Question:

You receive the results of a paired-comparison preference these of four soft drinks from a sample of 200 persons. The results are as follows:

Koak Zip Pabze Mr.Pep

Koak ---- 50 115 35
Zip 150 --- 160 70
Pabze 85 40 --- 45
Mr.Pep 165 130 155 ---

a). How does these brands rank in overall preference in this sample?

Koak Zip Pabze Mr.Peepers
Total 400 220 430 150
RankOrder 2 3 1 1

b). Develop an interval scale for these four brands. The results are as followed.

Please explain clearly how you came up with the results.

Sometimes copying and pasting doesn't work. Try typing the text here.

Koak Zip Pabze Mr.peppers


Mp .625 .40 .662 .312
Zj .32 - .254 .42 - .49
Rj .81 .24 .91 .00

What is MP, ZJ, and RJ stand for?

To rank the brands in overall preference in this sample, you can use the following steps:

Step 1: Calculate the total number of preferences for each brand by summing up the scores for each brand from the given table. This will give you the following total scores:
- Koak: 50 + 115 + 35 + 0 = 200
- Zip: 150 + 0 + 160 + 70 = 380
- Pabze: 85 + 40 + 0 + 45 = 170
- Mr.Pep: 165 + 130 + 155 + 0 = 450

Step 2: Rank the brands based on their total scores. In this case, we can see that Mr.Pep has the highest total score of 450, followed by Zip with a total score of 380, Koak with a total score of 200, and Pabze with a total score of 170.

Based on these rankings, the overall preference of the brands in this sample is as follows:
1. Mr.Pep
2. Zip
3. Koak
4. Pabze

To develop an interval scale for these four brands, we can use the following steps:

Step 1: Calculate the average score for each brand by dividing its total score by the number of respondents (200 in this case). This will give you the following average scores:
- Koak: 200 / 200 = 1
- Zip: 380 / 200 = 1.9
- Pabze: 170 / 200 = 0.85
- Mr.Pep: 450 / 200 = 2.25

Step 2: Normalize the average scores by dividing each average score by the highest average score (in this case, Mr.Pep's average score of 2.25). This will give you the following normalized scores:
- Koak: 1 / 2.25 ≈ 0.444
- Zip: 1.9 / 2.25 ≈ 0.844
- Pabze: 0.85 / 2.25 ≈ 0.378
- Mr.Pep: 2.25 / 2.25 = 1

The interval scale for these four brands based on the normalized scores is as follows:
- Koak: 0.444
- Zip: 0.844
- Pabze: 0.378
- Mr.Pep: 1

These interval scores indicate the relative preferences of each brand in the sample, with a higher score indicating a higher preference.