msu/~whitery2/mkt317slides.html

1. www.msu.edu/~whitery2/mkt317slides.html Slides are available at:

2. Type I Error / Type II Error Levels of Measurement (NOIR) Test of Two Means (t or z) Paired Samples (t test) Two Proportions (z test) F–test One Way ANOVA Tukey test Two Way Anova w/ Interactions Simple Regression Correlation Multiple Regression Adjusted R2 Dummy Variables Time Series Autoregressive Model Moving (Centered) Average Seasonal Index Chi-Square Goodness of Fit Chi-Square Test of Independence *p value TOPICS COVERED

3. Error Types • Type 1: Rejecting a True H0 • Type 2: Accepting a False H0

4. Levels of Measurement (NOIR) Nominal: IDENTIFY Ordinal: ORDER Interval: COMPARE INTERVALS Ratio: COMPARE ABSOLUTE MAGNITUDES

5. Test of Two Means (t or z) Criterion: n > 30 for both: z-Test n < 30 for either: t-Test H0: μ1 – μ2 = ≤ ≥ 0 H1: μ1 – μ2≠< > 0 df = n1 + n2 - 2 T FORMULA Z FORMULA

6. Paired Samples (t test) • How to know a paired sample test: • Average difference or D-BAR given H0: μD= ≤ ≥ 0 H1: μD≠< > 0 df = n-1

7. Two Proportions (z test) D0 = ????? D0 = 0 POOL D0≠ 0 NOT POOL H0: p1 – p2 = ≤ ≥ 0 H1: p1 – p2≠< > 0

8. F–test • Test of Equality of Variance (σ2) • H0: σ12= ≤ ≥σ22H1: σ12≠ < > σ22 • Dfnum = (n of sample in numerator – 1) • Dfdenom = (n of sample in denominator – 1)

9. One Way ANOVA n = total sample size r = number of groups H0: μ1 = μ2 = … μr H1: not all means equal df = r-1, n-r

10. Tukey test • Which means are different? H0: μi = μj for each pair of means H1: μi ≠ μj for at least one pair of means Reject H0 if r = number of groups n = total sample size

11. Two Way ANOVA w/Interactions • Effects on means due to: • factor a (αi ) • factor b (βj) • and interaction between factor a and factor b (αβij) H0: αi = 0, for all i=1 to α H1: not all αi = 0 H0: βj = 0, for all j=1 to β H1: not all βj = 0 H0: α βij = 0, for all i and j H1: not all αβij = 0

12. Two Way ANOVA w/Interactions(cont.) a= number of levels of a b= number of levels of b n= sample size per cell (combination of a and b)

13. Simple Regression • Parameter estimates • Coefficient of determination • Overall model test H0: β1=0 H1: β1≠0 • Individual parameters test H0: β1=0 H1: β1≠0 • Confidence intervals

14. Correlation H0: ρ = 0 H1: ρ ≠ 0 -1 = Strong negative (inverse) relationship 0 = no linear relationship +1 = strong positive (direct) relationship

15. Multiple Regression • Overall model test H0: β1=… βi=0 H1: at least one βi≠0 • Individual parameters test H0: β1=0 H1: β1≠0 H0: β2=0 H1: β2≠0 • Coefficient of Multiple Determination • Adjusted R2 • Confidence intervals

16. Dummy Variables Example Four Seasons: Winter, Spring, Summer, Fall

17. TIME SERIES

18. Autoregressive Model

19. Moving Average and Centered Moving Average

20. Seasonal Index Average of Ratio to Centered Moving Average for same time periods Given a seasonal index of .932 adjusted the predicted sales value of 5.03: 5.03 * .932 = 4.69

21. Chi-Square Goodness of Fit K = number of categories Oi = the observed frequency Ei = the expected frequency df = K-1 Ei = n*pi n = sample size pi = appropriate probability from the null hypothesis Proportions are the same: H0: p1 = p2 = p3 = …pk H1: at least one proportion is not equal Proportions are not all the same: H0: p1 = p1H0 ... pk = pkH0

22. Chi-Square Test of Independence Oij = observed value for cell ij Ei = expected value for cell ij df = (r-1)(c-1) Eij = (ri*cj)/n n = sample size H0: The two classification variables are independent. H1: The two classification variables are not independent.

23. P-Value p value < alpha: REJECT H0 p value > alpha: DO NOT REJECT H0