Chapter 10

Question 1

positive monotonic relationship

Answer 1

there is a positive relationship between the variables, but it is not a strictly positive linear relationship. An experiment with only two levels cannot yield such exact information.

Question 2

Factorial designs

Answer 2

are experimental designs with more than one independent variable (or factor). In a factorial design, all levels of each independent variable are combined with all levels of the other independent variables. The simplest factorial design—known as a 2 × 2 (two by two) factorial design—has two independent variables, each having two levels.

Question 3

The general format for describing factorial designs is

Answer 3

Number of levels of first IV x Number of levels of second IV x Number of levels of third IV

Question 4

Factorial designs yield

Answer 4

two kinds of information. The first is information about the effect of each independent variable taken by itself: this is called the main effect of an independent variable. The second type of information is called an interaction.

Question 5

In a design with two independent variables, there are

Answer 5

two main effects—one for each independent variable.

Question 6

The second type of information is called an interaction. If there is an interaction between two independent variables, the effect of one independent variable depends on the particular level of the other variable. In other words, the effect that an independent variable has on the dependent variable depends on the
level of the other independent variable. Interactions are a new source of information that cannot be obtained in a

Answer 6

simple experimental design in which only one independent variable is manipulated.

Question 7

One common type of factorial design includes both experimental (manipulated) and nonexperimental
(measured or nonmanipulated) variables. These designs—sometimes called IV × PV designs (i.e., independent variable by participant variable)—allow researchers to investigate how different types of individuals (i.e., participants) respond to the same manipulated variable.

Answer 7

These “participant variables” are personal attributes
such as age, ethnicity, participant sex, personality characteristics, and clinical diagnostic category. You will sometimes see participant variables described as subject variables or attribute variables. This is only a difference of terminology.

Question 8

The simplest IV × PV design includes one manipulated independent variable that has at least two levels
and one participant variable with at least

Answer 8

two levels

Question 9

A statistical procedure called analysis of variance is used to

Answer 9

assess the statistical significance of the main effects
and the interaction in a factorial design. When a significant interaction occurs, the researcher must statistically evaluate the individual means.

Question 10

When there is a significant interaction, the next step is to look at the

Answer 10

simple main effects

Question 11

A simple main effect analysis examines

Answer 11

mean differences at each level of the independent variable.

Question 12

the main effect of an independent variable averages across the levels of the other

Answer 12

independent variable; with simple main effects, the results are analyzed as if we had separate experiments at each level of the other independent variable.

Question 13

mixed factorial design

Answer 13

a combination of (1) In an independent groups design, different participants are assigned to each of the conditions in the study and (2) in a repeated measures design, the same individuals participate in all conditions in the study.

Question 14

In a 2 × 2 factorial design, there are four conditions. If we want a completely independent groups (between-subjects) design, a different group of participants will be assigned to each of the four conditions. The food intake modeling study illustrates a factorial design with different individuals in each of the conditions.

Answer 14

Suppose that you have planned a 2 × 2 design and want to have 10 participants in each condition; you will
need a total of 40 different participants

Question 15

In a completely repeated measures (within-subjects) design, the same individuals will participate in all
conditions. Suppose you have planned a study on the effects of marijuana: One factor is marijuana (marijuana
treatment versus placebo control) and the other factor is task difficulty (easy versus difficult). In a 2 × 2
completely repeated measures design,

Answer 15

each individual would participate in all of the conditions by completing both easy and difficult tasks under both marijuana treatment conditions. If you wanted 10 participants in each condition, a total of 10 subjects would be needed

Question 16

Mixed Factorial Design Using Combined Assignment

Answer 16

The third table in Figure 7 shows the number of participants needed to have 10 per condition in a 2 × 2 mixed factorial design. In this table, independent variable A is an independent groups variable. Ten participants are assigned to level 1 of this independent variable, and another 10 participants are assigned to level 2. Independent variable B is a repeated measures variable, however. The 10 participants
assigned to A1 receive both levels of independent variable B. Similarly, the other 10 participants assigned to A2 receive both levels of the B variable. Thus, a total of 20 participants are required.

Question 17

One way to increase complexity is to

Answer 17

increase the number of levels of one or
more of the independent variables. A 2 × 3 design, for example, contains two independent variables:
Independent variable A has two levels, and independent variable B has three levels. Thus, the 2 × 3 design has six conditions.

