Experimental Psyc Test 3 Chapter 7

correlation coefficient (142)

an index of the direction and magnitude of the relationship between two variables; the value ranges between -1 and 1

negative correlation (142)

an inverse relationship between two variables such that participants with high scores on one variable tend to have low scores on the other variable, and vice versa

9. Why may we not interpret or discuss a correlation coefficient that is not statistically significant?

because there is no correlation between the variables.

12. How do we know whether a particular score is an outlier?

Many researchers consider a score to be an outlier if it is farther than 3 standard deviations from the mean of the data

outlier (152)

an extreme score; typically scores that fall farther than 3 standard deviations from the mean are considered outliers

correlational research (141)

research designed to examine the nature of the relationship between two measured variables

coefficient of determination (144)

the square of the correlation coefficient; indicates the proportion of variance in one variable that can be accounted for by the other variable

18. What is a dichotomous variable? What correlations are used for dichotomous variables?

(A dichotomous variable is measured on a nominal scale but has only two levels) When both variables being correlated are dichotomous, a phi coefficient correlation is used; if only one vari- able is dichotomous (and the other is on an interval or ratio scale), a point biserial correlation is used.

2. Which is larger—a correlation of +.45 or a correlation of -.60? Explain.

-.6 Ignor the sign, look at the relationship between the variables.

15. Why can't we infer causality from correlation?

. Often people will conclude that because two phenomena are related, they must be causally related in some way. This is not neces- sarily so; one variable can be strongly related to another yet not cause it. The thickness of caterpil- lars' coats may correlate highly with the severity of winter weather, but we cannot conclude that caterpil- lars cause blizzards, ice storms, and freezing temper- atures. Even if two variables are perfectly correlated (r = 1.00 or 1.00), we cannot infer that one of the variables causes the other.

7. What does a coefficient of determination of .40 indicate

16% of variance is systematic. square it.

1. The correlation between self-esteem and shyness is -.50. Interpret this correlation.

As values of one variable increase, values of the other variable decrease. SO, there is an inverse relationship between self esteem and shyness

13. Do outliers increase or decrease the magnitude of correlation coefficients?

On-line outliers tend to artificially inflate correlation coefficients, making them larger than is warranted by the rest of the data. Figure 7.6(b) shows two off-line outliers. Off-line outliers tend to artificially deflate the value of r (correlation coefficients). The presence of even a few off-line outliers will cause r to be smaller than indicated by most of the data.

14. What impact does reliability have on correlation?

Unreliable measures attenuate the magnitude of cor- relation coefficients. All other things being equal, the less reliable our measures, the lower the correlation coefficients we will obtain.

17. When is the Spearman rank-order correlation used?

When one or both variables are measured on an ordinal scale—in which the numbers reflect the rank ordering of participants on some attribute—the Spearman rank-order correlation coefficient is used. For example, suppose that we want to know how well teachers can judge the intelligence of their students. We ask a teacher to rank the 30 students in the class from 1 to 30 in terms of their general intel- ligence. Then we obtain students' IQ scores on a standardized intelligence test. Because the teacher's judgments are on an ordinal scale of measurement, we calculate a Spearman rank-order correlation coefficient to examine the correlation between the teacher's rankings and the student's real IQ scores.

spurious correlation (156)

a correlation between two variables that is not due to any direct relationship between them but rather to their relation to other variables

Spearman rank-order correlation (158)

a correlation coefficient calculated on variables that are measured on an ordinal scale

perfect correlation (143)

a correlation of -1.00 or 1.00, indicating that two variables are so closely related that one can be perfectly predicted from the other

positive correlation (142)

a direct relationship between two variables such that participants with high scores on one variable tend also to have high scores on the other variable, whereas low scorers on one variable tend also to score low on the other

statistical significance (149)

a finding that is very unlikely to be due to error variance

scatter plot (142)

a graphical representation of participants' scores on two variables; the values of one variable are plotted on the x-axis and those on the other variable are plotted on the y-axis

nondirectional hypothesis

a prediction that does not express the direction of a hypothesized effect - for example, which of two means will be larger

directional hypothesis

a prediction that explicitly states the direction of a hypothesized effect; for example, a prediction of which two means will be larger

restricted range (151)

a set of data in which participants' scores are confined to a narrow range of the possible scores

11. What is a restricted range, and what effect does it have on correlation coefficients? How would you detect and correct a restricted range?

a set of data in which participants' scores are confined to a narrow range of the possible scores. It can misrepresent a correlation coefficient. Can be detected by observing the raw data.

phi coefficient (158)

a statistic that expresses the correlation between two dichotomous variables

3. Tell whether each of the following relationships reflects a positive or a negative correlation: a. the amount of stress in people's lives and the number of colds they get in the winter b. the amount of time that people spend suntanning and a dermatological index of skin damage due to ultraviolet rays c. happiness and suicidal thoughts d. blood pressure and a person's general level of hostility e. the number of times that a rat has run a maze and the time it takes to run it again

a. positive. direct relationship. b. positive. direct relationship. c. negatively. inverse relationship. d. positive. direct relationship. e. negative. inverse relationship.

5. The correlation between self-esteem and shyness is -.50, and the correlation between self-conscious- ness and shyness is .25. How much stronger is the first relationship than the second? (Be careful on this one.)

correlation is not on a ratio scale. to to compare numbers they must first be squared. SELF ESTEEM VS SHYNESS- -.5 squared= .25 SENF CONCIOUSNESS VS SHYNESS- .25squared= .0625

10. Using Table 7.3 ("Critical Values of r"), indicate whether each of the following correlation coefficients is statistically significant: a. r = .05, n = 300, directional hypothesis b. r = .00, n = 1,000, nondirectional hypothesis c. r = .26, n = 50, nondirectional hypothesis d. r = .15, n = 100, directional hypothesis e. r = .42, n = 112, directional hypothesis f. r = .25, n = 60, nondirectional hypothesis

r = .05, n = 300, directional hypothesis- not sig r = .00, n = 1,000, nondirectional hypothesis- not sig r = .26, n = 50, nondirectional hypothesis - not sig r = .15, n = 100, directional hypothesis- not sig r = .42, n = 112, directional hypothesis- sig r = .25, n = 60, nondirectional hypothesis- sig

point-biserial correlation (158)

the correlation between a dichotomous and a continuous variable

partial correlation (157)

the correlation between two variables with the influence of one or more other variables removed

Pearson correlation coefficient (142)

the most commonly used measure of correlation

16. How can partial correlation help researchers explore possible causal relationships among correlated variables?

they may be able to conclude that a particular causal explanation of the relationship between the variables is more likely to be correct than are other causal explanations, and they can certainly use correlational data to conclude that two variables are not causally related. Partial correlation allows researchers to examine a third variable's possible influence on the correlation between two other variables.

4. Why do researchers often examine scatter plots of their data when doing correlational research?

to be sure that the variables are not curvilinear related. Example: arousal. perform perform best when their arousal is very low or very high.

6. Why do researchers calculate the coefficient of determination?

to determine how much variance is systematic (how much one variability in one variable can be attributed to the other. )