Chapter 1

Question 1

Statistics

Answer 1

refers to a general field of mathematics, statistical procedures

refers to a set of mathematical procedures for organising, summarising, and interpreting information

purposes of statistics:

1. Statistics are used to organise and summarise the information so that the researcher can see what happened in the research study and can communicate the results to others
2. Statistics help the researcher to answer the questions that initiated the research by determining exactly what general conclusions are justified based on the specific results that were obtained

• Statistical procedures help ensure that the information or observations are presented and interpreted in an accurate and informative way
• statistics provide researchers with a set of standardized techniques that are recognized and understood throughout the scientific communit

Question 2

Population

Answer 2

the set of all the individuals of interest in a particular study.

• Because populations tend to be very large, it usually is impossible for a researcher to examine every individual in the population of interest. Therefore, researchers typically select a smaller, more manageable group from the population and limit their studies to the individuals in the selected group. In statistical terms, a set of individuals selected from a population is called a sample

Question 3

Sample

Answer 3

a set of individuals selected from a population, usually intended to represent the population in a research study.

A sample is intended to be representative of its population, and a sample should always be identified in terms of the population from which it was selected

Question 4

Relationship between a population and a sample

Answer 4

1. The population - all of the individuals of interest ->
2. The sample - is selected from the population ->
3. THE SAMPLE - The individuals selected to participate in the research study ->
4. The results from the sample are generalised to the population

Question 5

Variable

Answer 5

A variable is a characteristic or condition that changes or has different values for different individuals

Question 6

Data

Answer 6

measurements or observations

Question 7

Data set

Answer 7

A collection of measurements or observations

Question 8

Datum

Answer 8

a single measurement or observation and is commonly called a score or raw score

Question 9

Parameter

Answer 9

is a value, usually a numerical value, that describes a population. A parameter is usually derived from measurements of the individuals in the population.

for example, the average score for the population—is called a parameter

Question 10

Statistic

Answer 10

is a value, usually a numerical value, that describes a sample. A statistic is usually derived from measurements of the individuals in the sample.

• A characteristic that describes a sample is called a statistic. Thus, the average score for a sample is an example of a statistic

Typically, the research process begins with a question about a population parameter. However, the actual data come from a sample and are used to compute sample statistics

Question 11

Descriptive statistics

Answer 11

are statistical procedures used to summarize, organize, and simplify data

• Often the scores are organized in a table or a graph so that it is possible to see the entire set of scores. Another common technique is to summarize a set of scores by computing an average

Question 12

Inferential statistics

Answer 12

consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected.

Question 13

Sampling error

Answer 13

is the naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter

Question 14

correlational method

Answer 14

Two different variables are observed to determine whether there is a relationship between them

• When the data from a correlational study consist of numerical scores, the relationship between the two variables is usually measured and described using a statistic called a correlation

Question 15

Limitations of the correlational method

Answer 15

The results from a correlational study can demonstrate the existence of a relationship between two variables, but they do not provide an explanation for the relationship - does not give a cause-and-effect

Question 16

Comparing Two (or More) Groups of Scores: Experimental and Nonexperimental Methods

Answer 16

• In this situation, the relationship between variables is examined by using one of the variables to define the groups, and then measuring the second variable to obtain scores for each group.
• we examine descriptive statistics that summarize and describe the scores in each group and we use inferential statistics to determine whether the differences between the groups can be generalized to the entire population

Question 17

Experimental and non-experimental methods

Answer 17

• The results from an experiment allow a cause-and-effect explanation
• A nonexperimental study does not permit a cause-and effect explanation

Question 18

The experimental method

Answer 18

In the experimental method, one variable is manipulated while another variable is observed and measured. To establish a cause-and-effect relationship between the two variables, an experiment attempts to control all other variables to prevent them from influencing the results.

To accomplish this goal, the experimental method has two characteristics that differentiate experiments from other types of research studies:

• Manipulation: The researcher manipulates one variable by changing its value from one level to another
• Control: The researcher must exercise control over the research situation to ensure that other, extraneous variables do not influence the relationship being examined.

There are two general categories of variables that researchers must consider:

• Participant Variables: These are characteristics such as age, gender, and intelligence that vary from one individual to another. Whenever an experiment compares different groups of participants (one group in treatment A and a different group in treatment B), researchers must ensure that participant variables do not differ from one group to another.
• Environmental Variables: These are characteristics of the environment such as lighting, time of day, and weather conditions. A researcher must ensure that the individuals in treatment A are tested in the same environment as the individuals in treatment B.

Question 19

three basic techniques to control other variables

Answer 19

• random assignment - each participant has an equal chance of being assigned to each of the treatment conditions. The goal is to distribute the participant characteristics evenly between the two groups so that neither group is noticeably smarter (or older, or faster) than the other. Random assignment can also be used to control environmental variables.
• matching - to ensure equivalent groups or equivalent environments. For example, the researcher could match groups by ensuring that every group has exactly 60% females and 40% males.
• holding them constant - For example, in the video game violence study discussed earlier (Polman et al., 2008), the researchers used only 10-year-old boys as participants (holding age and gender constant). In this case the researchers can be certain that one group is not noticeably older or has a larger proportion of females than the other.

Question 20

Independent variable

Answer 20

The independent variable is the variable that is manipulated by the researcher. In behavioral research, the independent variable usually consists of the two (or more) treatment conditions to which subjects are exposed. The independent variable consists of the antecedent conditions that were manipulated prior to observing the dependent variable

Question 21

Dependent variable

Answer 21

The dependent variable is the one that is observed to assess the effect of the treatment

Question 22

Control condition

Answer 22

Individuals in a control condition do not receive the experimental treatment. Instead, they either receive no treatment or they receive a neutral, placebo treatment. The purpose of a control condition is to provide a baseline for comparison with the experimental condition.

