is administrated in English. Fortunately, you have data from candidates who applied for positions last year (See Table 1 with data). You are currently using a personality measure(Test X)and a cognitive ability measure(Test Z). Both psychological measures have 20 items each.

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TABLE 1

Applicant	Personality MeasureTest Xscores	Cognitive Ability MeasureTest Zscores
	Score for odd items (x1)	X12	Score for even items (x2)	X22	Product of items x1x2	Total score (X)	Score for odd items (z1)	Z12	Score for even items (z2)	Z22	Product of items z1z2	Total score (Z)	Product XZ
Allisha	6	36	8	64	48	14	6	36	2	4	12	8	52
Megan	7	49	7	49	49	14	6	36	4	16	24	10	70
Brendon	7	49	6	36	42	13	2	4	4	16	8	6	38
Candy	6	36	8	64	48	14	4	16	5	25	20	9	64
Porsha	5	25	6	36	30	11	4	16	3	9	12	7	38
Sammy	8	64	9	81	72	17	5	25	3	9	15	8	67
Ashton	4	16	5	25	20	9	2	4	6	36	12	8	38
Nkosizana	5	25	4	16	20	9	6	36	3	9	18	9	42
Hilton	8	64	7	49	56	15	7	49	4	16	28	11	84
Jennifer	8	64	9	81	72	17	4	16	2	4	8	6	50
	1	12	2	22	1x2		1	12	2	22	1z2
	64	428	69	501	457	133	1	2	3	4	5	6	543

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In order to formulate a response to the HPCSA, you need to compile a technical report which contains all the psychometric information about the personality and cognitiveabilitymeasures that you are using for selection.

Questions1-6

To start off with,calculate the values for the shaded cells in the table above.Youwill need this informationfor the rest of the calculations.(3)

PLEASE INCLUDE ONLY THE ANSWER TO YOUR CALCULATIONS IN THE SECOND COLUMN BELOW:

Question	ANSWER
11
212
32
422
512
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Questions7-11

Next, we needtocalculate the meanandvariancevalues for tests X and Z.Remember that both measures have 20 items.(5)

YOU DONOTNEED TO INCLUDE ANY FORMULAS OR SHOW ANY CALCULATIONS. PLEASE INCLUDE ONLY THEFINALANSWER TO YOUR CALCULATIONS IN THE SECOND COLUMN BELOW:

Question	ANSWER
7Mean of X
8Mean ofZ
9Variance of X
10Variance ofZ

Question11

What can you conclude regardingmeasure X andZfrom these values of central tendency and variability?

11What can you conclude regarding the measures from these values?

Questions12-22

Reliability is an important prerequisite for psychometric testsin South Africa.Please assist in calculating the split-half reliability ofTestX(thePersonalitymeasure)?You do not need to show any formulas. Please indicate the correct values to be substituted in the formula for questions12-21. Include only your final answerof the calculated reliabilityfor Question22.

Question	ANSWER
12 Value to be substituted
13 Value to be substituted
14 Value to be substituted
15 Value to be substituted
16 Value to be substituted
17 Value to be substituted
18 Value to be substituted
19 Value to be substituted
20 Value to be substituted
21 Value to be substituted
22 Calculated reliability (final answer only - rounded off to two decimals).

Questions 23-26

You read in your IPS 232 textbook that using the split-half method to establish reliability may underestimate the reliability of a measure since only half of the items are used. One can use another formula to calculate the corrected split half reliability coefficient to account for the shortening of the measure. Show the correct value to be substituted in this formula (questions 23-24) and present the corrected split half reliability coefficient as the answer to question 25. YOU DO NOT NEED TO INCLUDE ANY FORMULAS OR SHOW ANY CALCULATIONS. PLEASE INCLUDE ONLY THE FINAL ANSWER. What is the normative cut-off value for reliability? Given the corrected reliability in question 25, what can we conclude about the reliability of Test X? (3)

=

Question	ANSWER
23 Value to be substituted
24 Value to be substituted
25 Final answer rounded off to two decimals
26 Conclusion regarding the reliability of Test X

Questions 27-31

Assume that the reliability of the current 90 items measure Y is 0.85. How many items should the new assessment be reduced to in order to still achieve a reliability of 0.75? Show the values to be substituted in the formula and the final answer. (3)

n=

Question	ANSWER
27 Value to be substituted
28 Value to be substituted
29 Value to be substituted
30 Value to be substituted
31 Final answer