# Appendix B: Statistical Reasoning: An Introduction

Psychology

Q 1Q 1

The two properties about a set of measurements of a dependent variable that we are most interested in describing are
A) frequency and average.
B) average and correlation.
C) central tendency and dispersion.
D) histograms and polygons.

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C

Q 2Q 2

The ________________ is the sum of all the scores divided by the number of scores.
A) median
B) mean
C) mode
D) standard deviation

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B

Q 3Q 3

The generally preferred measure of central tendency is usually the
A) range.
B) mean.
C) standard deviation.
D) median.

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B

Q 4Q 4

The mean is
A) the arithmetic average.
B) the middle score.
C) the average of the highest and lowest scores.
D) the most common score.

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Q 6Q 6

An advantage of the median over the mean is that the median is
A) easier to calculate.
B) more sensitive to each of the sample scores.
C) a measure of dispersion.
D) less influenced by extreme scores..

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Multiple Choice

Q 7Q 7

Which of the following is the most useful descriptive statistic for measuring dispersion?
A) range
B) variance
C) mean deviation
D) standard deviation

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Q 8Q 8

The standard deviation is
A) the square of the variance.
B) the square root of the variance.
C) smaller than the mean.
D) the difference between the highest and lowest scores.

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Multiple Choice

Q 9Q 9

All of the following statements are true of the normal distribution EXCEPT
A) the mean and median coincide.
B) the most common scores lie near the mean.
C) the more rare the score is, the further from the mean it lies.
D) nearly all the scores lie outside of two standard deviations of the mean.

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Multiple Choice

Q 10Q 10

A score that lies one standard deviation above the mean
A) has the same X value as the point of inflection.
B) has a z?value of +1.0.
C) has a z-value of -1.0.
D) has a z-score equal to the mean.

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Multiple Choice

Q 11Q 11

If the mean I.Q. score is 100 and the standard deviation of I.Q. scores is 15, then an I.Q. of 130 will have a z-score (or standard score) of
A) 1.00.
B) 0.00.
C) 2.00.
D) ?2.00.

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Multiple Choice

Q 12Q 12

Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to _______________ or ________________.
A) manipulation; chance
B) manipulation; experimental error
C) sampling error; independent variable
D) independent variable; experimental error

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Multiple Choice

Q 13Q 13

The ___________ is the standard deviation of sample means.
A) absolute mean deviation
B) central dendency
C) point biserial
D) standard error

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Multiple Choice

Q 14Q 14

The null hypothesis suggests that the two samples come from ___________ distribution(s), and the experimental hypothesis suggests that the two samples come from _____________ distribution(s).
A) different; different
B) different; the same
C) the same; different
D) the same; the same

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Multiple Choice

Q 15Q 15

In comparison with a confidence level of 0.05, a confidence level of 0.01 means
A) you are less sure that the null hypothesis is wrong.
B) you are more sure that the null hypothesis is wrong.
C) you are absolutely sure that the null hypothesis is wrong.
D) you are more sure that the experimental hypothesis is wrong.

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Multiple Choice

Q 16Q 16

Rejecting the null hypothesis when it is actually false is
A) a Type I error.
B) a Type II error.
C) more likely with two-tailed tests.
D) a correct decision.

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Multiple Choice

Q 17Q 17

Failing to reject the null hypothesis when it is actually true is a
A) Type I error.
B) Type II error.
C) reasonable thing to do.
D) result of an inappropriate level of confidence.

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Multiple Choice

Q 18Q 18

Failing to reject the null hypothesis when it is actually false is a
A) Type I error.
B) Type II error.
C) standard error.
D) silly thing to do.

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Multiple Choice

Q 19Q 19

A conservative statistical test is one that
A) minimizes both Type I and Type II errors.
B) minimizes Type I errors, but increases the chance of Type II errors.
C) minimizes Type II errors, but increases the chance of Type I errors.
D) increases the chance of both Type I and II errors.

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Multiple Choice

Q 20Q 20

As the sample size (n) increases,
A) the standard error of the mean increases.
B) the power of the statistical tests decreases.
C) the probability of the Type II error increases.
D) the power of the statistical tests increases.

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Q 21Q 21

The power of a statistical test refers to its ability to
A) reject false null hypotheses.
B) reject false experimental hypotheses.
C) reject true null hypotheses.
D) reject true experimental hypotheses.

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Q 22Q 22

The larger the sample, the more we can trust the sample ___________ to be an estimate of the population ___________.
A) mean; mean
B) standard error of the mean; standard deviation
C) standard error of the mean; variance
D) difference; mean

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Multiple Choice

Q 23Q 23

In comparison with one-tailed tests, two-tailed tests are
A) less conservative.
B) more conservative.
C) less likely to lead to a Type II error.
D) more likely to lead to a Type I error.

