Statistics for the Social Sciences

1
Statistics for the Social Sciences

• Psychology 340
• Spring 2005

Course Review
2
The Relationship Among Major Statistical Methods

• The general linear model

Multiple regression/correlation
Bivariate correlation
ANOVA
t-test
3
The Relationship Among Major Statistical Methods

• The general linear model

Multiple regression/correlation
Bivariate correlation
ANOVA
t-test
4
The General Linear Model

• Multiple correlation (R)
• Proportionate reduction in error (R2)

• Bivariate regression Bivariate correlation
• Special case of multiple regression

5
The Relationship Among Major Statistical Methods

• The general linear model

Multiple regression/correlation
Bivariate correlation
ANOVA
t-test
6
The t Test as a Special Case of ANOVA

• t test
• Two groups
• ANOVA (F ratio)
• More than two groups
• Parallels in their basic logic
• Numeric relationship of the procedures

7
Links Between the t Test for Independent Means
and ANOVA
8
The Relationship Among Major Statistical Methods

• The general linear model

Multiple regression/correlation
Bivariate correlation
ANOVA
t-test
9
ANOVA as a Special Case of the Significance Test
of Multiple Regression

• ANOVA for two groups as a special case of the
  significance of a bivariate correlation

• ANOVA Correlation/Regression
• SSWithin SSError
• SSTotal SSTotal
• SSBetween SSTotal SSError
• R2 r2

10
ANOVA as a Special Case of the Significance Test
of Multiple Regression

• ANOVA for more than two groups as a special case
  of the significance of a multiple correlation

11
ANOVA as a Special Case of the Significance Test
of Multiple Regression

• ANOVA for more than two groups as a special case
  of the significance of a multiple correlation

• Factorial ANOVA
• Each main effect will have have a ? associated
  with it.
• Each interaction term will also have a ?
  associated with it.

12
The Relationship Among Major Statistical Methods

• The general linear model

Multiple regression/correlation
Bivariate correlation
ANOVA
t-test
13
The t Test as a Special Case of the Significance
Test for the Correlation Coefficient

• Correlation coefficient
• Degree of association between two variables
• t test
• Significance of the difference between the two
  population means
• Both use the t distribution to determine
  significance
• Recall test statistic to test significance of
  Pearsons r

14
Relation Between Correlation and t Test for
Independent Means
15
Choice of Statistical Tests

• t test, ANOVA, and correlation can all be done as
  multiple regression
• However, each usually used in specific research
  contexts
• Correlation and regression automatically give
  estimates of effect size and not just significance

16
Final Exam

• Topics

• Basic Probability
• Discriptive statistics
• Means
• Standard deviation
• Normal Distribution
• Distribution of sample means (Central Limit
  Theorem)
• Error types
• Type 1 (?)
• Type 2 (?)
• Statistical power

• Hypothesis testing
• 1-sample z test
• T-tests
• 1-sample
• Related samples
• Independent samples
• ANOVA
• 1 factor
• Factorial
• Correlation regression