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MKTG 368 All Statistics PowerPoints

MKTG 368 All Statistics PowerPoints. Setting Up Null and Alternative Hypotheses One-tailed vs. Two-Tailed Hypotheses Single Sample T-Test Paired Samples T-Test Independent Samples T-Test ANOVA Correlation and Regression One-Way and Two-Way Chi-Square.

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MKTG 368 All Statistics PowerPoints

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  1. MKTG 368All Statistics PowerPoints • Setting Up Null and Alternative Hypotheses • One-tailed vs. Two-Tailed Hypotheses • Single Sample T-Test • Paired Samples T-Test • Independent Samples T-Test • ANOVA • Correlation and Regression • One-Way and Two-Way Chi-Square

  2. Translating a Problem StatementInto the Null and Alternative Hypotheses

  3. Initial Problem Statement Example: • Let’s say we are interested in whether a flyer increases contributions to National Public Radio. We know that last year the average contribution was $52. This year, we sent out a flyer to 30 people explaining the benefits of NPR and asked for donations. This year’s average contribution with the flyer ended up being $55, with a standard deviation of $12. • How do we translate this into the null and alternative hypotheses (in terms of both a sentence and a formula)?

  4. Gleaning Information from the Statement Direction of Alternative Hypothesis Example: • Let’s say we are interested in whether a flyer increasescontributions to National Public Radio. We know that last year the average contribution was $52. This year, we sent out a flyer to 30 people explaining the benefits of NPR and asked for donations. This year’s average contribution with the flyer ended up being $55, with a standard deviation of $12. Population Information Sample Information

  5. Translating Information into Null and Alternative Hypotheses Set up Alternative Hypothesis First Null is exact opposite of Alternative Null + Alternative must include all possibilities Hence, we say ‘less than or equal to’ rather than just ‘less than’ Ho (Null Hypothesis): A flyer does not increase contribution to NPR: Flyer$ ≤ Last Year$ H1 (Alternative Hypothesis): A flyer increases contributions to NPR: Flyer$ > Last Year$ Subscript = Dependent Variable (what you are comparing them on) Groups, Conditions, or Levels of the Independent Variable

  6. On One-Tailed (Directional) vs. Two-Tailed (Non-Directional) Hypotheses

  7. Basics on the Normal Distribution Negative Values Positive Values 68% 95% 99%

  8. One-Tailed Hypothesis (H1: Condition 1 > Condition 2) Ho (Null Hypothesis): A flyer does not increase contribution to NPR: Flyer$ ≤ Last Year$ H1 (Alternative Hypothesis): A flyer increases contributions to NPR: Flyer$ > Last Year$ In H1, b/c Flyer > Last Year Alpha region is on right side “Alpha Region” α = .05, 1-tailed (positive) t-critical

  9. One-Tailed Hypothesis (H1: Condition 1 < Condition 2) Ho (Null Hypothesis): A poster does not decrease lbs of litter in park: Posterlbs ≤ Last Yearlbs H1 (Alternative Hypothesis): A poster decreases lbs of litter in park: Posterlbs < Last Yearlbs In H1, b/c Poster < Last Year Alpha region is on left side “Alpha Region” α = .01, 1-tailed (negative) t-critical

  10. Two-Tailed Hypothesis (H1: Condition 1 ≠ Condition 2) Ho (Null Hypothesis): People are willing to pay the same for Nike vs. Adidas: NikeWTP = AdidasWTP H1 (Alternative Hypothesis): People not willing to pay same for Nike vs. Adidas: NikeWTP ≠ AdidasWTP In H1, b/c NikeWTP ≠ AdidasWTP Alpha region is on both sides; Half of .05 goes on each side “Alpha Region” α = .025 “Alpha Region” α = .025 (positive) t-critical (negative) t-critical

  11. T-TestsSingle SamplePaired Samples (Correlated Groups)Independent Samples Single Sample Independent Samples Paired Samples

  12. Single Sample T-Test(Example 1) Comparing a sample mean to an existing population mean

  13. Gleaning Information from the Statement Direction of Alternative Hypothesis Example: • Let’s say we are interested in whether a flyer increases contributions to National Public Radio. We know that last year the average contribution was $52. This year, we sent out a flyer to 30 people explaining the benefits of NPR and asked for donations. This year’s average contribution with the flyer ended up being $55, with a standard deviation of $12. Single Sample T-test: df = N-1 = 30-1 = 29 Population Information Sample Information Use alpha = .05 How do we get a t-critical value? 

