Review of Factorial ANOVA, correlations and reliability tests

COMM 420.8

Fall, 2007

Nan Yu

Factorial ANOVA(ANOVAdata.sav)More than one IV, both are nominal,DV is interval or ratio-level

Behavioral intention will vary as a function of the type of ads that are featured on the web site and the gender of the participants.

IVs? DV?

Put the interval orratio-level variablehere. (DV)

Put the variablesrepresenting thegroups here. (IVs)

Then Click "Options"

Put the group variable in the right window. Then click "continue" and "Ok."

Select Compare main effects, Descriptive Statistics, Estimates of effect size, Homogeneity tests.

Tests of Between-Subjects Effects

Dependent Variable: binent-Behavioral Intention

26.478a 7 3.783 5.333 .000 .341

689.535 1 689.535 972.217 .000 .931

1.573 3 .524 .739 .532 .030

22.377 1 22.377 31.551 .000 .305

2.528 3 .843 1.188 .320 .047

51.065 72 .709

767.079 80

77.544 79

SourceCorrected Model

Intercept

condit

gender

condit * gender

Error

Total

Corrected Total

Type III Sumof Squares df Mean Square F Sig.

Partial EtaSquared

R Squared = .341 (Adjusted R Squared = .277)a.

Main Effects

Interaction

Test statisticsDegrees of freedom P-values

Significant main effect for Gender, F (1, 72) = 31.55, < . 001, partial η2 = .31

No significant Main Effect for Condition, F (3, 72) = .74, p =.53, partial η2 = .03

No significant Gender X Condition interaction, F (3, 72) = 1.19, p =.32, partial η2 = .05

Effect size

Creating Graphs

Highlight these two numbers with mouse, right click

Create Graph Bar

Significant main effect for Gender, F (1, 72) = 31.55, < . 001, partial η2 = .31

Male Female

gender-Gender of Respondent

0.000

1.000

2.000

3.000V

alu

es

2.407

3.465

Estimates

Dependent Variable : binent-Behavioral IntentionStatistics : Mean

Text Only Static Ad Animated Ad Pop-up Ad

condit-Condition

0.000

1.000

2.000

3.000

Val

ues

2.822

3.160

2.8132.949

Estimates

Dependent Variable : binent-Behavioral IntentionStatistics : Mean

No significant main effect for Condition, F (3, 72) = .74, p =.53, partial η2 = .03

How to Create Line Graphs for Interaction Effects?

3. condit-Condition * gender-Gender of Respondent

Dependent Variable: binent-Behavioral Intention

2.007 .266 1.476 2.538

3.636 .266 3.105 4.167

2.818 .266 2.287 3.349

3.502 .266 2.971 4.033

2.282 .266 1.751 2.813

3.344 .266 2.813 3.875

2.520 .266 1.989 3.051

3.377 .266 2.846 3.908

gender-Genderof RespondentMale

Female

Male

Female

Male

Female

Male

Female

condit-ConditionText Only

Static Ad

Animated Ad

Pop-up Ad

Mean Std. Error Lower Bound Upper Bound

95% Confidence Interval

Double click this table, then right

click

Select Pivoting Trays

Move the small square from

bottom to the left

Then, the means table will

look at this.

Highlight these numbers with mouse, then right click

Create Graph Line

Graphs for the Interaction Effects

Text Only

Static Ad

Animated Ad

Pop-up Ad

condit-Condition

Male Female

gender-Gender of Respondent

2.000

2.500

3.000

3.500

Val

ues

3. condit-Condition * gender-Gender of Respondent

Dependent Variable : binent-Behavioral IntentionStatistics : Mean

No significant Gender X Condition interaction, F (3, 72) = 1.19, p =.32, partial η2 = .05

These lines are not parallel, we can suspect that there might be interaction effects. But they are not statistically significant.

Correlations

Correlations indicate the strength and direction of the relationship between variables.

Correlation Coefficients

Dichotomous (dummy coded)Male=0Female=1

Low=0High=1

Hypothesis for correlations

People’s liking toward sad movies will be positively related to the liking toward horror movies.

Two variables, both interval.

SPSS and correlations

Go to Analyze Correlate Bivariate

SPSS and correlations

Put the two variablesin this box, click OK

Correlations

1 .276**

.002

124 124

.276** 1

.002

124 124

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Liking of Movie Sad Films

Liking of Movie Horror

Liking ofMovie Sad

FilmsLiking of

Movie Horror

Correlation is significant at the 0.01 level (2-tailed).**.

r=.28, p<.01

Consistent with the Hypothesis, respondents’ rating of their liking of sad files was significantly positively associated with their ratings of horror movies, r=.28, p<.01.

Reliability Test

If multiple interval of ratio measures were used to measure one construct, we need to know whether these measures are “hanging together” or not.

Measurement of Fear:Scared 1 2 3 4 5Frightened 1 2 3 4 5Nervous 1 2 3 4 5

SPSS and Correlation

Please open Correlationdata.sav

Three items were used to measure “happiness”

happy 1 2 3 4 5 6 7

content 1 2 3 4 5 6 7

joyful 1 2 3 4 5 6 7

SPSS and Reliability Test

Go to Analyze Scale Reliability Analysis

Cronbach’s Alpha:

Reliability Statistics

.901 3

Cronbach'sAlpha N of Items

Item-Total Statistics

8.3468 11.269 .843 .823

7.7984 13.463 .753 .899

7.7903 12.135 .819 .844

Mood: happiness

Mood: content

Mood: joyful

Scale Mean ifItem Deleted

ScaleVariance if

Item Deleted

CorrectedItem-TotalCorrelation

Cronbach'sAlpha if Item

Deleted

If this number is greater than .70, meaning that three items

hang together well

Here you can see the changes of the reliability if one item is deleted,

1. Are both variables nominal?

2. Are both variables interval or ratio?

No (continue)

Chi-Square Test

No (skip to 3)

2a. Are you examining associations between variables? Correlation

2b. Are you comparing means of two variables?Paired T-Test

3. Assuming that some variables are nominal and some are interval / ratio...

3a. Are you comparing means between 2 groups? (IV is nominal with 2 levels, DV is interval or ratio)

ANOVA

3c. Are you comparing means as a function of more than 2 IV s (a factorial analysis)?

Factorial ANOVA

Decision Tree for Data Analysis

3b. Are you comparing means between more than 2 groups? (IV is nominal with more than 2 levels, DV is interval or ratio)

Independent sample T-test

In-Class Practice

Use the dataset of correlationdata.sav to

Test the following hypothesis:

Liking toward TV sports is positively related to total TV viewing per day. (tsports, totaltv)

Can we reject the null? (Report the correlations and significance levels).

Answers to In-Class Practice

Yes, we can reject the null.

r=.19, p<.05

Consistent with the hypothesis, liking toward TV sports is positively related to total TV viewing per day, r=.19, p<.05