Study Guide for Exam 1 in Psychology 138

 

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1. What is a nominal scale?
2. What is an ordinal scale?
3. What is an interval scale?
4. What feature distinguishes a ratio scale from an interval scale?
5. What is a population?
6. What is a sample?
7. What do we call descriptive characteristics of a population?
8. What do we call descriptive characteristics of a sample?
9. Define "Central Tendency"
10. Define mean.
11. Define mode.
12. Define median.
13. What is the only measure of central tendency that can be used for a nominal scale?
14. What types of central tendency can be used for an ordinal scale?
15. For which types of scales can the mean be used?
16. What does bimodal mean?
17. In a positively skewed distribution, which is higher, the mean or the median?
18. What is the best measure of central tendency for a skewed distribution?
19. Why is the mean a poor measure of central tendency for a skewed distribution?
20. If many samples are selected at random from the same population, which measure of central tendency is likely to be the most stable from sample to sample?
21. If many samples are selected at random from the same population, which measure of central tendency is likely to be the least stable from sample to sample?
22. Define variability.
23. Define outlier.
24. Name 3 reasons why measures of variability are important.
25. Define range
26. Name 2 disadvantages of using the range as a measure of variability.
27. Define variance.
28. Why is the formula for variance different depending on whether the distribution is a population or a sample?
29. Define standard deviation.
30. What is the relationship between the standard deviation and variance?
31. Name 2 advantages of using the standard deviation instead of the range as a measure of variability.
32. Define z-score
33. What is the mean and standard deviation of a set of z-scores?
34. Define correlation coefficient
35. A professor mentions in lecture that income and vocabulary ability have a correlation coefficient of 3.2. What is the proper thing to do?
36. If the correlation between achievement motivation and actual income earned is 0, what can we conclude about the relationship between these 2 variables?
37. If violent behavior and anxiety are negatively correlated, are highly violent people more likely to be anxious than less violent people?
38. If income and happiness are positively correlated, describe 3 possible patterns of how income and happiness are causally related.
39. If the correlation between variables X and Y is .45, what is the correlation between Y and X? 
40. Pretend that a researcher finds that the correlation between height and number of baskets per game for NBA starting players is very low. The researcher announces that height confers little advantage in the sport of basketball. Assume that the researcher's conclusion is not correct. Why might the researcher have obtained such a low correlation?
41. A researcher found that, in a sample of children and teenagers, vocabulary knowledge is highly correlated with age. The researcher concludes that because vocabulary is correlated with age, elderly people must have the best vocabulary. What is wrong with this conclusion?
42. A researcher found that in her small sample of 10 people, the 2 variables that she hypothesized would correlate, were not correlated at all. She decides to include 1 more person in the sample. Now, with 11 people, the 2 variables were highly correlated. Why should this researcher not trust her results?
43. Define regression
44. In the regression equation (Y = b0 + b1X), what does b1 represent?
45. In the regression equation (Y = b0 + b1X), what does b0 represent?
46. In regression, for any particular value of X, what do we call the difference between Y and the predicted value of Y?
47. What do we call the typical distance between the observed Y values and the regression line?
48. If IQ explains 36% of the variance in Academic Achievement, what is the correlation between IQ and Academic Achievement? (Assume that the correlation is positive.)
49. If the correlation between the personality trait of psychopathy (i.e., gross violations of the basic rights of others coupled with the inability to feel remorse) and anxiety is -0.35. What percentage of the variance in psychopathy is explained by anxiety?
50. With an IQ of 120, you were probably one of the smartest people in your high school. The mean IQ in your high school was 90 and the standard deviation was 10. What percentage of people had the same or lower IQ as you did?
51. Then you went to a selective university where the mean IQ was 115 and the standard deviation was 13. What percentage of people at your university had your IQ or above?
52. Now you go to graduate school where the mean IQ is 130 and the standard deviation is 8.What percentage of the graduate students has your IQ or lower?
53. Consider the following scores for X and Y

X         Y
2          4
5          20
6          12
12        20
10        14 

Calculate the correlation between X and Y.

