Differences Between Population Averages

Testing the Difference Is there a difference between two populations? Null Hypothesis: H 0 or Alternate Hypothesis: H a or Test Statistic: If Z is too large or too small, reject Null Hypothesis

The Wallace and Gromit Hypothesis Potential Hypothesis about the Wallace and Gromit (W&G): –Males prefer W&G to Females –Greeks prefer the W&G over independents –If you have heard about W&G you will prefer them over people who have not heard of the W&G –If you have watched the W&G you will prefer them over people who have not watched the W&G –If you have lived outside the USA for more than 6 months you will prefer W&G over people who have lived in the USA –A greater percentage of people who have lived outside of the USA have watched W&G previously

The Wallace and Gromit Hypothesis

Hypothesized Mean How Unusual is Z = ?

The Wallace and Gromit Hypothesis p-value pr(z 0.858) = 2xpr(z>0.858) = 2x =

Dummy Variable Regression Formula –Rating (like W&G): –Overall mean, Average for Female: –Adjustment for being Male Adjustment: Dummy Variable: –Error Term to Represent Uncertainty:

Dummy Variable Regression Data –Observed Rating: How much like W&G –Dummy Variable: Identifies Gender

Dummy Variable Regression Estimate For Average Female Estimate For Average Male because

Regression Output, Using SPSS

Is there a difference? Automatic Hypothesis Test is Conducted by SPSS Test 1-- Null Hypothesis: H 0 Test 2-- Null Hypothesis: H 0

Is there a difference? If t is far away from zero reject the Null Hypothesis The t-statistic for :

Is there a difference? If t is far away from zero reject the Null Hypothesis The t-statistic for How unusual is this t-statistic?

Is there a difference? If t is far away from zero reject the Null Hypothesis The t-statistic for How unusual is this t-statistic? sig = p-value If p-value < 0.05, reject

Is there a difference? If t is far away from zero reject the Null Hypothesis The t-statistic for :

Is there a difference? If t is far away from zero reject the Null Hypothesis The t-statistic for : How unusual is this t-statistic?

Is there a difference? If t is far away from zero reject the Null Hypothesis The t-statistic for : How unusual is this t-statistic? sig = p-value If p-value < 0.05, reject

Dummy Variable Regression Estimate For Average Female because

Dummy Variable Regression Estimate For Average Female Estimate For Average Male because

Difference Not Significant Run the Analysis Again Using

Difference Not Significant Run the Analysis Again Using No difference between Male and Female, use the overall average.

Designing The Lion King Assume That There Were 4 Different Jokes That Could Have Been Used. Which Joke Should They Use?

The Data 500 Randomly Chosen People Saw one of Four Different Version of the Lion King—Different Jokes for Each Version. The Rated the Lion King on a likert Scale of 1 to 7 With Regards to How Much the Enjoyed the Lion King.

The Data

Dummy Variable Regression Need 3 Dummy Variables To Describe 4 Categories

Dummy Variable Regression Estimate For Average Viewer That Saw Joke 1?

Dummy Variable Regression Estimate For Average Viewer That Saw Joke 1? Estimate For Average Viewer That Saw Joke 2?

Dummy Variable Regression Estimated Response for Average Viewer that Saw Joke 1?

Dummy Variable Regression Increase in Response if They Saw Joke 2 instead of Joke 1

Dummy Variable Regression Is There a Difference Between Response for Joke 1 the Joke 2?

Dummy Variable Regression Is There a Difference Between Response for Joke 1 and Joke 3?

Dummy Variable Regression Is There a Difference Between Response for Joke 2 and Joke 3?

Analysis of Variance Analysis of Variance (ANOVA) –Allows for Testing Whether Means are Different

Analysis of Variance Analysis of Variance (ANOVA) –Allows for Testing Whether Means are Different –Tests the Claim that Each Group Has the Same Average Value

Analysis of Variance Analysis of Variance (ANOVA) –Allows for Testing Whether Means are Different –Tests the Claim that Each Group Has the Same Average Value –Is Based on Analyzing different types of Variance Variance From Individuals with-in a group Variance Between Different Groups

Overall Average Sum of Squares: Between Groups Sum of Squares: With-in Groups If Between Group Variance is “Large” Compared to With-in Group Variance, Reject the Idea that All of the Groups have the Same Mean.

ANOVA Output from SPSS F-statistic Tests Hypothesis that Each Group has the Same Mean (Average Value).

ANOVA Output from SPSS F-statistic Tests Hypothesis that Each Group has the Same Mean (Average Value). Large F-statistic, Reject the Hypothesis. At least two Groups have Different Means

ANOVA Output from SPSS Joke 4 is Different from Joke 1, 2 and 3. Joke 1 and 3 are not Different from each other. They are Different from Joke 2 and 4. Joke 2 is Different from Joke 1, 3 and 4.