Question 18

THERE ARE TWO WAYS IN WHICH STATISTICS HELP US UNDERSTAND DATA COLLECTED IN RESEARCH INVESTIGATIONS.

Answer 18

First, statistics are used to describe the data.
Second, statistics are used to make inferences and draw conclusions about a population on the basis of sample
data.

Question 19

The levels of nominal scale variables have

Answer 19

no numerical, quantitative properties. The levels are simply different categories or groups. Most independent variables in experiments are nominal—for example, as in an experiment that compares behavioral and cognitive therapies for depression. Variables such as eye color, hand dominance, college major, and marital status are nominal scale variables; left-handed and right-handed people differ from each other, but not in a quantitative way.

Question 20

Variables with ordinal scale levels exhibit minimal quantitative distinctions. We can rank order the levels
of the variable being studied from lowest to highest. The clearest example of an ordinal scale is one that asks people to make rank-ordered judgments. For example, you might ask people to rank the most important problems facing your state today.

Answer 20

If education is ranked first, health care second, and crime third, you know the order but you do not know how strongly people feel about each problem: Education and health care may be deemed very close together in seriousness, with crime a distant third. With an ordinal scale, the intervals between items probably are not equal.

Question 21

Interval scale and ratio scale variables have much more detailed quantitative properties. With an interval
scale variable, the intervals between the levels are equal in size. The difference between 1 and 2 on the scale, for example, is the same as the difference between 2 and 3.

Answer 21

Interval scales generally have five or more
quantitative levels. You might ask people to rate their mood on a 7-point scale ranging from a “very negative” to a “very positive” mood. There is no absolute zero point that indicates an “absence” of mood.

Question 22

In the behavioral sciences, it is often difficult to know precisely whether an ordinal or an interval scale is
being used. However, it is often useful to assume that the variable is being measured on an interval scale,
because interval scales allow for

Answer 22

more sophisticated statistical treatments than do ordinal scales. Of course, if the measure is a rank ordering (for example, a rank ordering of professors on the basis of popularity), an ordinal scale clearly is being used.

Question 23

Ratio scale variables have both equal intervals and an absolute zero point that indicates the absence of the
variable being measured. Time, weight, length, and other physical measures are the best examples of ratio
scales. Interval and ratio scale variables are conceptually different; however, the statistical procedures used to analyze data with such variables are identical.

Answer 23

An important implication of interval and ratio scales is that data can be summarized using the mean, or arithmetic average. It is possible to provide a number that reflects the mean amount of a variable—for example, “the average mood of people who won a contest was 5.1” or “the mean weight of the men completing the weight loss program was 187.7 pounds.”

Question 24

Depending on the way the variables are studied, there are three basic ways of describing the results:

Answer 24

(1) comparing group percentages, (2) correlating scores of individuals on two variables, and (3) comparing group means.

Question 25

we are focusing on percentages because the travel variable is

Answer 25

nominal: Liking and disliking are simply two different categories.

Question 26

Aggression is a ratio scale variable because

there are

Answer 26

equal intervals and a true zero on the scale.

Question 27

frequency distribution

Answer 27

indicates the number of individuals who receive each possible score on a variable. Frequency
distributions of exam scores are familiar to most college students—they tell how many students received a given score on the exam. Along with the number of individuals associated with each response or score, it is useful to examine the percentage associated with this number.

Question 28

Pie charts

Answer 28

divide a whole circle, or “pie,” into “slices” that represent relative percentages. Pie charts are particularly useful when representing nominal scale information. They are useful in applied research reports and articles written for the general public. Articles in
scientific journals require more complex information displays.

Question 29

Bar graphs

Answer 29

use a separate and distinct bar for each piece of information. In this graph, the x or horizontal axis shows the two possible responses. The y or vertical axis shows the number who chose each response, and so the height of each bar represents the number of people who responded to the “like” and “dislike” options.

Question 30

Frequency polygons

Answer 30

use a line to represent the distribution of frequencies of scores. This is most useful when the data represent interval or ratio scales as in the modeling and aggression data

Question 31

Each frequency polygon is anchored at scores that

Answer 31

were not obtained by anyone (0 and 6 in the no-model group; 2 and 8 in the model group).

