The first product in brand one has 38 units of sugar. Take a look at the scale at the bottom of the window. It shows that any value between 37 and 43 would be rated 1. That's why the rating for the first product is a 1. Now look at the 5th product from Brand 1. It has 45 units of sugar. Since this is more than 43, it is rated 2. Examine other products and make sure you understand how the sugar contents combined with the scale produce the ratings.

This demonstration allows you to change the way sugar units are transformed into ratings. Lets suppose that out rater would not give a brand a sweetness rating of 1 unless it was truly not sweet at all. For example, the rater might only give ratings of 1 if the sugar content was less than 40. To see what would happen, move the vertical line above 43 to the left. Notice that as you move it, its label reflects its current value. Keep moving it to the left until it equals 39. Now look at the ratings of the products. With our original "mapping," the first 4 Brand-one products were rated 1. Now the only the first product has so little sugar to get a rating of 1. Now suppose that our rater was pretty generous in awarding 3's. Lets say that all a brand needed to get a 3 was a 43. So move the divider between 2 and 3 from 49 to 43. And, just for the sake of the example, let's assume that the rater required a product to be very sweet to get a rating of 4. Specifically, lets say that it needed a sugar content of 60. Move the divider between 3 and 4 from 56 to 60. Notice how the ratings are automatically updated. Finally, lets assume that our rater does not require much more sweetness in order to give a rating of 5. So lets leave the cutoff between 4 and 5 at 62.

Our rater is generating very "non-interval" ratings. A difference between a 4 and a 5 could represent, at most, 2 units. In contrast, a difference between a 2 and a 3 could represent as much as 17 units.

Now consider how the mapping of the sugar content onto the sweetness rating affects our interpretation of the difference between Brand 1 and Brand 2. The mean difference in sugar content is 55. With the original mapping, the mean difference in ratings is 0.69. When we changed the mappings so that the boundary between ratings of 1 and 2 became 39, between 2 and 3 became 43, and the boundary between 3 and 4 became 60, the difference in ratings became 3.23-2.85 = 0.38. You can see that the mappings did make a difference. But qualitatively, whether you were looking at the sugar content or the ratings, you would conclude that Brand 2 is sweeter than Brand 1. Experiment by changing the various boundaries. You will find that qualitative conclusions based on the mean ratings are valid.

Now choose Data Set 2. Just as with Data Set 1, the mean difference in sweetness is 5.0. The data are quite, different, though. Brand 2 has the three lowest sweetness levels as well as the three highest. Brand 1 is in the middle. The initial difference in ratings is 3.08-2.62 = 0.46. If you change the boundaries you get slightly different results, but you will probably find that the mean difference on the ratings is not misleading. However, there are ways of getting a misleading result. Notice that there are four 43's for Brand 1 and that these are associated with sweetness ratings of 2. Move the boundary between ratings of 2 and 3 to 42. Then you will see that the ratings for these products changes from 2 to 3. With all the sugar contents of 43 receiving a rating of 3, Brand 1 now has a higher mean sweetness rating than Brand 2 even though the mean sugar content for Brand 2 is higher. This effect can be made even larger by moving the boundary between 4 and 5 to 75. This will lower the ratings for the Brand 2 products with 71 and 72 from 5 to 4 thus lowering the Brand 2 mean without affecting the Brand 1 mean. The mean for Brand 1 will be 3.23 compared to a mean for Brand 2 of 2.92. Again the important point is that even though Brand 1 has a lower mean sugar content than Brand 2, it has a higher mean rated sweetness score.