  14. Critical T-Table For single sample t-test, df = N-1

  15. One-Tailed Hypothesis (H1: Condition 1 > Condition 2) Ho (Null Hypothesis): A flyer does not increase contribution to NPR: Flyer$ ≤ Last Year$ H1 (Alternative Hypothesis): A flyer increases contributions to NPR: Flyer$ > Last Year$ In H1, b/c Flyer > Last Year Alpha region is on right side “Alpha Region” α = .05, 1-tailed If t-obtained > t-critical, reject Ho (i.e., if t-obtained falls in the critical region, reject Ho). t-critical = 1.699

  16. Computation of Single Sample T-test Decision? Because t-obtained (1.37) < t-critical (1.699), retain Ho. Conclusion? The flyer did not increase contributions to NPR. “Alpha Region” α = .05, 1-tailed t-obtained = 1.37 t-critical = 1.699

  17. Single Sample T-Test(Example 2) Comparing a sample mean to an existing population mean

  18. Gleaning Information from the Statement Direction of Alternative Hypothesis Example: • Let’s say we are interested in whether a poster decreases amount of litter in city parks. We know that last year the average amount of litter in city parks was 115 lbs. This year, we placed flyers in 25 parks that said “Did you know that 95% of people don’t litter? Join the crowd.” Later, when we weighed the litter, the average amount of litter was 100 lbs, with a standard deviation of 10 lbs. Single Sample T-test: df = N-1 = 25-1 = 24 Population Information Sample Information Use alpha = .01 How do we get a t-critical value? 

  19. Critical T-Table For single sample t-test, df = N-1

  20. One-Tailed Hypothesis (H1: Condition 1 < Condition 2) Ho (Null Hypothesis): A poster does not decrease lbs of litter in park: Posterlbs ≤ Last Yearlbs H1 (Alternative Hypothesis): A poster decreases lbs of litter in park: Posterlbs < Last Yearlbs In H1, b/c Poster < Last Year Alpha region is on left side “Alpha Region” α = .01, 1-tailed t-critical = -2.492

  21. Computation of Single Sample T-test Decision? Because t-obtained (-7.50) < t-critical (-2.492), reject Ho. Conclusion? The signs did decrease lbs of trash in the park. “Alpha Region” α = .01, 1-tailed t-critical = -2.492 t-obtained = -7.50

  22. Paired Samples T-Test Comparing two scores from the same Individual (or unit of analysis)

  23. Gleaning Information from the Statement Non-Directional (Two-Tailed) Alternative Hypothesis; doesn’t say “is higher” or “is lower”; just says “affects” Example: • Let’s say we are interested in whether a brand name (Nike vs. Adidas) affects willingness to pay for a sweatshirt. To explore this question, we take 9 people and have them indicate their WTP for a Nike sweatshirt and for an Adidas sweatshirt. The only difference between the sweatshirts is the brand name. Paired Samples T-test: df = N-1 = 9-1 = 8 Paired Scores From Same Person Use alpha = .05 How do we get a t-critical value? 

  24. Two-Tailed Hypothesis (H1: Condition 1 ≠ Condition 2) Ho (Null Hypothesis): People are willing to pay the same for Nike vs. Adidas: NikeWTP = AdidasWTP H1 (Alternative Hypothesis): People not willing to pay same for Nike vs. Adidas: NikeWTP ≠ AdidasWTP In H1, b/c NikeWTP ≠ AdidasWTP Alpha region is on both sides; Half of .05 goes on each side “Alpha Region” α = .025 “Alpha Region” α = .025 (negative) t-critical (positive) t-critical

  25. Critical T-Table For paired samples t-test, df = N-1

  26. Two-Tailed Hypothesis (H1: Condition 1 ≠ Condition 2) Ho (Null Hypothesis): People are willing to pay the same for Nike vs. Adidas: NikeWTP = AdidasWTP H1 (Alternative Hypothesis): People not willing to pay same for Nike vs. Adidas: NikeWTP ≠ AdidasWTP In H1, b/c NikeWTP ≠ AdidasWTP Alpha region is on both sides; Half of .05 goes on each side “Alpha Region” α = .025 “Alpha Region” α = .025 t-critical = + 2.306 t-critical = -2.306

  27. Defining Symbols in Paired T-test _ D = average difference score. D = difference score (eg., time 1 vs. time 2; midterm vs. final; husband vs. wife) N = # Paired Scores (not the # of numbers in front of you).  = average difference score in the Null Hypothesis Population (most often = 0) SSD = Sum of Squared Deviations for the Difference Scores = D2– [(D)2/N] tobt = the t statistic which is compared to tcrit with N-1 df

  28. Paired Samples T-testNike vs. Adidas Sweatshirt Example First, Compute SSD Then, Compute t

  29. Decision and Conclusion? t-obtained = 3.07 “Alpha Region” α = .025 “Alpha Region” α = .025 Decision? Because t-obtained (3.07) < t-critical (2.306), reject Ho. Conclusion? People willing to pay more for Nike than for Adidas. We know this, because the average difference score was positive. (Nike – Adidas) t-critical = + 2.306 t-critical = -2.306

