Statistics: A Tool ForSocial Research

Seventh EditionJoseph F. Healey

Chapter 1

Introduction

Chapter Outline

Why Study Statistics? The Role of Statistics in Scientific

Inquiry The Goals of This Text Descriptive and Inferential Statistics Discrete and Continuous Variables Level of Measurement

In This Presentation

The role of statistics in the research process

Statistical applications Types of variables

The Role Of Statistics

Statistics are mathematical tools used to organize, summarize, and manipulate data.

Data

Scores on variables. Information expressed as numbers

(quantitatively).

Variables

Traits that can change values from case to case.

Examples: Age Gender Race Social class

Case The entity from which data is gathered. Examples

People Groups States and nations

The Role Of Statistics:Example

Describe the age of students in this class.

Identify the following: Variable Data Cases Appropriate statistics

The Role Of Statistics: Example

Variable is age. Data is the actual agesactual ages (or scores

on the variable age): 18, 22, 23, etc. Cases are the students.

The Role Of Statistics: Example

Appropriate statistics include: average - average age of students in

this class is 21.7 years. percentage - 15% of students are older

than 25

Statistical Applications

Two main statistical applications: Descriptive statistics Inferential statistics

Descriptive Statistics

Summarize variables one at a time. Summarize the relationship between

two or more variables.

Descriptive Statistics

Univariate descriptive statistics include: Percentages, averages, and various

charts and graphs. Example: On the average, students are

20.3 years of age.

Descriptive Statistics

Bivariate descriptive statistics describe the strength and direction of the relationship between two variables. Example: Older students have higher

GPAs.

Descriptive Statistics

Multivariate descriptive statistics describe the relationships between three or more variables. Example: Grades increase with age for

females but not for males.

Inferential Statistics

Generalize from a sample to a population. Population includes all cases in

which the research is interested. Samples include carefully chosen

subsets of the population.

Inferential Statistics Voter surveys are a common

application of inferential statistics. Several thousand carefully selected

voters are interviewed about their voting intentions.

This information is used to estimate the intentions of all voters (millions of people).

Example: The Republican candidate will receive about 42% of the vote.

Types Of Variables

Variables may be: Independent or dependent Discrete or continuous Nominal, ordinal, or interval-ratio

Types Of Variables

In causal relationships: CAUSE EFFECTindependent variable dependent variable

Types Of Variables

Discrete variables are measured in units that cannot be subdivided. Example: Number of children

Continuous variables are measured in a unit that can be subdivided infinitely. Example: Age

Level Of Measurement

The mathematical quality of the scores of a variable. Nominal - Scores are labels only, they

are not numbers. Ordinal - Scores have some numerical

quality and can be ranked. Interval-ratio - Scores are numbers.

Nominal Level Variables

Scores are different from each other but cannot be treated as numbers. Examples:

Gender 1 = Female, 2 = Male

Race 1 = White, 2 =Black, 3 = Hispanic

Religion 1 = Protestant, 2 = Catholic

Ordinal Level Variables

Scores can be ranked from high to low or from more to less.

Survey items that measure opinions and attitudes are typically ordinal.

Ordinal Level Variables: Example

“Do you agree or disagree that University Health Services should offer free contraceptives?” A student that agreed would be more in

favor than a student who disagreed. If you can distinguish between the

scores of the variable using terms such as “more, less, higher, or lower” the variable is ordinal.

Interval-ratio Variables

Scores are actual numbers and have a true zero point and equal intervals between scores.

Examples: Age (in years) Income (in dollars) Number of children

A true zero point (0 = no children) Equal intervals: each child adds one unit

Level of Measurement

Different statistics require different mathematical operations (ranking, addition, square root, etc.)

The level of measurement of a variable tells us which statistics are permissible and appropriate.