Multivariate Statistics Analyzing More than One Variable at a Time

1. Multivariate StatisticsAnalyzing More than One Variable at a Time 1. Chi Square for two variables 2. T-test for two means 3. ANOVA 4. Regression

2. Chi-square for Two Variables • When to use: • number of variables ________ • scaling of variables ________ • Basic Idea: • Compare the values you actually get from your study to the values you would expect if there was ____________between the two variables

3. Chi-square for Two Variables • Ho: There is no relationship between ____ and _____ • Ha: There is a relationship between ____ and _____; SPECIFICALLY _________________ • NO CALCULATIONS!! SPSS DOES THIS ONE

4. Chi-Square for Two Variables • COMPARE: • Alpha level • Probability level

5. Do it yourself using SPSS • Want to test the relationship between gender and drinking a soft drink for breakfast • Ho: • Ha: • Chi-square calculated: • Use pearson chi square • P-value level: • Alpha level • Phi: • Conclusion:

6. Chi-Square for Two Variables If the p-value is > .05, ____________ Ho, conclude________________ If the probability level is < .05 then ______ Ho, conclude ______________ (Make sure to specify the nature of the relationship). CAREFUL--Do not just assume that the relationship you predicted is correct

7. If you Reject HO – AND ONLY IF YOU REJECT HOLook at Phi to determine how strong the relationship is…. • Phi < 0.10 is ______ • Between 0.11 and 0.40 is __________ • Phi > 0.40 is _______

8. T-test for Two Means • When to use: • Number of variables = _______ • One variable (the groups) is _______ scaled (in SPSS = “grouping variable”) • One variable (the dependent variable) is ________ scaled (in SPSS = “test variable”

9. Hypotheses for T-test for Two Means • Is there a difference between the number of sodas males drink per day and the number of sodas females drink per day? • Ho: The two groups are the same with respect to __________. • Ha: The two groups are different with respect to _______. Specifically, ______________.

10. More on T-tests for Two Means • No calculations • STEP 1: Check to see if variances are equal or unequal • Look at “Levene’s Test Equality of Variances” – • Ho: variances are equal • Ha: variances are not equal • If (sig) p>.05 accept Ho and use equal variances • If (sig) p<.05 reject Ho and use unequal variances

11. More on T-tests for two means • STEP 2: Check the T-test table to see if you should accept or reject your Ho: • T-value = • (either for equal or unequal variance depending on Step 1) • P-value =

12. Rules • If the probability level is > 0.05, then ________ Ho. Conclude that the two groups are the same. • If the probability level is < 0.05, then __________ Ho. Conclude that the two groups are different. LOOK AT THE DATA TO DETERMINE WHAT THE DIFFERENCE IS.

13. Your Turn • Is there a difference in the number of sodas drunk per day between people who drink soda with breakfast, and people who do not? • Nominal variable= ___________ • Interval variable = ___________ • Ho: • Ha: • Probability level • Conclude--reject or do not reject ho • Managerial Implication

14. ANOVA • When to use: • Testing mean differences between groups • Have more than 2 groups • Want to test interactions between 2 variables • Same as a t-test except that you have more than two groups • Number of variables = _______ • Some variables (the groups) are _______ scaled (in SPSS = “fixed factors”) • One variable (the dependent variable) is ________ scaled

15. One –Way ANOVA • Ho: all the means are equal • Ha: one of the means differs (specify how the mean differs)

16. Do it yourself using SPSS • You want to test whether age has an impact on the number of sodas consumed per day HO: HA:

17. X 18-24 = • X 25-29= • X 30-34 = • X 35-39 = • X >40 = • F-calculated • Alpha • P-value (sig) • Conclusion:

18. Interactions- Two Way ANOVA • Want to test interactions between 2 variables • You want to see if drinking a soft drink for breakfast and gender interact to have an impact on the number of soft drinks consumed per day. E.g. males who drink a soft drink for breakfast tend to drink more (and it has a synergistic effect) • HO: • HA:

19. Look at “Interaction Effects” – the combined effect of both variables together NOTE - if interaction is significant then do NOT look at Main effects • Look at “Main Effects” – the impact of each variable independent of the others

20. Overall F Variable 1 F= Variable 2 F = Interaction = Adjusted R2 = INTERPRETATION: P-value (sig) P-value 1 (sig) = P-value 2 (sig) = P-value (sig) =

21. REGRESSION Trying to predict/forecast some outcome or behavior Specify a probabilistic model (basically fitting a line to data): Y = C + 1X1 + 2X2 + 3X3 + Y = dependent variable X1,2,3… are the independent variables

22. Example • You believe that the number of soda’s consumed per day is a function of availability, selection and price of soft drinks • Specify your model: Perday = C + 1Availabilty+ 2selection + 3Price +

23. Run the model • Insert the Coefficient and Unstandardized Beta’s into the model • Look at the overall model significance • If the overall model is not significant then don’t go any further. • BUT if the overall model is significant, then: • Look at t-values and p-values to see which variables are significant • Check R2