Deck 6: Descriptive Statistics

Question 1

The size of the correlation between achievement test scores and school grades might be smaller in which population?

A) Gifted 12-year-old students
B) Grades three to five, including children with learning disabilities
C) Nontraditional college students
D) None of these are true.

Answer 1

A

Question 2

Which standard score has a mean of 0 and a standard deviation of 1?

A) Percentile
B) T-score
C) z-score
D) None of these are true.

Answer 2

C

Question 3

In a positively skewed distribution:

A) the mean is greater than the median.
B) the median is greater than the mean.
C) either of the above may be true.

Answer 3

A

Question 4

You would find curves rather than right angles in a

A) Polygon.
B) Histogram.
C) frequency distribution.
D) Scatterplot.

Question 5

Which of the following is an above-average score?

A) 100
B) z = +1.5
C) T = 49
D) z = -2.99

Question 6

Exhibit 6-2: Use the distribution for the following questions.51, 52, 55, 56, 57, 57, 57, 58, 59, 59, 60, 60, 60
Refer to Exhibit 6-2.The mode of this distribution is

A) 57.
B) 59.
C) 60.
D) none of these are true.

Question 7

Exhibit 6-3: Use the distribution for the following questions.51, 52, 55, 56, 57, 57, 57, 58, 59, 59, 60, 60, 60
Refer to Exhibit 6-3.What is the standard deviation of this distribution?

A) 2.8
B) 3.63
C) 57
D) None of these are true.

Question 8

Descriptive statistics are used to:

A) tell us how accurately we can infer from the part to the whole.
B) Enable us to organize, summarize and describe our observations.
C) Both a and b

Question 9

A distribution with the mean lower than the median:

A) is a symmetrical distribution.
B) is a negatively skewed distribution.
C) is a positively skewed distribution.
D) is both a and b

Question 10

Standard procedure in organizing a frequency distribution is to

A) list scores from the lowest at bottom to highest at top.
B) list scores from the lowest at top to highest at bottom.
C)include score values that are higher than the lowest and lower than the highest that have zero frequency.
D)a and c.
E)b and c.

Question 11

Exhibit 6-2: Use the distribution for the following questions.51, 52, 55, 56, 57, 57, 57, 58, 59, 59, 60, 60, 60
Refer to Exhibit 6-2.The median of this distribution is

A) 56.5.
B) 57.
C) 57.33.
D) None of these are true.

Question 12

The measure of central tendency that indicates the point below which half the scores fall is the:

A) standard deviation.
B) mean.
C) median.
D) mode.
E) Spearman rho.

Question 13

A T-score of 40 is higher than about what percent of the scores in a distribution?

A) 16 percent
B) 50 percent
C) 68 percent
D) 84 percent

Question 14

If your test score was one standard deviation above the mean score, your best estimate is that you scored better than what percent of the test takers?

A) 50%
B) 68%
C) 84%
D) 98%

Question 15

A student with a z-score of 1.5

A) got three-fourths of the answers correct.
B) scored at the 75 percentile.
C) scored in the highest 1 percent of the cases.
D) None of these are true.

Question 16

Which measure of central tendency is best for describing this distribution? 13, 13, 13, 20, 21, 24, 25, 25, 27, 28, 28, 29, 30, 32, 31, 60

A) Mode
B) Median
C) Mean

Question 17

Exhibit 6-3: Use the distribution for the following questions.51, 52, 55, 56, 57, 57, 57, 58, 59, 59, 60, 60, 60
Refer to Exhibit 6-3.What is the range of this distribution?

A) 9
B) 10
C) 11
D) None of these are true.

Question 18

A 100-point math test has a mean of 40 and a standard deviation of 15.A 60-point English test has a mean of 40 and a standard deviation of 5.Pat scored a 50 on both tests.

A) Pat scored better on the English test.
B) Pat scored better on the math test.
C) Pat scored about the same on both tests.
D) None of these are true.

Question 19

Exhibit 6-2: Use the distribution for the following questions.51, 52, 55, 56, 57, 57, 57, 58, 59, 59, 60, 60, 60
Refer to Exhibit 6-2.The mean for this distribution is

A) 57.
B) 75.33.
C) 52.4
D) None of these are true.

Question 20

Exhibit 6-2: Use the distribution for the following questions.51, 52, 55, 56, 57, 57, 57, 58, 59, 59, 60, 60, 60
Refer to Exhibit 6-2.The most frequently occurring score is

A) 57.
B) 75.33.
C) 52.4
D) none of these are true.