Question 23

Experimental condition

Answer 23

Individuals in the experimental condition do receive the experimental treatment.

Question 24

Experiment

Answer 24

a real experiment must include manipulation of an independent variable and rigorous control of other, extraneous variables

Question 25

nonequivalent groups

Answer 25

A research study in which the different groups of participants are formed under circumstances that do not permit the researcher to control the assignment of individuals to groups and the groups of participants are, therefore, considered nonequivalent.

Question 26

pre-post study

Answer 26

Quasi-experimental and nonexperimental designs consisting of a series of observations made over time. The goal is to evaluate the effect of an intervening treatment or event by comparing observations made before versus after the treatment.

• In a pre–post study the researcher also has no control over other variables that change with time. For example, the weather could change from dark and gloomy before therapy to bright and sunny after therapy. In this case, the depression scores could improve because of the weather and not because of the therapy. Because the researcher cannot control the passage of time or other variables related to time, this study is not a true experiment.

Question 27

quasi-independent variable

Answer 27

In a nonexperimental study, the “independent variable” that is used to create the different groups of scores is often called the quasi-independent variable.

Question 28

Constructs

Answer 28

Constructs are internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior

Question 29

Operational definition

Answer 29

An operational definition identifies a measurement procedure (a set of operations) for measuring an external behavior and uses the resulting measurements as a definition and a measurement of a hypothetical construct. Note that an operational definition has two components. First, it describes a set of operations for measuring a construct. Second, it defines the construct in terms of the resulting measurements.

Question 30

Discrete variables

Answer 30

A discrete variable consists of separate, indivisible categories. No values can exist between two neighboring categories

Question 31

Continuous variables

Answer 31

For a continuous variable, there are an infinite number of possible values that fall between any two observed values. A continuous variable is divisible into an infinite number of fractional parts.

• When measuring a continuous variable, it should be very rare to obtain identical measurements for two different individuals
• When measuring a continuous variable, each measurement category is actually an interval that must be defined by boundaries.

Question 32

Real limits

Answer 32

Real limits are the boundaries of intervals for scores that are represented on a continuous number line. The real limit separating two adjacent scores is located exactly halfway between the scores. Each score has two real limits. The upper real limit is at the top of the interval, and the lower real limit is at the bottom.

• The concept of real limits applies to any measurement of a continuous variable, even when the score categories are not whole numbers.

Question 33

Nominal scale

Answer 33

A nominal scale consists of a set of categories that have different names. Measurements on a nominal scale label and categorize observations, but do not make any quantitative distinctions between observations.

Question 34

Ordinal scale

Answer 34

An ordinal scale consists of a set of categories that are organized in an ordered sequence. Measurements on an ordinal scale rank observations in terms of size or magnitude.

Question 35

Interval scale vs ratio scale

Answer 35

• Both an interval scale and a ratio scale consist of a series of ordered categories
• interval scale - one interval (1 inch, 1 second, 1 pound, 1 degree) is the same size, no matter where it is located on the scale. The fact that the intervals are all the same size makes it possible to determine both the size and the direction of the difference between two measurements
• The factor that differentiates an interval scale from a ratio scale is the nature of the zero point. An interval scale has an arbitrary zero point. That is, the value 0 is assigned to a particular location on the scale simply as a matter of convenience or reference. In particular, a value of zero does not indicate a total absence of the variable being measured
• A ratio scale is anchored by a zero point that is not arbitrary but rather is a meaningful value representing none (a complete absence) of the variable being measured. The existence of an absolute, non-arbitrary zero point means that we can measure the absolute amount of the variable; that is, we can measure the distance from 0. This makes it possible to compare measurements in terms of ratios.

Question 36

interval scale

Answer 36

An interval scale consists of ordered categories that are all intervals of exactly the same size. Equal differences between numbers on scale reflect equal differences in magnitude. However, the zero point on an interval scale is arbitrary and does not indicate a zero amount of the variable being measured.

Question 37

ratio scale

Answer 37

A ratio scale is an interval scale with the additional feature of an absolute zero point. With a ratio scale, ratios of numbers do reflect ratios of magnitude.

Question 38

Raw scores

Answer 38

Raw scores are the original, unchanged scores obtained in the study. Scores for a particular variable are typically represented by the letter X

When observations are made for two variables, there will be two scores for each individual. The data can be presented as two lists labeled X and Y for the two variables.
- Each pair X, Y represents the observations made of a single participant

• The letter N is used to specify how many scores are in a set. An uppercase letter N identifies the number of scores in a population
• and a lowercase letter n identifies the number of scores in a sample.

Question 39

Summation Notation

Answer 39

The expression ΣX means to add all the scores for variable X.

Σ = The Sum Of

• The summation sign, Σ , is always followed by a symbol or mathematical expression. The symbol or expression identifies exactly which values are to be added. To compute , for example, the symbol following the summation sign is X, and the task is to find the sum of the X values.
• The summation process is often included with several other mathematical operations, such as multiplication or squaring. To obtain the correct answer, it is essential that the different operations be done in the correct sequence.

Question 40

Order of Mathematical Operations

Answer 40

1. Any calculation contained within parentheses is done first.
2. Squaring (or raising to other exponents) is done second.
3. Multiplying and/or dividing is done third. A series of multiplication and/or division operations should be done in order from left to right.
4. Summation using the Σ notation is done next.
5. Finally, any other addition and/or subtraction is done.