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Q 24Q 24

The Mann-Whitney U test is
A) nonparametric.
B) distribution free.
C) designed for two groups of scores.
D) all of these

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Q 25Q 25

The Wilcoxon signed-ranks test
A) is used for between-subjects designs.
B) takes into account both the magnitude and the direction of the difference between paired scores.
C) cannot be used for within-subjects designs.
D) is a parametric test.

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Q 26Q 26

The F statistic is
A) the ratio of between-group variance to within-group variance.
B) between-groups variance minus within-groups variance.
C) within-groups variance minus between-groups variance.
D) a measure of error variance.

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Q 27Q 27

If experimental treatments produce an effect,
A) between-groups variance will increase.
B) between-groups variance will decrease.
C) within-groups variance will increase.
D) within-groups variance will decrease.

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Multiple Choice

Q 28Q 28

In a multifactor analysis of variance, how the variables affect one another is called
A) a main effect.
B) an interaction effect.
C) an experimental effect.
D) a variance effect.

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Q 29Q 29

Simple analysis of variance is used in designs having
A) one independent variable.
B) more than one independent variable.
C) more than one independent variable (IV) but less than four IVs.
D) more than one dependent variable.

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Q 30Q 30

Which of the following is a parametric test?
A) Mann?Whitney U Test
B) sign test
C) t test
D) Χ2 Test of Independence

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Q 31Q 31

The Pearson product?moment correlation coefficient is referred to as
A) z?score.
B) s.d.
C) r.
D) p.c.c.

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Q 32Q 32

In hypothesis testing, both the magnitude of the difference and the direction of the difference between two groups are considered in
A) two?tailed tests.
B) one?tailed tests.
C) parametric tests.
D) nonparametric tests.

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Q 33Q 33

The inflection point in the normal curve is _____________ from the mean.
A) less one standard deviation
B) two standard deviations
C) three standard deviations
D) one standard deviation

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Q 34Q 34

Which of the following is NOT a measure of dispersion?
A) range
B) standard deviation
C) variance
D) median

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Q 35Q 35

If a person's score is part of a normal distribution of scores, we can determine the relative rank of that score if we know
A) the person's score.
B) the mean of the distribution.
C) the standard deviation of the distribution.
D) we must know all of these

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Q 37Q 37

In a histogram, the values for the dependent variable are displayed on the ordinate (Y?axis) and the frequency with which each value of the dependent value occurred is displayed on the abscissa (X?axis).

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True False

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True False

Q 39Q 39

In describing an array of data, psychologists typically present two descriptive statistics, the mean and the variance.

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True False

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True False

Q 41Q 41

Characteristics of a population of scores are called parameters, while characteristics of a sample of scores drawn from a larger population are called statistics.

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True False

Q 42Q 42

If an experiment involving an experimental group and a control group were performed over and over and the distribution of the difference between the means of the experimental and control groups was plotted, this distribution would approximate a normal distribution.

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True False

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True False

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True False

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True False

Q 46Q 46

As the level of significance is changed from .01 to .05, the probability of making a type I error increases and the probability of making a type II error decreases.

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True False

Q 47Q 47

The power of a test is the probability of rejecting the null hypothesis when it is actually true.

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True False

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True False

Q 49Q 49

The Mann?Whitney U test can only be used for between?subject designs and the Wilcoxon signed?ranks test can only be used for related measures designs.

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True False

Q 50Q 50

The variance of a distribution is defined as the sum of the squared deviations from the mean divided by the number of scores.

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True False

Q 51Q 51

Approximately 68 percent of the scores in a normal distribution have z values between ?2.0 and +2.0.

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True False

Q 52Q 52

Approximately 96 percent of the scores in a normal distribution have z values between ?2.0 and +2.0.

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True False

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True False

Q 54Q 54

The absolute mean deviation is an adequate measure of dispersion, and it is preferable over the standard deviation and variance because of its usefulness in inferential statistics.

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True False

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True False

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True False

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True False

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True False

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True False

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True False

Q 61Q 61

Manipulation of type of instructions given is an example of quantitative variation of an independent variable.

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True False

Q 62Q 62

What is the difference between inferential statistics and descriptive statistics? Give two examples of each type.

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Q 65Q 65

What is the difference between parametric and nonparametric tests? Give two examples of each type.

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Q 68Q 68

What are type I and type II errors? Under what conditions would you be willing to risk a type I error?

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Q 69Q 69

Discuss the various measures of dispersion (i.e., absolute mean deviation, variance, and standard deviation). Which of them do you think is the most useful? Why?

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Q 70Q 70

What are the properties of the normal curve? What does knowing these properties do for us? What is a standard score?

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Q 71Q 71

If the null hypothesis is true, F should be 1.0. If the null hypothesis is false, F should be greater than 1.0. However, sometimes Fs less than 1.0 are observed. Explain the logic behind the F test and how Fs less than 1.0 can be obtained.

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