Download Document

Exam 1 for Psychology 138 Fall 2008
1. Complete this analogy: As sample is to statistic, population is to _________________
2. What kind of measurement scale requires that you use the mode as the measure of central
tendency?
3. Suppose there is a population of 1000 scores. I randomly draw many samples of 100
scores each from the population. Which measure of central tendency is likely to be the
most stable (i.e., the closest to being the same in all the samples)?
4. If the mean is much lower than the median, what can be concluded about the shape of the
distribution?
5. On which of these statistics is an outlier going to have the least influence? Pick 1.
mean, median, range, standard deviation, correlation
6. Just by looking at the variables depicted in the scatterplot below, make a good estimate of
the correlation between them. (Precision is not needed here. Just make the estimate
reasonable. Your answer should be just a single number.)
Correlation between X and Z
3
2
1
Variable Z
0
-1
-2
-3
-3
-2
-1
0
1
2
3
Variable X
7. Sample A has a large standard deviation and Sample B has a small one. Both samples
have the same mean. For which sample is the mean a better summary of the data?
8. In a distribution of z-scores, the mean = _____ and the standard deviation = ______.
9. Create a list of 7 numbers of your choosing that has a bimodal distribution.
10. Suppose that it has been shown conclusively that family size (i.e., # of siblings) is
negatively correlated with IQ. Does this mean that people from large families are more
likely to score lower on IQ tests than people from small families? Simply answer yes or
no.
11. In the regression equation (Ŷ = b0 + b1X), what does b0 represent?
12. List all of the following numbers that cannot be correlation coefficients:
-1, 0, .5, 1, 2
13. Complete: In a regression of X predicting Y, an error (or residual) is the difference
between the observed value of Y and ___________.
14. Draw a picture of a histogram of a negatively skewed variable.
15. How are ordinal and nominal scales different?
16. How are interval and ordinal scales different?
17. How are interval and ratio scales different?
18. Under what circumstances would it be better to use the median as a measure of central
tendency of a ratio scale instead of the mean?
19. In what ways is the standard deviation better than the range as a measure of variability?
20. If the correlation between desire for intimacy and the number of divorces a person has
had is 0, what can we conclude about the nature of the statistical relationship between
these 2 variables?
21. Conceptually, what does a single z-score measure?
22. Explain what it means that a regression equation produces the “best fitting line.”
23. A researcher surveyed recent Oscar winners about their general life satisfaction. He
correlates life satisfaction with each actor’s known earnings for the year. Because the
correlation was near 0, researcher concludes that an actor’s income is unrelated to the
actor’s happiness. Assume that the measures of life satisfaction and income are perfectly
accurate and valid. Explain why the correlation of zero may not accurately represent the
true statistical relationship between income and happiness in the general population of
actors.
24. Conceptually, what does the standard error of the estimate measure?
25. Suppose that variable A correlates with variable B. Explain why variable A does not
necessarily cause variable B.
Exam 1 for Psychology 138-Key
1. Complete this analogy: As sample is to statistic, population is to _________________
Parameter
2. What kind of measurement scale requires that you use the mode as the measure of central
tendency?
Nominal
3. Suppose there is a population of 1000 scores. I randomly draw many samples of 100
scores each from the population. Which measure of central tendency is likely to be the
most stable (i.e., the closest to being the same in all the samples)?
Mean
4. If the mean is much lower than the median, what can be concluded about the shape of the
distribution?
Two good answers:
It is negatively skewed.
There are extreme outliers on the low end of the scale.
5. On which of these statistics is an outlier going to have the least influence? Pick 1.
mean, median, range, standard deviation, correlation
Median
6. Just by looking at the variables depicted in the scatterplot below, make a good estimate of
the correlation between them. (Precision is not needed here. Just make the estimate
reasonable. Your answer should be just a single number.)
Correlation between X and Z
3
2
1
Variable Z
0
-1
-2
-3
-3
-2
-1
0
Variable X
1
2
3
Any number between 0 and -1 but not 0 and not -1.