54. Using the data above, calculate the slope of the regression line.
55. Using the data above, calculate the Y-intercept of the regression line.
56. Using the regression equation from above, what would you estimate Y to be if X equaled 9?
57. Consider the following population of scores: 4 1 12 -5 -10 22
Calculate the standard deviation.
58. Consider the following sample of scores: 1 3 5 6 5
Calculate the estimated variance of the population from which this sample was selected.
59. In the following distribution, what is the mode? 5 45 45 88 109
60. In the following distribution, what is the median? 1 2 3 1000000 1000001
61. In the following distribution, what is the median? 1 2 3 7 20000 2000012121
62. In the following distribution, what is the mean? 1 2 4 5
63. What is the range of this distribution? 4 6 5 7 9 25 -9
64. Which of the following is the strongest correlation? 0.5, 0.09, -0.3, 0, 0.7, -0.8, 0.29

Answers

Note: These answers need not be memorized word-for-word. You do, however, need to define the terms clearly and precisely.

1. What is a nominal scale?
            A nominal scale is a set of categories that have no numerical order.        

2. What is an ordinal scale?
            An ordinal scale is a set of categories that have a numerical order (i.e., the categories can be ranked) but the distance between categories is not equal.

3. What is an interval scale?
            An interval scale is a set of ordered categories like an ordinal scale with the additional requirement that the numerical distance between categories is equal.

4. What feature distinguishes a ratio scale from an interval scale?
            A ratio scale has an absolute zero (i.e., the point at which there is none of the quantity being measured).

5. What is a population?
            The entire set of participants (or objects) that are of interest to the research question.

6. What is a sample?
            A subset of individuals intended to represent a population.

7. What do we call descriptive characteristics of a population?
            Parameters
 
8. What do we call descriptive characteristics of a sample?
            Statistics

9. Define Central Tendency
            Central Tendency is a statistical measure that identifies a single score as a representative for an entire distribution or set of data. 

10. Define "mean."
The mean is the average score in a distribution. 

11. Define "mode."
The mode is the most frequently occurring score in a distribution. 

12. Define "median."
The median is the midpoint of the distribution.
Another good answer: The score that half of the scores in the distribution are above and half are below

13. What is the only measure of central tendency that can be used for a nominal scale?
Mode

14. What types of central tendency can be used for an ordinal scale?
Mode and Median 

15. For which types of scales can the mean be used?
Interval and Ratio

16. What does bimodal mean?
The distribution has 2 modes.

17. In a positively skewed distribution, which is higher, the mean or the median?
The mean (NOTE: The mean is always closer than the median to the tail of a skewed distribution.)

18. What is the best measure of central tendency for a skewed distribution?
The median 

19. Why is the mean a poor measure of central tendency for a skewed distribution?
A skewed distribution has outliers in the tail. Outliers can make the mean unrepresentative of the distribution as a whole.

20. If many samples are selected at random from the same population, which measure of central tendency is likely to be the most stable from sample to sample?
The mean 

21. If many samples are selected at random from the same population, which measure of central tendency is likely to be the least stable from sample to sample?
The mode 

22. Define variability.
Variability is a measure of the degree to which scores in a distribution are spread out or clustered together. 

23. Define outlier.
Outliers are extreme scores in a distribution.

24. Name 3 reasons why measures of variability are important.

Here are good answers:

1.They help us identify outliers.
2.They tell us how well the measure of central tendency summarizes the entire distribution.
3. They are used to compute other statistics.
4.They can be theoretically important in and of themselves.

25. Define range
The range is the difference between the highest score and the lowest score in the distribution.


26. Name 2 disadvantages of using the range as a measure of variability.

1.It does not take into account the variability of all of the scores in the distribution.
2.It is extremely sensitive to outliers.

