PSY201F

PSY201F - Term Test I - 12/10/00

Duration: 90 minutes

Part I. Multiple Choice (10 marks)

Instructions. For each of the following 10 questions, circle the letter (a-e) in front of the most correct option. Each question is worth one mark.

1. (day section) A left-skewed distribution of x values produces the mirror-image right-skewed distribution when x is transformed. What kind of transformation was used?

a) logarithmic

b) exponential

c) radical

d) linear *

e) non-linear

1. (evening section) A linear transformation is applied to the variable x in a sample. What is the new variance?

a) bs_old

b) b²s_old

c) bs²_old

d) b²s²_old*

e) none of the above

2. In bivariate least-squares regression, a tripling of the standard deviation of x where both the standard deviation of y and the slope stay the same would have what effect on the correlation coefficient?

a) triple it *

b) multiply it by 9

c) multiply it by

d) no effect

e) decrease it by an unknown degree

3. The correlation of x and y is .90 in each of two samples. When the two samples are combined, however, the correlation in the total sample is .10. The two samples have identical distributions of y. What does this suggest about their distributions of x?

a) approximately normal in one sample but non-normal in the other

b) non-normal in both

c) nothing

d) errors in the data

e) very different means *

4. A pollster draws a SRS of 20 electoral districts from all those possible in the province of Ontario. Within each district, she then draws a SRS of 100 households. This strategy is an example of:

a) blocking

b) percentile sampling

c) systematic sampling

d) stratified sampling

e) multi-stage sampling *

5. In a univariate distribution, Q₁ is 12.35, Q₂ is 40.23, and Q₃ is 90.45. The distribution is:

a) approximately normal

b) right-skewed *

c) left-skewed

d) probably bimodal

e) probably unimodal

6. The mean of the sampling distribution of is:

a) a biased estimator of p

b) an unbiased estimator of p *

c) equal to

d) an adjusted estimator of a

e) an adjusted estimator of b

7. An infectious disease is known to gradually destroy a particular region of the cortex. y, the total number of neurons lost at any point in time during the course of the disease, is equal to 1.5^x, where x is the number of days that the victim has been infected. When x is plotted against y, the pattern of association will appear as:

a) logarithmic (common log)

b) logarithmic (natural log)

c) upward curling *

d) downward curling

e) linear

8. Random assignment of individuals to experimental conditions helps increase:

a) external validity

b) internal validity *

c) representativeness

d) causal ambiguity

e) sampling validity

9. In a sample of 50 Alzheimer’s patients, severity of symptoms is regressed on acetylcholine (ACh) concentration in the brain. The slope of the least-squares regression line is found to be

-.30. When a single suspected outlier is eliminated, however, the slope doubles to -.60. This suggests that the eliminated individual was most clearly an outlier on:

a) ACh concentration *

b) severity of symptoms

c) both variables

d) neither variable

e) an unidentified lurking variable

10. For any normal population distribution, what percentage of the population falls between 1 and 2 standard deviations below the mean?

a) 47.5

b) 34.0

c) 13.5 *

d) 5.0

e) 2.5

______________________________________________________________________________

Part II. Short Answer (9 marks)

Instructions. For each of the following 2 questions, provide a legible, grammatical, and concise written response. The mark value of each question is indicated beside it.

1. (day section) Dr. Baddezine is a dermatologist who decides to test the effects of monosodium glutamate (MSG) on the skin sensitivity of adult Canadians. He invites a number of his patients to take part in the study and tests those who are willing to volunteer their time. He asks the first 40 participants to consume a large amount of MSG and tests their skin sensitivity a few hours later. In contrast, he tests the skin sensitivity of the next 40 participants right away, without given them anything to consume beforehand. He finds that participants in the MSG condition show higher sensitivity on average. Describe the validity problems of this study. (6 marks)

Internal: 1) lack of random assignment, made worse by running one entire condition after the other; 2) participants know which condition they are in, inviting differential expectations and demand characteristics; 3) the doctor also knows which condition participants are in, inviting experimenter effects and the possibility of measurement bias; 4) delay before measurement in the MSG condition but not in the no-MSG condition raises the possibility of time-related effects

External: 1) dermatology patients are probably not representative of the wider adult population; 2) patients who agree to participate in such a study when asked are probably even less representative.