7. Sample A has a large standard deviation and Sample B has a small one. Both samples
have the same mean. For which sample is the mean a better summary of the data?
Sample B
8. In a distribution of z-scores, the mean = __0__ and the standard deviation = __1__.
9. Create a list of 7 numbers of your choosing that has a bimodal distribution.
Infinite number of correct answers. Here are two of them:
2, 2, 3, 4, 5, 5, 6
22, 22, 22, 24, 24, 24, 27
10. Suppose that it has been shown conclusively that family size (i.e., # of siblings) is
negatively correlated with IQ. Does this mean that people from large families are more
likely to score lower on IQ tests than people from small families? Simply answer yes or
no.
Yes.
11. In the regression equation (Ŷ = b0 + b1X), what does b0 represent?
Intercept
12. List all of the following numbers that cannot be correlation coefficients:
-1, 0, .5, 1, 2
2
13. Complete: In a regression of X predicting Y, an error (or residual) is the difference
between the observed value of Y and ___________.
14. 4 points for either answer
1) Y-hat (Ŷ)
2) The predicted value of Y
15. Draw a picture of a histogram of a negatively skewed variable.
Infinite number of correct answers. Here is one of them.
16. How are ordinal and nominal scales different?
Ordinal scales have ordered categories, nominal scales have unordered categories.
17. How are interval and ordinal scales different?
Interval scales have ordered categories in which the numerical distance between
categories is equal (or the distance between numbers have a consistent meaning). The
distance between categories in ordinal scales has no meaning.
18. How are interval and ratio scales different?
A ratio scale has an absolute zero (a zero that means that there is none of the thing that is
being measured). If an interval scale has a zero, the zero does not mean that there is no
quantity of the thing being measured.
19. Under what circumstances would it be better to use the median as a measure of central
tendency of a ratio scale instead of the mean?
Two good answers:
When the data are highly skewed.
When there are extreme outliers.
20. In what ways is the standard deviation better than the range as a measure of variability?
1. It takes into account of all of the scores in the distribution.
2. It is less sensitive to outliers.
21. If the correlation between desire for intimacy and the number of divorces a person has
had is 0, what can we conclude about the nature of the statistical relationship between
these 2 variables?
There is no linear relationship between the variables.
22. Conceptually, what does a single z-score measure?
A z-score is a standard score that indicates how many standard deviations a raw score
deviates from the mean.
23. Explain what it means that a regression equation produces the “best fitting line.”
24. A researcher surveyed recent Oscar winners about their general life satisfaction. He
correlates life satisfaction with each actor’s known earnings for the year. Because the
correlation was near 0, researcher concludes that an actor’s income is unrelated to the
actor’s happiness. Assume that the measures of life satisfaction and income are perfectly
accurate and valid. Explain why the correlation of zero may not accurately represent the
true statistical relationship between income and happiness in the general population of
actors.
Many good answers. Here are some:
1) Oscar winners usually earn a lot more money than most actors and correlations are
sensitive to outliers.
2) Oscar winners have a restricted range of incomes (and possibly a restricted range in
happiness) and range restrictions typically decrease the true correlation.
3) You cannot generalize conclusions to ranges outside of the ranges studied.
25. Conceptually, what does the standard error of the estimate measure?
Two good answers:
1) The typical distance between the observed Y values and the regression line
2) The standard deviation of the error scores (or residuals).
26. Suppose that variable A correlates with variable B. Explain why variable A does not
necessarily cause variable B.
A might not cause B because
1) B might cause A. For example, taking painkillers is correlated with having headaches.
It is possible that taking painkillers cause headaches but more likely that headaches
cause people to take painkillers.
2) Variable C causes both B and A but B and A have no influence on each other. For
example, having a lot of money might be the cause of owning expensive cars and
eating fancy cheeses. Therefore, many people who have expensive cars might also eat
fancy cheese. However, owning expensive cars does not cause people to eat fancy
cheeses.