Question 21

Exhibit 6-4: Use the data for the following questions.Score 1: 34, 40, 42, 24, 30; Score 2: 40, 38, 41, 49, 42
Refer to Exhibit 6-4.What percent of the variance of scores in Group 1 is common with the variance of scores in Group 2?

A) 56 percent
B) 69 percent
C) 72 percent
D) None of these are true.

Question 22

The coefficient of determination of an r = -.60 is

A) -.36.
B) +.36.
C) -.77.
D) None of these are true.

Question 23

A study of a new reading training program achieved, with 100 subjects, the following results: experimental group mean = 20.25 (SD = 2.28) and control group mean = 25.14 (SD = 4.75).However, a second study with 541 subjects found experimental group mean = 28.81 (SD = 2.56) and control group mean = 26.62 (SD 2.01).

A) The first study had a higher effect size.
B) The second study had a higher effect size.
C) Both studies had similar effect sizes.
D) None of these are true.

Question 24

If the standard deviation of the score on this test is zero, we should conclude

A) nobody received even one question correct.
B) half the scores were below the mean.
C) half the scores were above the mean.
D) a computational error was made.
E) everybody received the same score.

Question 25

If you could have one wish granted concerning this test, you should choose a score

A) above the mean.
B) above both the mean and the median.
C) equal to the first quartile.
D) equal to a z-score of +1.5.
E) equal to a T-score of 55.

Question 26

The Pearson's product-moment correlation describes the relationship between variables by

A) summing the variable and dividing by N.
B) summing the deviation scores squared and dividing by N.
C) summing the product of z-scores and dividing by N.
D) None of these are true.

Question 27

The coefficient of correlation reflects the

A) relation of a score to its distribution.
B) relation between variables.
C) typical performance of a group of students.
D) heterogeneity of performance of a group of students.

Question 28

The closer the coefficient of correlation is to plus or minus 1, the greater will be the

A) effect size.
B) significance of the study.
C) strength of the correlation.
D) standard error.

Question 29

A third study with 2,000 subjects found an experimental group mean of 29.26 (SD = 2.5) and a control group mean of 29.26 (SD = 1.5).What is the average effect size of the three studies?

A) 1.09
B) 1.66
C) 1.84
D) None of these are true.

Question 30

Mary had a z-score of zero on the Graduate Record Examination and a percentile rank of 50 on the Law School Aptitude Examination.We can say

A) she failed both examinations.
B) she failed the GRE but not the LSAT.
C) she did better on GRE than on LSAT.
D) she did better on LSAT than on GRE.
E) she did equally well on LSAT and GRE.

Question 31

"Analysis of analyses" refers to

A) analysis of variance.
B) Pearson's product moment correlation.
C) meta-analysis.
D) standardization scores.

Question 32

The z-scores for X and Y variables are exactly the same except they have opposite signs.The coefficient of determination is

A) 0.00.
B) -1.00.
C) +1.00.
D) not possible to compute with this information.

Question 33

Exhibit 6-4: Use the data for the following questions.Score 1: 34, 40, 42, 24, 30; Score 2: 40, 38, 41, 49, 42
Refer to Exhibit 6-4.Compute the Pearson's r from the data.

A) .74
B) .83
C) .92
D) None of these are true.

Question 34

____ would be associated with a scattergram with a moderately wide band of dots going from upper left to lower right.

A) A Pearson's product moment correlation of +1.00
B) A Pearson's product moment correlation between zero and +1.00
C) A Pearson's product moment correlation of zero
D) A Pearson's product moment correlation between zero and -1.00
E) A Pearson's product moment correlation of -1.00

Question 35

Meta-analysis is used for

A) searching across similar studies for statistically similar conclusions.
B) systematically combining data from similar studies.
C) finding differences between statistical conclusions of several similar studies.
D) determining whether a study's results fit within the distribution of previous research.

Question 36

If every Y-score is exactly one-half its paired X-score, we have ____.

A) A Pearson's product moment correlation of +1.00
B) A Pearson's product moment correlation between zero and +1.00
C) A Pearson's product moment correlation of zero
D) A Pearson's product moment correlation between zero and -1.00
E) A Pearson's product moment correlation of -1.00

Question 37

A distribution with many high scores and a few scattered low scores is a ____ distribution:

A) symmetrical.
B) positively skewed.
C) negatively skewed.

