Statistical Methods for Psychology

58 Chapter 2 Describing and Exploring Data

c. calculate the square root of the answer for part (b).

d. what are the units of measurement for parts (b) and (c)?

2.18 Using the data from Exercises 2.14 and 2.15, record the two data sets side by side in

columns, name the columns Xand Y, and treat the data as paired.

a. Calculate.

b. Calculate

c. Calculate (You will come across these calculations again in Chapter 9.)

2.19 Use the data from Exercises 2.14 and 2.15 to show that

a.

b.

c. (where C represents any arbitrary constant)

d.

2.20 In Table 2.1 (p. 17), the reaction time data are broken down separately by the number of dig-

its in the comparison stimulus. Create three stem-and-leaf displays, one for each set of data,

and place them side-by-side. (Ignore the distinction between positive and negative in-

stances.) What kinds of differences do you see among the reaction times under the three

conditions?

2.21 Sternberg ran his original study (the one that is replicated in Table 2.1) to investigate whether

people process information simultaneously or sequentially. He reasoned that if they process in-

formation simultaneously, they would compare the test stimulus against all digits in the compar-

ison stimulus at the same time, and the time to decide whether a digit was part of the comparison

set would not depend on how many digits were in the comparison. If people process information

sequentially, the time to come to a decision would increase with the number of digits in the com-

parison. Which hypothesis do you think the figures you drew in Exercise 2.20 support?

2.22 In addition to comparing the three distributions of reaction times, as in Exercise 2.23,

how else could you use the data from Table 2.1 to investigate how people process

information?

2.23 One frequent assumption in statistical analyses is that observations are independent of one

another. (Knowing one response tells you nothing about the magnitude of another response.)

How would you characterize the reaction time data in Table 2.1, just based on what you

know about how they were collected? (A lack of independence would not invalidate any-

thing we have done with these data in this chapter.)

2.24 The following figure is adapted from a paper by Cohen, Kaplan, Cunnick, Manuck, and

Rabin (1992), which examined the immune response of nonhuman primates raised in stable

and unstable social groups. In each group, animals were classed as high or low in affilia-

tion, measured by the amount of time they spent in close physical proximity to other ani-

mals. Higher scores on the immunity measure represent greater immunity to disease. How

would you interpret these results?

Stable

High affiliation

Stability

Immunity

5.10

4.80

5.05

5.00

4.95

4.90

4.85

Unstable

Low affiliation

gX^2 ±(gX)^2.

gCX=CgX.

gXY±gXgY.

g(X 1 Y)=gX 1 gY.

gXY 2

©X©Y

N

N 21

gXgY.

gXY