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Business Finance

Statistics

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Participant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 Condition Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Calorie Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Regular Menu Healthy (1 = Do not seem healthy at all, … , 9 = Seem extremely healthy) 2 1 5 2 3 4 3 5 5 2 6 2 6 4 8 9 2 5 5 1 2 4 2 2 3 1 6 5 2 3 3 5 1 5 5 3 6 4 3 8 7 4 7 8 2 3 3 6 6 2 8 4 2 8 2 6 4 3 5 7 7 6 2 7 8 4 8 9 5 3 8 4 5 6 5 3 7 8 4 3 Would purchase (1 = No, 2 = Yes) 1 1 2 1 1 2 2 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 2 1 1 1 1 1 1 2 2 1 2 1 2 1 2 1 1 2 2 1 2 2 1 2 2 1 3,72973 5,2093 1,98114 2,15537 37 43 12 25 26 17 2 2 1 2 2 1 2 1 1 2 2 2 2 2 2 1 2 1 2 1 1 2 1 2 1 2 2 2 2 1 2 1 Participant Liking (1 = Would like the 70's theme night much worse than a regular night, … , 4 = Would like the 70's 1 1 2 5 3 3 4 7 5 5 6 6 7 5 8 7 9 2 10 7 11 1 12 2 13 5 14 5 15 5 16 5 17 4 18 6 19 5 20 6 21 5 22 5 23 4 24 7 25 5 26 6 27 1 28 2 29 5 30 4 31 7 32 5 33 7 34 6 35 4 36 6 37 5 38 5 39 6 40 7 Would attend 80's theme night the weekend before finals (1 = No, 2 = Yes) 1 1 2 1 1 2 2 1 1 1 1 2 2 1 1 1 1 2 1 1 2 1 2 1 1 1 1 2 1 2 1 1 2 1 2 1 1 1 1 1 Participant Condition Purchase Vase (1 = No, 2 = Yes) 1 $4 2 $4 3 $4 4 $4 5 $4 6 $4 7 $4 8 $4 9 $4 10 $4 11 $4 12 $4 13 $4 14 $4 15 $4 16 $4 17 $4 18 $4 19 $4 20 $4 21 $4 22 $4 23 $4 24 $4 25 $4 26 $4 27 $4 28 $4 29 $4 30 $4 31 $4 32 $4 33 $4 34 $4 35 $4 36 $4 37 $4 38 $4 39 $4 40 $4 41 $5 42 $5 43 $5 44 $5 45 $5 46 $5 2 2 1 2 1 2 1 2 2 2 2 2 1 2 1 2 1 2 2 2 2 2 1 2 1 2 1 2 2 2 2 2 1 2 1 2 1 2 2 2 1 1 2 1 2 1 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $5 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 2 1 1 1 1 1 2 1 2 1 2 1 1 1 1 1 1 1 2 1 2 1 1 1 2 1 2 1 2 1 2 1 1 1 2 1 1 1 2 1 2 1 2 1 1 1 1 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 1 2 1 1 1 2 2 2 2 2 2 2 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 1 Participant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Condition Plan To Purchase (1 = No, 2 = Yes) Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny 1 2 2 1 1 1 1 1 2 2 2 2 2 1 2 1 2 1 1 1 1 2 2 2 2 2 1 2 1 2 1 1 2 1 1 1 1 2 1 1 2 1 2 1 1 1 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Funny Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute Cute 1 2 1 1 1 2 2 2 2 2 2 2 1 2 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 2 2 1 Participant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Condition Rating (1 to 7) Unsweetened 4 Unsweetened 6 Unsweetened 5 Unsweetened 6 Unsweetened 4 Unsweetened 4 Unsweetened 4 Unsweetened 5 Unsweetened 4 Unsweetened 4 Unsweetened 5 Unsweetened 4 Unsweetened 5 Unsweetened 6 Unsweetened 4 Unsweetened 5 Unsweetened 6 Unsweetened 4 Unsweetened 6 Unsweetened 5 Unsweetened 6 Unsweetened 6 Unsweetened 4 Unsweetened 5 Unsweetened 5 Unsweetened 5 Unsweetened 5 Unsweetened 5 Unsweetened 5 Splenda 4 Splenda 5 Splenda 4 Splenda 6 Splenda 5 Splenda 4 Splenda 4 Splenda 6 Splenda 6 Splenda 6 Splenda 5 Splenda 5 Splenda 4 Splenda 6 Splenda 6 Splenda 6 Splenda 4 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 Splenda Splenda Splenda Splenda Splenda Splenda Splenda Splenda Splenda Splenda Splenda Splenda Splenda Splenda Splenda Splenda Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar Sugar 5 5 4 5 6 6 6 4 6 5 5 6 6 5 5 5 4 6 6 5 5 5 5 4 5 6 4 6 5 4 6 6 6 5 6 5 5 5 5 4 5 6 5 4 6 4 5 Participant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Condition Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 1 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Rating (1 to 7) 5 5 6 5 6 6 2 2 6 6 5 6 5 5 2 6 5 6 6 6 4 4 4 6 6 6 6 5 6 5 6 6 6 6 6 6 5 5 6 6 6 6 5 5 6 5 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 2 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 2 5 5 1 5 6 6 4 2 3 3 6 6 6 6 6 6 5 5 5 6 6 6 5 6 5 5 6 5 6 6 7 5 4 5 5 4 4 5 4 5 7 5 5 5 4 7 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 Logo 3 3 3 3 4 3 4 3 5 6 6 4 3 1 5 4 4 4 Marketing Research Chapter 17 Statistical Testing With More Than Two Conditions Common Tests That Marketing Researchers