Statistics: Introduction Healey Ch. 1

Outline 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 Concepts in numerical form that can vary in value 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. actual ages Data is the actual 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 Conservative 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  EFFECT independent variable  dependent variable Independent variables (“causal” or “explanatory”) are those that are manipulated. Designated as X. Dependent (“outcome” or “response” variables are only measured or registered. Designated as Y.

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

Relations Between Variables Hypothesis: a statement that describes the relationship between two or more variables. Null hypothesis: What is actually tested in a statistical test Alternate hypothesis: The research hypothesis. “Rejection” of the null builds up evidence for the research hypothesis

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 = Other Religion  1 = Protestant, 2 = Catholic, 3 = Other

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 (see note p. 22) Scores are actual numbers and have a true zero point (ratio) 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.

In Class Exercise Chapter 1: 1.4 a-j and 1.5 a-j.