Statistics 2

Statistics Part Two

ANOVARelationships

T-test

• One independent variable of two samples of people

• Works for control/treatment pretest/posttest and posttest only designs

• Limited to two means being compared

Analysis of variance (ANOVA)

• Several levels of an independent variable• Several independent variables• Several different groups in dependent variable

Examples

• Two different ad copies for purchase intention of high, moderate, and low users (different groups for DV) use ANOVA

• Three different ad copies for purchase intention (3 levels for IV) use ANOVA

• Two different ad copies in print and video formats for purchase intention (2 IVs) use ANOVA

Extended example

• Want to examine effect of fear appeals on intentions to get flu shot– Compare high and low fear appeal on intention to

get flu shot• What is the IV?• What statistical test?

– Compare high, moderate, and low fear appeal on intention to get flu shot• What is the IV?• What statistical test?

Extended example

• Want to examine effect of fear appeals on intentions to get flu shot– Examine effect of high and low fear appeal on

three different ages: under 18, 18 to 25, and 26 to 50• What is the IV?• What statistical test?

Extended example

• Want to examine effect of fear appeals on intentions to get flu shot– High and low fear appeals– Web sites or blog posting of message• What is the IV?• What statistical test?

ANOVA

• Independent variables are called factors• One-way ANOVA has one independent

variable• Two-way ANOVA has two, etc• Use notation similar to factorial design– 2 x 2 ANOVA– Number of variables and levels of each variable

Assumptions

• Sample is normally distributed• Variance of each group is equal• Subjects randomly selected• Scores are independent

Statistics

• Significance level• Effects size (percent of variance explained)• Power

ANOVA application

• Can show if means are different– Significant– Meaningful

• If part of an experiment, can help to determine cause-effect– Change in fear appeal causes increase in flu shot

intention

Correlation

• It is a measure of the association, or co-variation of two or more dependent variables.

Correlation

• r scores range from -1 to +1• r= -1, perfect negative relation

example of a negative r: drinking in college and GPA

• r= 0, no relation example of a near zero r: hair length and GPA

• r= +1, perfect positive relation example of a positive r: GPA and scores on SAT

• Correlations have significance scores

Correlation and variance

• X and Y are the two variables• r2 = percent of variation accounted for by the

relation between x and y• Helps us address question of meaningful

Causation

• Correlation is first step toward causation but DOES NOT prove causation

• directionality problem:X <---> Y

• third variable problem: Z / \ X <----> Y

Example of faulty use

• Correlated trends in violent crime and trends in the publication of pornographic material

• This (upward) trend in the content of pornographic material is consistent with the Bureau of Justiceís recent study, showing an increase in crime and violence generally in North America

Example of faulty use

• Incidence of violent crime will positively correlate with anything that increased during the same period of time. Example: Correlation between the incidence of rape and membership in the Southern Baptist church was +.96 during the same time period

Again, correlation does not

• Prove directionality• Account for other variables (third variable

problem)

Partial correlation

• Remove (partial out) the influence of a potential third variable

Linear regression

• Use the association to predict • Score of one variable used to predict another

Simple linear regressions

Multiple regression

• Use two or more independent variables on a single dependent variable

• Can predict scores• Consider how much variance is explained

Regressions

• Have significance levels for each independent variable

• Have effects size through R squared (R2), coefficient of determination

Multiple regression

Prediction

• One goal of research is prediction• Regression helps to predict how change in one

or more variables (IVs) with affect another variable (DV)

• Use the information to create messages

Working example

• Test three IVs for flu shot intention– High verses moderate fear appeal (Fear appeal)– Vivid verses low key images (Images)– Statistics verses specific stories (Evidence)

Examples

• Regression analysis shows flu shot intentions can be predicted by (1) moderate fear appeal, (2) vivid image, and (3) specific story

• Advice for your campaigns– Moderate fear appeal– Vivid image– Specific story of a person affected by the flu

Causation?

• Regression is not causation either• Still a for of correlation--association

Causation example

• Effect of past crises (IV) on attributions of crisis responsibility (DV) and purchase intention (DV)

• Two scenarios, same organization and crisis. Difference is whether or not organization had a similar crisis in the past (manipulation of IV)

Causation example

• Hypotheses (predict differences)– Subjects exposed to crisis with crisis history will

report stronger attributions of crisis responsibility than subjects in the no crisis history condition.

– Subjects exposed to crisis with crisis history will report weaker purchase intentions than subjects in the no crisis history condition.

Causation example

• Random assignment to one of two conditions: previous crisis or no previous crisis

• Read crisis (Control exposure) and complete assessment of crisis responsibility and purchase intention measures (Control for order of events)

• ANOVA to compare for mean differences

Causation example

• ANOVA results– Crisis history condition had• Stronger crisis responsibility• Low purchase intention scores

– Effects size was moderate– Reject null hypothesis for both – Support for both hypotheses

Causation example

• Conclusion: crisis history does have a negative effect in a crisis

• Causes stronger attributions of crisis responsibility• Causes lower purchase intention

• Use information when creating crisis responses