27. Define variance.
Variance is the mean squared deviation from the mean of the distribution.

28. Why is the formula for variance different depending on whether the distribution is a population or a sample?
Using the same formula would mean that the sample variance would underestimate the population variance. The slightly different formula corrects the underestimation.

29. Define standard deviation.
The standard deviation is the typical distance of a set of scores from their mean. 

30. What is the relationship between the standard deviation and variance?
The standard deviation is the square root of the variance.
Another answer: The variance is the standard deviation squared. 

31. Name 2 advantages of using the standard deviation instead of the range as a measure of variability.
1. All of the scores in the distribution are used to calculate it.
2. It is less sensitive to outliers. (NOTE: The standard deviation is still sensitive to outliers, just not as much as the range

32. Define z-score
A z-score is a standard score that indicates how many standard deviations a raw score deviates from the mean. 

33. What is the mean and standard deviation of a set of z-scores?
The mean is 0 and the standard deviation is 1.  

34. Define correlation coefficient
The correlation coefficient is a statistic used to measure the linear relationship between 2 variables. (NOTE: A fully correct answer would have to include the word "linear.")

35. A professor mentions in lecture that income and vocabulary ability have a correlation coefficient of 3.2. What is the proper thing to do?
Stand up and denounce the professor as a fraud. Shout as loud as you can, "You FOOL! Don't you know that the correlation coefficient has a range of -1 to 1 and that values outside that range are IMPOSSIBLE?!!!!"
Okay, maybe that's a bit dramatic. Maybe just inform the professor later that there must be some mistake because correlations can only range from -1 to 1.

36. If the correlation between achievement motivation and actual income earned is 0, what can we conclude about the relationship between these 2 variables?
They do not have a linear relationship. 

37. If violent behavior and anxiety are negatively correlated, are highly violent people more likely to be anxious than less violent people?
No. 

38. If income and happiness are positively correlated, describe 3 possible patterns of how income and happiness are causally related. 
1.Higher income causes people to be happier.
2.Increased happiness causes people to earn more money.
3.Another variable causes both higher income and increased happiness.

39. If the correlation between variables X and Y is .45, what is the correlation between Y and X?
.45

 
40. Pretend that a researcher finds that the correlation between height and number of baskets per game for NBA starting players is very low. The researcher announces that height confers little advantage in the sport of basketball. Assume that the researcher's conclusion is not correct. Why might the researcher have obtained such a low correlation?
Any time there is a restriction of range in 1 or both variables, the correlation might be misleading. In this case, almost all players are in the NBA are very tall. If the NBA included very short players, the correlation would probably be much higher.

41. A researcher found that, in a sample of children and teenagers, vocabulary knowledge is highly correlated with age. The researcher concludes that because vocabulary is correlated with age, elderly people must have the best vocabulary. What is wrong with this conclusion?
It is improper to generalize a conclusion beyond the ranges that were sampled (e.g., Just because age and vocabulary are correlated in teenagers does not necessarily mean that they are correlated at other age ranges.). 

42. A researcher found that in her small sample of 10 people, the 2 variables that she hypothesized would correlate, were not correlated at all. She decides to include 1 more person in the sample. Now, with 11 people, the 2 variables were highly correlated. Why should this researcher not trust her results?
The 11thperson was probably an outlier, possibly yielding misleading results.

43. Define regression
Regression is a statistical procedure that finds the best fitting line through a set of data. 

44. In the regression equation (Y = b0 + b1X), what does b1 represent?
The slope of the best fitting line in the scatterplot of X and Y.

45. In the regression equation (Y = b0 + b1X), what does b0 represent?
The Y-intercept of the best fitting line in the scatterplot of X and Y.
Another answer: The estimated value of Y when X equals 0.

46. In regression, for any particular value of X, what do we call the difference between Y and the predicted value of Y (Y-hat)?
Error 

47. What do we call the typical distance between the observed Y values and the regression line?
The standard error of the estimate. 

