Statistical Methods for Psychology

are discussed in many more specialized texts. In general, smoothing takes place by the averaging of Yvalues close to the target ...

with your prediction would be the standard deviation of Y(i.e., ), since your prediction is the mean and deals with deviations a ...

conditional distributionof Ybecause it is the distribution of Yscores for those cases that meet a certain condition with respect ...

For large samples the fraction (N 2 1) (N 2 2) is essentially 1, and we can thus write the equation as it is often found in stat ...

In this equation, SSY, which you know to be equal to , is the sum of squares of Y and represents the totals of The part of the ...

life expectancy is attributable to variability in smoking behavior. In other words, we want a measure that represents As we have ...

The choice between r^2 and PIP is really dependent on how you wish to measure error. When we focus on r^2 we are focusing on mea ...

display boxplots of lnSymptoms for each quintile of the Stress variable. This plot is shown in Figure 9.4b. Given the fact that ...

the arrays of X—what we now know as conditional normality of Y. For the regression model, there is no assumption of normality of ...

Then Then The confidence interval is 4.041 to 4.731, and the probability is .95 that an interval com- puted in this way will inc ...

line itself, and you can see by inspection that the interval at a value of X 5 10 is smaller than the confidence interval we est ...

Section 9.10 A Computer Example Showing the Role of Test-Taking Skills 269 Mean 598.57 46.21 SAT Verbal Score Test Score Std. De ...

270 Chapter 9 Correlation and Regression SAT Verbal Score Test Score SAT Verbal Score Test Score SAT Verbal Score Test Score Pea ...

always capitalize that symbol. One thing to note is that Rhere is calculated as the square root of R^2 , and as such it will alw ...

272 Chapter 9 Correlation and Regression A legitimate t test can be formed from the ratio which is distributed as t on N 2 2 df. ...

It can be shown that bis normally distributed about with a standard error approxi- mated by^15 Thus, if we wish to test the hypo ...

in life expectancy between males and females. Suppose further that we obtained the following data: Males Females b 2 0.40 2 0.20 ...

Given , we can now solve for t: on 198 df. Since , we would fail to reject and would therefore con- clude that we have no reason ...

276 Chapter 9 Correlation and Regression Males Females r .50 .40 r .549 .424 N 53 53 Since is less than , we fail to reject and ...

therefore and thus For our stress example, r 5 .529 ( 5 .590) and N 5 107, so the 95% confidence limits are Converting from r ba ...