Conduct In Studies With More Than Two Conditions If I took any one of X actions, would the actions all have the same effect in terms of producing a specific outcome in my POI? Or would some of the actions produce the outcome at different rates than others? ◦ Example: Would a red, green, and blue version of my product lead to the same number of purchases by my POI? Or would there be differences in sales across at least two of the colors? ◦ Appropriate statistical test: Chi-square test. ◦ The dependent variable is a binary outcome (i.e., only two possible responses). ◦ (In simple terms: comparing more than two proportions.) If I took any one of X actions, would the actions all have the same effect in terms of what my POI’s mean response would be on an itemized rating scale? Or would some of the actions produce different mean responses than others? ◦ Example: Would a red, green, and blue version of my product be rated equally by my POI (on a 1-7 scale) in terms of how much the product is liked? Or would there be differences in the ratings for at least two of the colors? ◦ Appropriate statistical test: ANOVA. ◦ The dependent variable is continuous (i.e., several possible responses). ◦ (In simple terms: comparing more than two means.) Interpretation of These Tests Note that when there are more than two actions (i.e., conditions), and you do either a chi-square test or an ANOVA, these tests are not testing whether the POI would respond similarly to two specific actions (like in the previous tests that we discussed for studies with only two actions/conditions). Rather, they are testing whether the POI would respond similarly across all of the actions. Comparing More Than Two Proportions (i.e., A Chi-Square Test) Step 1 - State the null hypothesis and the alternative hypothesis: ◦ Null hypothesis: Proportion of time outcome would be produced in POI is = across Action X, Action Y, and Action Z. ◦ Alternative hypothesis: Proportion of time outcome would be produced in POI is ≠ across Action X, Action Y, and Action Z. Step 2 - Run a study and calculate the p-value for your results Needed information: ◦ # Of times outcome is produced in Condition X; # Of times outcome is not produced in Condition X ◦ # Of times outcome is produced in Condition Y; # Of times outcome is not produced in Condition Y # Of times outcome is produced in Condition Z; # Of times outcome is not produced in Condition Z ◦ (Calculator: https://www.socscistatistics.com/tests/chisquare2/default2.aspx. Group 1 = Condition X, Group 2 = Condition Y, Group 3 = Condition Z, Category 1 = # Of times outcome is produced in a condition, Category 2 = # Of times outcome is not produced in a condition). Step 3 - If p-value < .05, reject the null hypothesis (i.e., support the alternative hypothesis) If p-value > .05, do not reject the null hypothesis (i.e., do not support the alternative hypothesis) Example 1: Comparing More Than Two Proportions Kmart wants to determine whether the same proportion of customers would purchase a vase across three price points ($4, $5, and $6), or if there would be any differences in the proportion of its POI that would purchase the vase across the three prices. Therefore, Kmart runs a study in which it gives some participants the opportunity to purchase the vase at $4, others the opportunity to purchase it at $5, and others the opportunity to purchase it at $6. (See Example 1 in Chapter 17 excel document.) Example 1: Comparing More Than Two Proportions Step 1 ◦ Null hypothesis: Proportion of POI that would purchase is = across $4, $5, and $6. ◦ Alternative hypothesis: Proportion of POI that would purchase is ≠ across $4, $5, and $6. Step 2 ◦ # Of participants in $4 condition who [purchased / did not purchase] a mug: [28 / 12] (70%) ◦ # Of participants in $5 condition who [purchased / did not purchase] a mug: [13 / 29] (31%) ◦ # Of participants in $6 condition who [purchased / did not purchase] a mug: [16 / 24] (40%) ◦ p-value = .001 (which means there is a .1% probability of Kmart obtaining the results that it did, if the null hypothesis about its POI is correct). Step 3 ◦ Since the p-value (.001) is less than .05, Kmart rejects the null hypothesis. In other