  30. Independent Samples T-Test Comparing means of two conditions or groups

  31. Gleaning Information from the Statement Example: • Let’s say we are interested in how consumers respond to service failures, so we decide to run an experiment. We ask people to read about a hypothetical service failure scenario (e.g., delayed service at a restaurant). Then we randomly assign half of the subjects to the “apology” condition (we’ll call this Group 1), and the other half to a “control” condition (we’ll call this Group 2). Those in the apology condition read that the restaurant owner offered a sincere apology for having to wait so long. After this, we assess subjects’ self-reported anger (1 = not at all angry, 11 = fuming mad). We hypothesize that subjects will report less anger in the apology condition. Independent Samples t-test: df = N-2 = 20-2 = 18 Directional (One-Tailed) Alternative Hypothesis Scores come from two Independent groups Use alpha = .05 How do we get a t-critical value? 

  32. One-Tailed Hypothesis (H1: Condition 1 < Condition 2) Ho (Null Hypothesis): An apology does not decrease anger: ApologyAnger ≥ ControlAnger H1 (Alternative Hypothesis): Anger will be lower in the Apology Condition: ApologyAnger < ControlAnger In H1, b/c Aplogy< No Apology Alpha region is on left side “Alpha Region” α = .05, 1-tailed (negative) t-critical

  33. Critical T-Table For independent t-test, df = N-2

  34. One-Tailed Hypothesis (H1: Condition 1 < Condition 2) Ho (Null Hypothesis): An apology does not decrease anger: ApologyAnger ≥ ControlAnger H1 (Alternative Hypothesis): Anger will be lower in the Apology Condition: ApologyAnger < ControlAnger In H1, b/c Aplogy< No Apology Alpha region is on left side “Alpha Region” α = .05, 1-tailed t-critical = -1.734

  35. Defining Symbols in Independent T-test _ _ X1 and X2 = the means of X1 and X2 (our two conditions), respectively SS1 and SS2 = Sum of Squared Deviations for X1 and X2 where…SS= X2– [(X)2/N] for each group n = the number of subjects in each conditions. n1 + n2 = N. In other words, n  N! tobt = the t statistic which is compared tcrit with N-2 df.

  36. Independent Samples T-testApology vs. No Apology Example First, Compute SS for Each Condition Then, Compute t

  37. Decision and Conclusion? Decision? Because t-obtained (-2.50) < t-critical (-1.734), reject Ho. Conclusion? People report less anger after an apology “Alpha Region” α = .05, 1-tailed t-obtained = -3.07 t-critical = -1.734

  38. Analysis of Variance (ANOVA) Comparing means of three or more conditions or groups

  39. The F-Ratio: A Ratio of Variances Between and Within Groups

  40. Variance Within Group 3 Variance Within Group 1 Variance Within Group 2 Mean = 9 Mean = 3 Mean = 5 Between Groups Variance (Numerator of F-ratio)

  41. F-Distribution • Probability distribution • All values positive (variance ratio) • Positively skewed • Median = 1 • Shape varies with degrees of freedom (within and between) “Alpha Region” α = .05 0 1

  42. F-critical Table:If we have 3 conditions, N = 14, alpha = .05; F-crit = 3.98 Alpha Level df numerator = K-1 df denominator = N-K

  43. Null and Alternative Hypotheses Let’s say a marketing researcher is interested in the impact of music on sales at a new clothing store targeted to tweens. She sets up a mock store in her university’s research lab, gives each subject $50 spending money, and then randomly assigns subjects to one of three conditions. One third of the subjects browse the mock store with no music. One third browse the store with soft music. And the final third browse the store with loud music. The sales figures are shown below. Assume the researcher decides to use an alpha level of .01. Null Hypothesis (Ho): All of the means are equal (ucontrol = usoft music = uloud music) Alternative (H1): At least two means are different F-critical (based on alpha = .01; df-numerator = 2; df-denominator = 9): 8.02 Decision Rule: If Fobt ≥ Fcritical, then reject Ho. Otherwise, retain Ho

  44. The Data: Sales as a Function of Music Condition

  45. Subtract Group Mean from Each Score Then Square and Add Up This gives you the SS for that group

  46. Do this for each of the three conditions

  47. (See Statistics Notes Packet) Summarize in a Source Table

  48. ANOVA - Source Table

  49. F-critical in our example = 8.02 N = 12 K = 3 Alpha = .01

  50. Decision Rule and Conclusion? Reject Null Hypothesis At least two means are different “Alpha Region” α = .01 F-critical 8.02 F-obtained 23.47

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