statistics for the social sciences psychology 340 spring 2005 course review

Statistics for the Social Sciences

Psychology 340Spring 2005

Course Review


The Relationship Among Major Statistical Methods

• The general linear model

General

Specialized

Multiple regression/correlation

Bivariatecorrelatio

nANOVA

t-test


The General Linear Model

μY = β0 + β1X1 + β2X2 + β 3X3 + β 4X4 + ... + ε

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

• Bivariate regression & Bivariate correlation– Special case of multiple regression

μY = β0 + β1X1 + ε




General

Specialized


Bivariatecorrelatio

nANOVA

t-test


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

2tF = Ft =


Links Between the t Test for Independent Means and ANOVA




General

Specialized


Bivariatecorrelatio

nANOVA

t-test


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

ANOVA Correlation/RegressionSSWithin = SSError

SSTotal= SSTotal

SSBetween = SSTotal – SSError

R2 = r2

ANOVA Correlation/RegressionSSWithin = SSError

SSTotal= SSTotal

SSBetween = SSTotal – SSError

R2 = r2

μY = β0 + β1X1 + ε

Exp. Control

corresponds to the main effect

β1 X has two valuesExp & Control

X has two valuesExp & Control

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



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

μY = β0 + β1X1 + β2X2 + β 3X3 + ... + ε

Nominal coding



– Factorial ANOVA: • Each main effect will have have a β associated with it.

• Each interaction term will also have a β associated with it.

μY = β0 + β1X1 + β2X2 + β 3X3 + β 4X4 + ... + ε

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




General

Specialized


Bivariatecorrelatio

nANOVA

t-test


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 Pearson’s r

t =r( ) n−2( )

1−r2


Relation Between Correlation and t Test for Independent Means


Choice of Statistical Tests

General

Specialized


Bivariatecorrelatio

nANOVA

t-test

• 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


Final Exam

– Basic Probability– Discriptive statistics• Means• Standard deviation

– Normal Distribution– Distribution of sample means (Central Limit Theorem)

– Error types• Type 1 ()• Type 2 (β)• Statistical power

– Hypothesis testing• 1-sample z test• T-tests

– 1-sample– Related samples– Independent samples

• ANOVA– 1 factor– Factorial

• Correlation & regression

• Topics

statistics for the social sciences psychology 340 spring 2005 course review

Documents