Question 38

Compared with stanine scores, z-scores have the advantage of being

A) all positive.
B) more precise.
C) easier to learn to interpret.
D) based on rank rather than raw score.

Question 39

Under a scattergram, there is a notation that the coefficient of correlation is .06.This means that

A) most of the cases are plotted within a range of 6 percent above or below a sloping line in the scattergram.
B) plus and minus 6 percent from the mean includes about 68 percent of the cases.
C) there is a negligible correlation between the two variables.
D) most of the data plotted fall into a narrow band 6 percent wide.

Question 40

A student who sometimes scores high and sometimes scores low on a series of weekly tests will have a higher ____ than a student who makes the same score week after week.

A) Mean
B) Median
C) Mode
D) standard deviation
E) Polygon

Question 41

With a population of 100 children aged 7 through 14, we would expect ____ between height and reading vocabulary.

A) A Pearson's product moment correlation of +1.00
B) A Pearson's product moment correlation between zero and +1.00
C) A Pearson's product moment correlation of zero
D) A Pearson's product moment correlation between zero and -1.00
E) A Pearson's product moment correlation of -1.00

Question 42

A schedule for trains from Chicago to New Orleans in one column shows how far each stop on the route is from Chicago and in another column how far the same stops are from New Orleans.The correlation between the two columns is ____.

A) A Pearson's product moment correlation of +1.00
B) A Pearson's product moment correlation between zero and +1.00
C) A Pearson's product moment correlation of zero
D) A Pearson's product moment correlation between zero and -1.00
E) A Pearson's product moment correlation of -1.00

Question 43

Exhibit 6-5: Indicate your choice of statistics for solving the following questions.
Refer to Exhibit 6-5.We want to determine how a student's score compares with the scores of the rest of the class.

A) mean
B) standard deviation
C) z-score
D) Pearson's r

Question 44

The difference between experimental group mean and control group mean divided by the standard deviation of the control group is called the

A) coefficient of determination.
B) mean adjusted difference.
C) z-score
D) effect size.
E) deviation score

Question 45

There is no relationship between variables when the correlation is ____.

A) A Pearson's product moment correlation of +1.00
B) A Pearson's product moment correlation between zero and +1.00
C) A Pearson's product moment correlation of zero
D) A Pearson's product moment correlation between zero and -1.00
E) A Pearson's product moment correlation of -1.00

Question 46

The mean of the squared deviation scores is called

A) Pearson's r.
B) standard deviation.
C) variance.
D) range.

Question 47

Which of these is not an advantage of percentile ranks?

A) they have universal meaning.
B) they can be interpreted in the context of zero to 100 percent.
C) equal differences in percentile ranks have the same meaning at all points in the scale.
D) they are rank statistics.

Question 48

A Z-score of 51 is equal to a z-score of

A) .10.
B) .51.
C) 1.00.
D) 5.10.

Question 49

If the difference between r and zero is doubled, the portion of Y variance associated with X variance is

A) unchanged.
B) doubled.
C) halved.
D) quadrupled.

Question 50

An investigator found ____ when correlating weight and sex drive among adult males of average height, which led him to conclude that a fat man is more likely to have high sex drive than a thin man.

A) A Pearson's product moment correlation of +1.00
B) A Pearson's product moment correlation between zero and +1.00
C) A Pearson's product moment correlation of zero
D) A Pearson's product moment correlation between zero and -1.00
E) A Pearson's product moment correlation of -1.00

Question 51

Exhibit 6-5: Indicate your choice of statistics for solving the following questions.
Refer to Exhibit 6-5.We want to know how well the class as a whole did on an examination.

A) mean
B) standard deviation
C) z-score
D) Pearson's r

Question 52

A negative z-score is

A) always above the mean.
B) always below the mean.
C) sometimes below the mean.
D) sometimes above the mean.

Question 53

The coefficient of determination reveals

A) how well an individual did on a test.
B) how well a class as a whole did on at test.
C) how well an individual did in relation to the rest of the class.
D) whether a correlation is positive or negative.
E) how much relationship there is between two sets of scores.

Question 54

A positive correlation between self-concept and reading achievement would indicate

A) high self-concept is a cause of high achievement.
B) low self-concept is a cause of low achievement.
C) high achievement is a cause of high self-concept.
D) one is justified in predicting low achievement for those with low self-concept.
E) both a and b are correct.

