Psychological Testing Questions and Answers

Answer: B

Cross validation means that test validity is studied on a different sample.

When items are selected or a regression equation is built using one sample, the validity found in that sample is inflated by chance features of that sample. Cross validation checks the test, or the prediction equation, on a fresh, independent sample from the same population. The usual drop in the validity coefficient is called shrinkage.

Repeating item analysis on the same sample does not remove the chance factors. Deleting items of similar difficulty and comparing indices of item discrimination are item-analysis procedures, not cross validation.

Answer: C

The correct code is (P)-(2), (Q)-(3), (R)-(4), (S)-(1).

• The equal appearing interval scale is Thurstone's method (1928).
• The social distance scale is Bogardus's (1925).
• Scalogram analysis is Guttman's cumulative scaling method.
• The semantic differential is from Osgood, Suci and Tannenbaum (1957).

Options A, B and D attribute the Thurstone or Bogardus scale to the wrong author.

Answer: D

The speed tests are (I) and (II) only.

A speed test is made of easy items, and the score depends on how many the person completes within a strict time limit. The digit-symbol (coding) test, in which symbols are written under digits as fast as possible, is the classic example. Kohs' block design test is also scored on time, with credit for completing each design quickly, so it is treated as a speeded test.

Raven's Advanced Progressive Matrices is a power test: its items increase in difficulty, and the score reflects the level of difficulty the person can reach rather than speed. Options including (III), or leaving out (I) or (II), are therefore wrong.

Answer: C

The item discrimination indices are (I) and (II) only.

Item discrimination shows how well an item separates high scorers from low scorers. When item scores are dichotomous (right or wrong), it is computed as a correlation between the item and the total or criterion score. The point-biserial correlation relates the dichotomous item to a continuous total score, and the phi coefficient relates the item to a dichotomised criterion (for example upper versus lower group). Both are standard discrimination indices.

Spearman's rho is a rank-order correlation between two sets of ranks, not used as an item discrimination index, so options including (III) are wrong.

Answer: B

Orthogonal rotation results in an identical factor structure and pattern matrix.

In factor analysis the pattern matrix holds the regression weights of variables on factors, and the structure matrix holds the correlations between variables and factors. When factors are rotated orthogonally, as in varimax, they stay uncorrelated, so each weight equals the corresponding correlation and the two matrices are the same.

Correlated factors come from oblique rotation. With orthogonal factors the factor correlation (phi) matrix is the identity matrix, not something else. Higher-order factor analysis needs correlated first-order factors, so it follows oblique, not orthogonal, rotation.

Answer: B

The item to prefer is the one with P = 0.92.

The difficulty index P of an item is the proportion of test-takers who answer it correctly. A high P means an easy item: P = 0.92 means 92% got it right. To reduce the overall difficulty of a test, you would choose items with high P values, which raise the proportion of correct answers.

P = 0.18 and P = 0.25 are hard items, answered correctly by fewer than a quarter of candidates, so they would make the test harder. P = 0.58 is moderate. Only 0.92 lowers the difficulty substantially.

Answer: A

Reliability is ascertained by (I) only, studying the association of the test with itself.

Reliability is the consistency of a test's scores. All the usual methods correlate the test with itself in some form: the same test given twice (test-retest), two halves of the test (split-half), or every item with every other item (internal consistency, Cronbach's alpha).

Correlating the test with a different test or an external criterion assesses validity, for example concurrent or convergent validity, not reliability. Parallel forms are constructed as equivalent versions of the same test, which is why they count as the test 'itself' rather than another test. So (II) is not a method of establishing reliability.

Answer: B

The Spearman-Brown correction corrects the effect of inadequate length of the test.

Reliability increases with the number of items. In split-half reliability the correlation is between two halves, each half the length of the full test, so it underestimates the full test's reliability. The Spearman-Brown formula corrects for this:

\[ r_{tt} = \frac{2 r_{hh}}{1 + r_{hh}} \]

More generally it predicts how reliability changes when a test is lengthened or shortened by any factor.

It does not deal with inadequate content (a validity issue), time limits, or heterogeneity of variance.

Answer: B

The item discrimination index is based on the passing percentage of respondents on an item from the upper group and lower group on a criterion.

Test-takers are ranked on the total score (or another criterion), and the top and bottom groups, often 27% each, are compared. The index is the proportion passing the item in the upper group minus the proportion passing in the lower group, \(D = p_{U} - p_{L}\). A good item is passed by many more high scorers than low scorers.

The overall difficulty of the test is a different statistic, and using only the upper or only the lower group cannot show discrimination, which is by definition a comparison between the two.

Answer: A

They are called characteristic roots, that is, eigenvalues.

In an unrotated factor pattern matrix, each column holds the loadings of all variables on one factor. The sum of the squared loadings in a column is that factor's eigenvalue (characteristic root), the amount of total variance it explains. Dividing by the number of variables gives the proportion of variance.

Communalities are sums of squared loadings across a row, the variance of one variable explained by all factors. Percentage of variance is derived from the eigenvalue, and the root mean square residual is a fit index, so neither is the column sum itself.