words, Walmart supports the alternative hypothesis. Example 2: Comparing More Than Two Proportions Apple wants to determine whether three commercials (a standard commercial, a funny commercial, and a cute commercial) would result in the same proportion of its POI purchasing an iPad, or if there would be any differences in the proportion of its POI that would purchase an iPad across the three commercials. Therefore, it runs a study in which it has some participants view the standard commercial, others view the funny commercial, and others view the cute commercial. It then asks participants if they plan to purchase an iPad in the next few months. (See Example 2 in Chapter 17 excel document.) Example 2: Comparing More Than Two Proportions Step 1 ◦ Null hypothesis: Proportion of POI that would purchase is = across standard, funny, and cute. ◦ Alternative hypothesis: Proportion of POI that would purchase is ≠ across standard, funny, and cute. Step 2 ◦ # Of participants in standard condition who plan to [purchase / not purchase] an iPad: [14 / 15] (48%) ◦ # Of participants in funny condition who plan to [purchase / not purchase] an iPad: [19 / 14] (58%) ◦ # Of participants in cute condition who plan to [purchase / not purchase] an iPad: [17 / 14] (55%) ◦ p-value = .76 (which means there is a 76% probability of Apple obtaining the results that it did, if the null hypothesis about its POI is correct). Step 3 ◦ Since the p-value (.76) is greater than .05, Apple does not reject the null hypothesis. In other words, Apple does not support the alternative hypothesis. Comparing More Than Two Means (i.e., An ANOVA) Step 1 - State the null hypothesis and the alternative hypothesis: ◦ Null hypothesis: Mean POI response would be = across Action X, Action Y, and Action Z. ◦ Alternative hypothesis: Mean POI response would be ≠ across Action X, Action Y, and Action Z. Step 2 - Run a study and calculate the p-value for your results Needed information: ◦ Mean for Condition X; Standard deviation for Condition X; # Of Participants in Condition X ◦ Mean for Condition Y; Standard deviation for Condition Y; # Of Participants in Condition Y ◦ Mean for Condition Z; Standard deviation for Condition Z; # Of Participants in Condition Z ◦ (Calculator: https://www.danielsoper.com/statcalc/calculator.aspx?id=43. Group 1 = Condition X, Group 2 = Condition Y, Group 3 = Condition Z, Mean = Mean for a condition, Standard deviation = Standard deviation for a condition, Number of subjects = # Of participants in a condition) Step 3 - If p-value < .05, reject the null hypothesis (i.e., support the alternative hypothesis) If p-value > .05, do not reject the null hypothesis (i.e., do not support the alternative hypothesis) Example 3: Comparing More Than Two Means A soda company wants to determine whether three sweetness levels (unsweetened, sweetened with splenda, sweetened with sugar) would be liked equally by its POI, of if there would be any differences in liking across the three sweetness levels. Therefore, it runs a study in which it randomly assigns participants to taste either the unsweetened, splenda, or sugar version of the soda, and then rate it (from 1-7). (See Example 3 in Chapter 17 excel document.) Example 3: Comparing More Than Two Means Step 1 ◦ Null hypothesis: Mean POI rating would be = across unsweetened, splenda, and sugar versions. ◦ Alternative hypothesis: Mean POI rating would be ≠ across unsweetened, splenda, and sugar versions. Step 2 ◦ Mean rating in unsweetened condition: 4.90; SD in unsweetened condition: .77; # Of participants in unsweetened condition: 29 ◦ Mean rating in splenda condition: 5.15; SD in splenda condition: .80; # Of participants in splenda condition: 33 ◦ Mean rating in sugar condition: 5.10; SD in sugar condition: .75; # Of participants in sugar condition: 31 ◦ p-value = .41 (which means there is a 41% probability of the soda company obtaining the results that it did, if the null hypothesis about its POI is correct). Step 3 ◦ Since the p-value (.41) is greater than .05, the soda company does not reject the null hypothesis. In other words, the soda company does not support the alternative hypothesis. Example 4: Comparing More Than Two Means The