Statistical Methods for Psychology

Hays (1981) recommends reporting Wbut converting to for interpretation. Indeed, it

is hard to disagree with that recommendation, since no intuitive meaning attaches to W

itself. Wdoes have the advantage of being bounded by zero and one, whereas does not,

but it is difficult to attach much practical meaning to the statement that the variance of col-

umn totals is 80.7% of the maximum possible variance. Whatever its faults, seems

preferable.

A test on the null hypothesis that there is no agreement among judges is possible under

certain conditions. If k$7, the quantity

is approximately distributed as on N 2 1 degrees of freedom. Such a test is seldom used,

however, because Wis usually calculated in those situations in which we seek a level of

agreement substantially above the minimum level required for significance, and we rarely

have seven or more judges.

x^2

x^2 (N 2 1)=k(N 2 1)W

rs

rs

rs

Exercises 311

Key Terms

Correlational measures (Introduction)

Measures of association (Introduction)

Validity (Introduction)

Dichotomy (10.1)

Point-biserial coefficient ( ) (10.1)

f(phi) coefficient (10.1)

Biserial correlation coefficient ( ) (10.2)

Tetrachoric correlation coefficient ( )

(10.2)

Ranking (10.3)

Spearman’s correlation coefficient for

Ranked data (rs) (10.3)

Spearman’s rho (10.3)

Kendall’st(10.3)

Kendall’s coefficient of

concordance (W) (10.5)

rt

rb

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Exercises

10.1 Some people think that they do their best work in the morning, whereas others claim that

they do their best work at night. We have dichotomized 20 office workers into morning or

evening people (0 5 morning, 1 5 evening) and have obtained independent estimates of

the quality of work they produced on some specified morning. The ratings were based on

a 100-point scale and appear below.

Peak time of day: 0000000000

Performance rating: 65 80 55 60 55 70 60 70 55 70

Peak time of day: 0001111111

Performance rating: 40 70 50 40 60 50 40 50 40 60

a. Plot these data and fit a regression line.

b. Calculate and test it for significance.

c. Interpret the results.

10.2 Because of a fortunate change in work schedules, we were able to reevaluate the subjects

referred to in Exercise 10.1 for performance on the same tasks in the evening. The data are

given below.

Peak time of day: 000000000 0

Performance rating: 40 60 40 50 30 40 50 50 20 30

Peak time of day: 000111111 1

Performance rating: 40 50 30 30 50 50 40 50 40 60

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