Question 32

histogram

Answer 32

uses bars to display a frequency distribution for a quantitative variable. In this case, the scale values are continuous and show increasing amounts on a variable such as age, blood pressure, or stress. Because the values are continuous, the bars are drawn next to each other.

Question 33

What can you discover by examining frequency distributions?

Answer 33

First, you can directly observe how your
participants responded. You can see what scores are most frequent, and you can look at the shape of the
distribution of scores. You can tell whether there are any outliers—scores that are unusual, unexpected, or very different from the scores of other participants. In an experiment, you can compare the distribution of scores in the groups.

Question 34

Descriptive statistics

Answer 34

allow researchers to make precise statements about the data. Two statistics are needed to describe the
data. A single number can be used to describe the central tendency, or how participants scored overall.
Another number describes the variability, or how widely the distribution of scores is spread. These two
numbers summarize the information contained in a frequency distribution.

Question 35

three measures of central tendency

Answer 35

the mean, the median, and the mode.

Question 36

mean

Answer 36

a set of scores is obtained by adding all the scores and dividing by the number of scores. It is symbolized as ; in scientific reports, it is abbreviated as M. The mean is an appropriate indicator of central tendency only when scores are measured on an interval or ratio scale, because the actual values of the numbers
are used in calculating the statistic.

Question 37

the Greek letter Σ (sigma)

Answer 37

is statistical notation for summing a set of numbers. Thus, ΣX is shorthand for “sum of the values in a set of scores.”

Question 38

median

Answer 38

is the score that divides the group in half (with 50% scoring below and 50% scoring above the
median). In scientific reports, the median is abbreviated as Mdn. The median is appropriate when scores are
on an ordinal scale, because it takes into account only the rank order of the scores. It is also useful with
interval and ratio scale variables, however.

Question 39

mode

Answer 39

is the most frequent score. The mode is the only measure of central tendency that is appropriate if a nominal scale is used. The mode does not use the actual values on the scale, but simply
indicates the most frequently occurring value.

Question 40

The median or mode can be a better indicator of central tendency than the mean if a few unusual scores bias the mean. For example, the median family income of a county or state is usually a better measure of central tendency than the mean family income. Because

Answer 40

relatively small number of individuals have
extremely high incomes, using the mean would make it appear that the “average” person makes more money
than is actually the case.

Question 41

A measure of variability

Answer 41

is a number that characterizes the amount of spread in a distribution of scores. One such measure is the standard deviation

Question 42

standard deviation

Answer 42

all of these:
1) symbolized as s, which indicates the average deviation of scores from the mean. Income is a good example.
2) It is derived by first calculating the
variance, symbolized as s2 (the standard deviation is the square root of the variance). The standard deviation of a set of scores is small when most people have similar scores close to the mean. The standard deviation becomes larger as more people have scores that lie farther from the mean value.

Question 43

It is possible for measures of central tendency in two communities to be close with the variability

Answer 43

differing substantially.

Question 44

In scientific reports, the standard deviation is abbreviated as

Answer 44

SD

Question 45

as with the mean, the calculation of the standard deviation uses the actual values of the scores; thus, the standard deviation is appropriate only for

Answer 45

interval and ratio scale variables.

Question 46

range

Answer 46

all of these:

1) Another measure of variability
2) is simply the difference between the highest score and the lowest score.

Question 47

A common way to graph relationships between variables is to use

Answer 47

a bar graph or a line graph

Question 48

Bar graphs are used when the values on the x

axis are

Answer 48

nominal categories (e.g., a no-model and a model condition).

Question 49

Line graphs are used when the values on

the x axis are

Answer 49

numeric (e.g., marijuana use over time, as shown in the chapter “Asking People About Themselves”, Figure 1). In line graphs, a line is drawn to connect the data points to represent the relationship between the variables.

Question 50

Choosing the scale for a bar graph allows a common manipulation that is sometimes used by scientists and
all too commonly used by advertisers. The trick is to

Answer 50

exaggerate the distance between points on the

measurement scale to make the results appear more dramatic than they really are.

Question 51

It is always wise to look carefully at the numbers on the scales depicted in

Answer 51

graphs