Steelers want to determine whether three potential new logos (Logo 1, Logo 2, Logo 3) would be liked equally by its POI, or if there would be any differences in liking across the three logos. Therefore, it runs a study in which participants view one of the three logos and then rate how much they like it. (See Example 4 in Chapter 17 excel document.) Example 4: Comparing More Than Two Means Step 1 ◦ Null hypothesis: Mean POI rating would be = across Logo 1, Logo 2, and Logo 3. ◦ Alternative hypothesis: Mean POI rating would be ≠ across Logo 1, Logo 2, and Logo 3. Step 2 ◦ Mean rating in Logo 1 condition: 5.25; SD in Logo 1 condition: 1.18; # Of participants in Logo 1 condition: 36 ◦ Mean rating in Logo 2 condition: 5.12; SD in Logo 2 condition: 1.25; # Of participants in Logo 2 condition: 41 ◦ Mean rating in Logo 3 condition: 4.42; SD in Logo 3 condition: 1.30; # Of participants in Logo 3 condition: 33 ◦ p-value = .014 (which means there is a 1.4% probability of the Steelers obtaining the results that it did, if the null hypothesis about its POI is correct). Step 3 ◦ Since the p-value (.014) is less than .05, the Steelers reject the null hypothesis. In other words, the Steelers support the alternative hypothesis. Type I Error and Type 2 Error If the null hypothesis is really true, and you do not reject it, you are correct. If the null hypothesis is really true, and you reject it, this is called Type 1 error. If the null hypothesis is really false, and you do not reject it, this is called Type 2 error. If the null hypothesis is really false, and you reject it, you are correct. Marketing Research Assignment #7 Due: Monday, April 20th at 10:15 am EST. Note: These questions require the use of the assignment 7 excel document. ***You can work in groups of up to five*** ***Make sure to write your name(s) at the top of the assignment. ONE POINT WILL BE SUBTRACTED FOR NOT WRITING YOUR NAME*** Scenario 1 (see assignment 7 excel document) You are the owner of Oliverio’s (and your POI is all Oliverio’s customers). You are considering replacing your current dessert menu with a new dessert menu that is identical except that it includes the number of calories next to each dessert. You decide to run an online experiment in which participants (customers from your customer directory) are first randomly assigned to view one of two menus: 1) The ‘calorie menu’; or 2) The ‘regular menu.’ Next, they are asked the following: - Column C: To what extent do the desserts on this menu seem healthy? (1 = Do not seem healthy at all, … , 9 = Seem extremely healthy). - Column D: Would you purchase a dessert from this menu? (1 = No, 2 = Yes). You want to test whether or not your POI would perceive the desserts as equally healthy across the two menus (i.e., whether or not adding the number of calories to the menu influences the extent to which the desserts are perceived as healthy by your POI). To do so, you will do a between subjects t-test using the data in Column C. (Calculator: https://www.graphpad.com/quickcalcs/ttest1/?Format=SD) Q1: What is the null hypothesis? Q2: What is the alternative hypothesis? Q3: The mean rating for the calorie menu condition is ________. Q4: The standard deviation for the ratings of the calorie menu condition is ________. Q5: The number of participants in the calorie menu condition is ________. Q6: The mean rating for the regular menu condition is ________. Q7: The standard deviation for the ratings of the regular menu condition is ________. Q8: The number of participants in the regular menu condition is ________. Q9: The p-value is ________. Q10: Describe what this p-value means (Hint: Your answer should start with “If the null hypothesis about the POI is correct…”). Q11: Given this p-value, should you reject or not reject the null hypothesis? Q12: Does this p-value prove, for certain, whether the null hypothesis or the alternative hypothesis is correct? You want to test whether or not the proportion of your POI that would purchase a dessert is equal across the two menus (i.e., whether or not adding the number of calories to the menu influences the proportion of the POI that would purchase ...
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