1. (evening section) . Dr. N. Vallid is a clinical psychologist who suspects that confession of past sins reduces blood pressure in the general adult population. She places a newspaper ad offering payment for participation in a "blood pressure study." Those who respond are brought to the clinic where they are randomly assigned to either the confession or the no-confession condition. In both conditions, participants are asked if they feel a high degree of guilt over past actions. Those in the confession condition who answer no are immediately re-assigned to the no-confession condition. Those in the no-confession condition, in contrast, remain there regardless of their answer. The doctor then instructs participants in the confession condition to reveal the actions for which they feel guilty, whereas participants in the no-confession condition are instructed to merely think about such actions, if there happen to be any. After these instructions, but before participants are allowed to follow them, systolic and diastolic blood pressure are measured by the doctor. She measures them a second time after participants have talked or thought about their actions. The results reveal a greater drop in blood pressure for participants in the confession condition than for those in the no-confession condition. Describe the validity problems of this study. (6 marks)

Internal: 1) random assignment is undermined by re-assignment of participants who answer no in the confession condition; 2) participants know which condition they are in, inviting differential expectations and demand characteristics; this is made worse by the use of payment, which causes participants to feel obligated; 3) the doctor also knows which condition participants are in, inviting experimenter effects and the possibility of measurement bias; 4) different instructions in the two conditions may produce a difference in average blood pressure even before the "confession" takes place

External: 1) those who respond to an ad are probably not representative of the wider adult population; 2) those who respond to a specific ad describing a "blood pressure" study are probably even less representative.

2. Describe what one looks for in a scatterplot when describing the three aspects of any association between two variables. (3 marks)

Linearity or a specific expression of curvilinearity in the overall pattern of points gives the form of the association. The direction of association at any point in the overall pattern is reflected in the slope at that point of the straight or curved line used to summarize the pattern. The strength of association is reflected in the scatter of points around the line; the tighter the points are around the line, the stronger the association.

Part III. Computational (18 marks)

Instructions. For each of the following 2 questions, compute the required information. Remember that part marks can only be given where sequential calculations are shown. Please circle final answers for clarity. The mark value of each question is indicated beside it. Round all values to two decimal places unless the value is less than .01, in which case you should preserve the preceding zeros and round to two digits thereafter (e.g., .00627 . .0063, .0004124 . .00041). Finally, provide legible, grammatical, and concise written answers wherever required in this section.

1. Seventeen U of T undergraduate classes of equal size rated the overall effect over the past five years of Mike Harris’s "Common Sense Revolution" on higher education in Ontario. Ratings were made on a 1 ("very bad") to 10 ("very good") scale. Here are the average ratings for each class.

6.1, 3.4, 8.6, 5.3, 8.8, 2.2, 3.1, 7.5, 3.7, 3.8, 4.2, 2.5, 7.0, 7.6, 3.0, 3.6, 8.9

a) What are Q₁, Q₂, Q₃, and the IQR in this sample? (3 marks)

Rearrange: 2.2, 2.5, 3.0, 3.1, 3.4, 3.6, 3.7, 3.8, 4.2, 5.3, 6.1, 7.0, 7.5, 7.6, 8.6, 8.8, 8.9

Q₁= 3.25, Q₂= 4.2, Q₃= 7.55, IQR = 4.3

b) Are there any suspected outliers? Use the IQR-related rule to make this decision. Now construct a stemplot to display the distribution. What does the shape of the distribution, as shown in the stemplot, tell you about the appropriateness of a boxplot to display these data? (3 marks)

There are no suspected outliers according to the 1.5H IQR rule. The stemplot reveals a clearly non-normal (two-peaked) distribution. The sample appears somewhat polarized. A boxplot would disguise this important feature and is therefore inappropriate here.

c) As we move across the order of values, from smallest to largest, how many percentile points does each individual in the sample account for? (1 mark)

5.88

2. The banded mongoose (Mungos mungo) lives in large groups. Adult females often put themselves at risk for the benefit of the group by sounding an alarm in the presence of a nearby predator. A comparative psychologist suspects that the tendency to do so is inversely related to the ratio of adults to young in the group (higher ratios mean a higher proportion of adults in the group). The psychologist records the number of alarms made by adult females on a typical day in 12 different mongoose groups. Here are the results:

ratio 1.1 0.5 0.1 0.9 0.6 0.3 1.2 0.2 1.0 0.4 0.8 0.7

no. of alarms 10 26 27 19 25 27 04 27 15 26 22 24

a) Using your calculator=s statistical functions, determine the least-squares regression line that predicts number of alarms from adults:young ratio. Give the equation for the line. Again using your calculator=s statistical functions, compute the means and standard deviations for alarms and ratio, and give the value of r. (4 marks)

b) Calculate the residuals for all 12 groups and display them in a residual plot. Describe the pattern of residuals and decide whether the use of linear regression was appropriate here. Why or why not? (4 marks)

12.53 23.82 31.35 16.30 21.94 27.58 10.65 29.47 14.42 25.70 18.18 20.06

-2.53 2.18 -4.35 2.70 3.06 -0.58 -6.65 -2.47 0.58 0.30 3.82 3.94

When plotted against x, the residuals form a systematic, curvilinear pattern. There is over-prediction followed by under-prediction and then over-prediction again. This pattern points to a clearly curvilinear association in the scatterplot, indicating that a linear equation was not an appropriate summary.

c) What is the value for SS_Reg in the above regression? (2 marks)

d) What percentage of the variance in alarm calls was accounted for by differences in adult:young ratio across groups? (1 mark)

.79

Formulae