Question 55

An investigator found strong evidence that elderly teachers and young teachers scored low on an aptitude test while middle-aged teachers scored high on this test.This is an example of

A) high positive Pearson's r correlation.
B) high negative Pearson's r correlation.
C) curvilinear relationship.
D) lack of relationship between variables.

Question 56

Which of the following is not true of the normal curve?

A) Many physical and psychological measures will produce a polygon similar to this curve.
B) The mode is equal to the median.
C) The median is equal to the mean.
D) Large z-scores occur more often than small z-scores.
E) It is useful for estimating what percent of scores will fall above and below certain points.

Question 57

Multiplying all raw scores by two will

A) double the z-scores.
B) halve the z-scores.
C) not change the z-scores.

Question 58

Exhibit 6-5: Indicate your choice of statistics for solving the following questions.
Refer to Exhibit 6-5.We want to know how spread out or heterogeneous the scores of a class are.

A) mean
B) standard deviation
C) z-score
D) Pearson's r

Question 59

The sign of the Pearson's r is related to the strength of the relationship.

A) Positively
B) Negatively
C) Not related

Question 60

Exhibit 6-5: Indicate your choice of statistics for solving the following questions.
Refer to Exhibit 6-5.We want to see how scores on this examination are related to scores on another examination.

A) mean
B) standard deviation
C) z-score
D) Pearson's r

Question 61

In order to compute a correlation coefficient between traits A and B, it is necessary to have:

A) one group of subjects, some of whom possess characteristics of trait A, the remainder possessing those of trait B.
B) measures of trait A on one group of subjects and of trait B on another.
C) one group of subjects, some of whom have both A and B, some have neither, and some have one but not the other.
D) two groups of subjects, one which could be classified as A or not A, the other as B or not B.
E) measure of traits A and B on each subject in one group.

Question 62

What purpose does meta-analysis serve?

Question 63

Correlating the scores of 50 students on two tests, an investigator found that the sum of the z-score cross-products was 20.The Pearson's product moment coefficient in this case is:

A) impossible to compute with the information given.
B) .02.
C) .20.
D) .40.
E) None of these are true.

Question 64

Standard deviation is

A) from the same statistical family as the mean.
B) used in conjunction with the median.
C) less stable than variance.
D) a measure of central tendency.

Question 65

Why do effect sizes have universal meaning?

Question 66

Why might you prefer to teach a fifth grade class with a mean grade level equivalent of 5.1 and a standard deviation of 1.9 rather than a class with a mean grade level equivalent of 5.1 and a standard deviation of 3.2?

Question 67

When we have statistically significant results, what does an effect size tell us?

Question 68

A negative z score is always

A) above the median.
B) below the median.
C) a good score.
D) a poor score.
E) below the mean.

Question 69

A stanine score of six would have a T-score of

A) 60.
B) above 50.
C) between 45 and 55.
D) between 55 and 65.
E) below 60.

Question 70

How are Cohen's d and Smith and Glass's ? alike.How are they different?

Question 71

The mean of all z-scores in a distribution is equal to

A) zero.
B) number in the distribution.
C) the sum of all squared scores.
D) the sum of all squared z-scores divided by N.

Question 72

Why do z-scores have universal meaning?

Question 73

Explain a research situation when you would run a Pearson's product moment correlation, with attention given to the types of variables under study, the variables' level of measurement(s), and what the potential findings might mean in terms of the directionality and magnitude of the correlation.

Question 74

Why is standard deviation usually preferred to range as a measure of dispersion?

Question 75

The Pearson's r is not appropriate when the data are

A) from a population.
B) heterogeneous.
C) bivariate.
D) curvilinear.

Question 76

The sum of the z-scores squared in any distribution is equal to

A) zero.
B) 1.00.
C) cN.
D) N2.

Question 77

Why is the mean the most widely used measure of central tendency?

Question 78

The denominator of the Smith and Glass effect size is

A) the standard deviation of the control group.
B) the difference between means.
C) a weighted estimate of the population mean based on the means of both groups.
D) a weighted estimate of the population standard deviation based on the variability within both groups.

Question 79

Which of the following is a bivariate distribution?

A) Incomes of Denver teachers
B) Reading test scores of 50 children taught by the phonics method
C) Nursing license examination results for only male candidates
D) Home-economics aptitude test scores of this year's freshmen
E) Number of arrests made and years of experience of San Francisco policemen

Question 80

What are the advantages and disadvantages of percentile ranks?