Assignment 1
Rock1027
T-TestANOVAMultipleRegression.pptx9. T-test/ANOVA/Multiple Regression
CONTENT
T-test
ANOVA
Regression
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T-test
Difference between two groups
Difference in one interval variable between two categories in one nominal variable
Different in attitude between two gender groups
Difference in one ratio variable between two categories in one nominal variable
Difference in sales volume between two car models
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T-test
Sample data
09_T-test ANOVA
X1: Sales volume
X2: Car model
1: 811
2: Coxtan
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Data View
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Variable View
Analyze ->Compare Means -> Independent-Samples T Test
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Select Sales (X1) from the variable list and next click on the top arrow to enter it into Test Variable(s)
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Sales (X1) is now in Test Variable(s). Select Model (X2) from the variable list and next click on the bottom arrow to enter it into Grouping Variable.
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Model (X2) now in Grouping Variable, click on Define Groups.
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On Define Groups, enter 1 in Group 1, which refers to 811 in X2, and 2 in Group 2, which refers to Coxtan in X2. Next, click on Continue to close this window.
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Click on OK to run the t-test.
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Below is the output for the t-test. The first table “Group Statistics” reports the sales of the two models. The second table “Independent Samples Test” reports the results of the difference test, and the difference test is insignificant (Sig (2-tailed) = .382 > .05).
Interpretation: On average, 86.5 units of 811 were sold and 84.5 units of Coxtan were sold. There is no difference in sales volume between 811 and Coxtan.
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Hypothetically, there was another study that compared the difference in sales between A9 and Zebra. Below is the output for that hypothetical t-test. In the second table “Independent Samples Test,” the difference test is significant (Sig (2-tailed) = .001 < .05).
Interpretation: On average, 90 units of A9 were sold and 60 units of Zebra were sold. The sales volume of A9 is significantly higher than that of Zebra.
ANOVA
Difference between three or more groups
Difference in one interval variable between three or more categories in one nominal variable
Different in attitude across three income groups (low, middle-class, high)
Difference in one ratio variable between three or more categories in one nominal variable
Difference in sales volume across three countries
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ANOVA
Sample data
09_T-test ANOVA
X1: Sale volume
X3: Country
1: France
2: Germany
3: Italy
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Variable View
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Analyze ->Compare Means -> One-Way ANOVA
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Select Sales (X1) from the variable list and next click on the top arrow to enter it into Dependent List
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Sales (X1) is now in Dependent List. Select Country (X3) from the variable list and next click on the bottom arrow to enter it into Factor.
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Country (X3) now in Factor, click on Post Hoc.
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Post Hoc
ANOVA only exams whether there is any difference across three or more groups.
ANOVA doesn’t pinpoint which two groups are different from each other.
Post Hoc tests compare the difference between every two groups
Scheffe Post Hoc test is preferred it is more robust.
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On One-Way ANOVA: Post Hoc Multiple…, check Scheffe. Next, click on Continue to close this window.
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Click on OK to run the ANOVA test.
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Below is the output for the ANOVA (more on the next slides). The first table “ANOVA” reports the difference test across the three countries, and the difference test is significant (Sig = .000 < .05).
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The second table “Multiple Comparisons” reports the Scheffle Post Hoc tests between every two of the three countries. Germany is significantly different from both France (Sig = .000 < .05) and Italy (Sig = .011 < .05), but France is not different from Italy (Sig = .173 > .05).
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The third table “Homogeneous Subsets” not only groups countries that are not different in sales based on the Scheffe test but also reports the sales in each country.
Interpretation for the entire output: On average, 81 units were sold in France, 84.63 units were sold in Italy, and 90.88 units were sold in Germany. There is no difference in sales volume between France and Italy. There are significant differences in sales volume between Germany and France and between Germany and Italy.
Homogeneous Subsets
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Hypothetically, there was another study that compared the difference across China, Japan, and Korea. The first table “ANOVA” reports the difference test across the three countries, and the difference test is insignificant (Sig = .755 > .05).
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The second table “Multiple Comparisons” reports the Scheffle Post Hoc tests between every two of the three countries. No country is different from any of the other two: Sig = .185 > .05 between China and Japan; Sig = .165 > .05 between China and Korea; Sig = .201 > .05 between Japan and Korea.
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The third table “Homogeneous Subsets” groups all the three countries in one group based on the Scheffe test and also reports the sales in each country.
Interpretation for the entire output: On average, 50 units were sold in China, 52 units were sold in Japan, and 53 units were sold in Korea. There is no difference in sales volume across the three countries.
Homogeneous Subsets
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Regression
Dependent variables: Y
Interval/ratio variables
Attitude toward brand
Sales volume
Independent variables: X
Interval/ratio variables
Knowledge about brand
Expenditure on advertising, sales promotion
Y = a + b1X1 + b2X2 + …..
Regression Coefficients: b
The relative impact (significant or insignificant) of the independent variables in predicting dependent variable
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Regression
Sample data
09_Regression
Y: Sales volume in millions of $
X1: Advertising expenditure in millions of $
X2: Sales promotion in millions of $
Are X1 and X2 significant predictors of Y?
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Analyze -> Regression -> Linear
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Select Sales in million $ (Y) from the variable list, and click on the top arrow to enter it into Dependent.
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Sales in million $ (Y) is now in Dependent. Select Advertising in million $ X1 from the variable list, and click on the second arrow from the top to enter it into Independent(s).
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Select Sales Promotion in million $ from the variable list, and click on the second arrow from the top again to enter it into Independent(s).
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All independent variables are entered into Independent(s). Then click on “OK” to run regression.
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SPSS gives you more outputs than you need. You only need the “Coefficients” table to determine the relative impact of the independent variables in predicting the dependent variable. In this analysis, the coefficient for Advertising in million $ is .329, and it is an insignificant predictor of Sales in million $ (Sig = .199 > .05). The coefficient for Sale Promotion in million $ is .634, and it is a significant predictor of Sales in million $ (Sig = .029 < .05).
Interpretation: Sales promotion has a significant positive impact on sales volume, whereas advertising has no impact on sales volume.
WRAP-UP
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Difference between T-test and ANOVA
Functions of T-test/ANOVA/Regression
SPSS procedures for T-test/ANOVA/Regression
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