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### Chapter 1

Introduction to Statistics and Research

Going Forward

Your goals in this chapter are to learn:

- The logic of research and the purpose of statistical procedures
- What a relationship between scores is
- When and why descriptive and inferential statistical procedures are used
- What the difference is between an experiment and a correlational study, and what the independent variable, the conditions, and the dependent variable are
- What the four scales of measurement are

What is Statistics?

Statistics help make sense of data in four ways:

- Organize scores to see patterns
- Summarize data to understand general characteristics
- Communicate results of a study
- Interpret what the data indicate

Studying Statistics

- Carefully read and study the material
- Use the in-chapter “Quick Practice”
- Learn the terminology
- Do the end-of-chapter study questions
- Review the Chapter Summary tear-out card
- Complete the Putting It All Together tear-out card
- Visit the CourseMate website

Behavioral Research

The goal of behavioral research is to understand the “laws of nature” that apply to the behaviors of living organisms.

Samples and Populations

- The entire group to which a law of nature applies is the population
- A sample is a relatively small subset of a population intended to represent, or stand in for, the population
- The individuals measured in a sample are called the participants

Samples and Populations

- Use the scores in a sample to infer—that is, to estimate—the scores we would expect to find in the population.
- This assumes a sample is representative of the population.
- If a sample is unrepresentative, it inaccurately reflects the population. Unrepresentative samples may give misleading results.

Understanding Variables

A variable is anything that can produce two or more different scores. Some common variables in behavioral research are:

- Age
- Race
- Gender
- Personality type
- Physical attributes

Types of Variables

The two categories of variables are:

- Quantitative variables in which a score indicates the amount of a variable that is present and
- Qualitative variables that classify or categorize an individual on the basis of some characteristic

Relationships

In a relationship, as the scores on one variable change, the scores on the other variable change in a consistent manner.

Types of Relationships

Simple relationships have one of two patterns. If we call one variable X and the other variable Y, then

- Pattern 1: The more you X, the more you Y
- Pattern 2: The more you X, the less you Y

Example: The more you drive distracted, the more likely it is you will have an accident (Pattern 1).

Relationship Consistency

- If a score on one variable is always paired with one and only one score on the other variable, we have a perfectly consistent relationship.
- Perfect consistency is not required to have a relationship, only some degree of consistency. This means as the scores on one variable change, the scores on the other variable tend to change in a consistent fashion.

Relationship Consistency

When essentially the same set of Y scores are paired with every X score, a relationship does not exist.

Applying Statistics

- Descriptive statistics are procedures for organizing and summarizing sample data
- Inferential statistics are procedures for drawing inferences about the scores and relationship that would be found in the population

Statistics Vs. Parameters

- A statistic is a number describing an aspect of the scores in a sample
- A parameter is a number describing an aspect of the scores in the population

Statistics Vs. Parameters

- Statistics are represented using English letters such as A, B, C, etc.
- Parameters are represented using Greek letters such as a, b, c, etc.

Research Designs

- A study’s design is the way the study is laid out
- Different designs require different descriptive and inferential procedures, so learn when to use each procedure
- There are two major types of designs:
- Experiments
- Correlational studies

Experiments

In an experiment, the researcher actively changes or manipulates one variable and then measures participants’ scores on another variable to see if a relationship is produced.

The Independent Variable

- The independent variable is changed or manipulated by the experimenter
- A condition is the specific amount or category of the independent variable creating the specific situation under which participants are studied

The Dependent Variable

The dependent variable is the variable measuring a behavior or attribute of participants we expect will be influenced by the independent variable.

Can You?

Identify the independent variable, the conditions of the independent variable, and the dependent variable for the following study:

The effect of an intensive summer school college preparatory program (compared to no program) on the GPAs of at-risk freshmen students.

Correlational Studies

In a correlational study,the researcher measures participants’ scores on two variables and then determines whether a relationship exists.

Measurement Scales

The kind of information scores convey depends on the scale of measurement used. There are four types of measurement scales:

- A nominal scale does not measure an amount; rather, it categorizes or classifies individuals.
- An ordinal scale indicates rank order. There is no score of 0 (zero), and the same amount does not separate every pair of adjacent scores.

Measurement Scales (cont’d)

- An interval scale indicates an actual quantity, and there is an equal amount separating any adjacent scores. Interval scales do not have a “true” 0.
- A ratio scale alsomeasures an actual quantity. There is an equal amount separating any adjacent scores, and 0 truly means none of the variable is present.

Continuous Versus Discrete

Any variable also may be either continuous or discrete.

- A continuous variable can be measured in fractional amounts and so decimals make sense
- A discrete variable can only be measured in fixed amounts, which cannot be broken into smaller amounts

Examples

For each of the following variables, indicate (1) the measurement scale and (2) whether it is continuous or discrete:

- The number of tickets sold to an event
- Your flavor preferences in soft drinks
- Weight
- IQ

Examples

The number of tickets sold to an event

- ratio, discrete

Your flavor preferences in soft drinks

- ordinal, discrete

Weight

- ratio, continuous

IQ

- interval, continuous

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