48. If IQ explains 36% of the variance in Academic Achievement, what is the correlation between IQ and Academic Achievement? (Assume that the correlation is positive.)
0.6 (NOTE: The percentage of variance explained equals the correlation coefficient squared.) 

49. If the correlation between the personality trait of psychopathy (i.e., gross violations of the basic rights of others coupled with the inability to feel remorse) and anxiety is -0.35. What percentage of the variance in psychopathy is explained by anxiety?
12.25% (NOTE: The percentage of variance explained equals the correlation coefficient squared.)

 50. With an IQ of 120, you were probably one of the smartest people in your high school. The mean IQ in your high school was 90 and the standard deviation was 10. What percentage of people had the same or lower IQ as you did?
Z = (X-mu)/sigma
Z = (120-90)/10
Z = 3.00
From the Excel worksheet, you can calculate that 99.9% of the students had an IQ of 120 or less.

51. Then you went to a selective university where the mean IQ was 115 and the standard deviation was 13. What percentage of people at your university had your IQ or above?
Z = (120-115)/13
Z = .38
From the Excel worksheet, you can calculate that 35% of the students had an IQ of 120 or above.

52. Now you go to graduate school where the mean IQ is 130 and the standard deviation is 8.What percentage of the graduate students has your IQ or lower?
Z = (120-130)/8
Z = -1.25
From the Excel worksheet, you can calculate that 11% of the students have an IQ of 120 or below.

53. Consider the following scores for X and Y

X         Y
2          4
5          20
6          12
12        20
10        14 

Calculate the correlation between X and Y.

 


X Y (X-μX) (X-μX)2 (Y-μY) (Y-μY)2 (X-μX)(Y-μY)

2 4 -5 25 -10 100 50

5 20 -2 4 6 36 -12

6 12 -1 1 -2 4 2

12 20 5 25 6 36 30

10 14 3 9 0 0 0
Sums 35 70 0 64 0 176 70
Means 7 14




SSX = 64
SSY =  176
SP = 70
r = 70 / sqrt(64 * 176) = .66

54. Using the data above, calculate the slope of the regression line.

b1 = SP/SSX = 70/64 = 1.09 

55. Using the data above, calculate the Y-intercept of the regression line.

 

b0 = 14 - 1.09 * 7 = 6.36

56. Using the regression equation from above, what would you estimate Y to be if X equaled 9?


16.17 = 6.36 + 1.09 * 9

 
57. Consider the following population of scores: 4 1 12 -5 -10 22

Calculate the standard deviation.
μ = ΣX/N = 24 / 6 = 4


SSX =Σ(X - μ)2
SSX =(4 - 4)2 + (1 - 4)2 + (12 - 4)2 + (-5 - 4)2 + (-10 - 4)2 + (22 - 4)2 = 674
σ = √(674/6) = 10.60

(NOTE: I used the formula for the standard deviation for a population.)

 

58. Consider the following sample of scores: 1 3 5 6 5

Calculate the estimated variance of the population from which this sample was selected..

mean = ΣX/n = 20/5 = 4


SSX =Σ(X - μ)2

SSX = (1 - 4)2 + (3 - 4)2 + (5 - 4)2 + (6 - 4)2 + (5 - 4)2 = 16

s2 =16 / (5 - 1) = 4


59. In the following distribution, what is the mode? 5 45 45 88 109
45 

60. In the following distribution, what is the median? 1 2 3 1000000 1000001
3

61. In the following distribution, what is the median? 1 2 3 7 20000 2000012121
5
NOTE: Because 3 and7 are the middle scores, we average them.

62. In the following distribution, what is the mean? 1 2 4 5
3

63. What is the range of this distribution? 4 6 5 7 9 25 -9
34
NOTE: Range = 25 - (-9) = 34)

64. Which of the following is the strongest correlation? 0.5, 0.09, -0.3, 0, 0.7, -0.8, 0.29
-.8