PSY 555 Homework 15

Chapter 9: #9,12,17,23,24,25

9.9(a).   Cerebral hemorrhage in low-birthweight infants and cognitive deficit at age 5:

Power calculation:

d=.20     N=25      r=.20

Power=.17

The power of the test is approximately .17.

9.9(b).   Power of .80    r=.20

2.80=.20

197 infants would be required to have a power of .80.

9.12.

The 95% confidence limits on b* are -.0019 and .1397.

9.17.

For several different values of X (i.e., 0,10,15,22,30,55,80), calculate the corresponding predicted values of Y and s'Y.X and plot the results.

Y(30)=97.453

Y(22)=91.1882

Y(15)=85.7065

Y(10)=81.791

Y(80)=136.539

Y(0)=73.891

Y(55)=117.0305

s'Y.X(30)=17.632

s'Y.X(22)=17.597

s'Y.X(15)=17.617

s'Y.X(10)=17.66

s'Y.X(80)=19.169

s'Y.X(0)=17.816

s'Y.X(55)=18.128

CI Y(30)=62.471 to 132.435

CI Y(22)=56.276 to 126.100

CI Y(15)=50.754 to 120.659

CI Y(10)=46.754 to 116.828

CI Y(80)=98.508 to 174.570

CI Y(0)=38.544 to 109.238

CI Y(55)=81.065 to 152.996

9.23(a).  r1=.68    N=17

r2=.53    N=28

z=.716not significant, p=.4716

The relations were not significantly different, z=.716, p=.4716.

9.23(b).  There is no support, based on this data, for the hypothesis that reading the passage affects the relation between SAT verbal score and the 100-item test performance.

9.24.     r1=.88    N=52

r2=.72    N=74

These correlations are significantly different, z=2.52, p<.0018.

9.25.     The significance achieved by the second set of correlations is probably due to the larger N values (74 and 52), although it could possibly be due to the fact that the correlations originally were higher in the second problem (so these values are more likely to differ b/c smaller differences will be significant).  The higher sample sizes, however, are most likely responsible for the difference in terms of significant findings between the two problems.

1.             When you restrict the range of the data points you examine, the correlation may be altered from what it would have been if the range was not restricted.  The altered correlation may be either larger or smaller than t unrestricted range correlation, although generally the altered correlation will be smaller.  An example would be standardized test scores (e.g., SAT, GRE) that are used to predict college performance.  While the relation between such measures is assumed to be high, the correlations are generally moderate in size (e.x., r=.65).  This lower correlation (at least lower than would be expected) is due to the fact that only a portion of the people who take these tests get into college (generally, the people with better scores).  So, the correlation between SAT and college performance, as measured by GPA, is based on a restricted range of data and is, in all likelihood, smaller than the correlation that would be obtained if all people who took the SAT went to college and all this data was examined.

Heterogeneous subsamples pose a problem for correlations.  For example, many relations between variables can be obscured by the presence of a third variable (e.g., gender).  Many relations are not obvious when both genders are examined.  However, when genders are examined separately, these relations are evident.  So, anytime data is collected from separate groups (or data sources), researchers should be cautious when examining relations for the aggregate data.  It probably would be more prudent to examine the desired relation for each group separately.

2(a).     r=.53

r=.42

H0=There is no significant difference between correlations obtained in the two studies (r1=r2).

H1=There is a significant difference between the correlations obtained in the two studies (r1r2).

2(b).     The correlation found in the first study (r=.53) is significantly greater than the correlation found in subsequent study (r=.42), z=2.5, p<.0124.