Purpose: The purpose of this project was to determine if the sugar content of boxed cereals is related to their shelf placement in a grocery store. One suggested hypothesis was that sugary cereals are kept on lower shelves so that they are more accessible to children. This project will explore the relationship between sugar content in cereal and shelf placement.
Sample: A random sample of 10 cereal boxes per shelf (there were 5 shelves) were taken at the Midtown HyVee in Lincoln, Nebraska. The shelf locations were described as shelf 1 (the bottom shelf), shelf 2 (above the bottom shelf), shelf 3 (the middle shelf), shelf 4 (above shelf 3), and shelf 5 (the top shelf). Duplicate boxes on the same row were counted as one number (duplicate boxes were not repeated in the same sample), and miniature boxes packaged together as a set were disregarded. The data consisted of shelf location, cereal name, cereal brand, grams per serving, grams of sugar per serving, and the ratio of grams of sugar per serving/grams per serving. The ratio was utilized the most in this project. The cereal aisle and shelves can be seen in the following picture.
Results:
Data
The following table shows the sample mean and standard deviation for each shelf in sugar (g)/serving size (g).
Shelf | Sample Mean | Standard Deviation |
1 | 0.2619 | 0.1314563 |
2 | 0.3169 | 0.1450168 |
3 | 0.2786 | 0.09430353 |
4 | 0.2558 | 0.09966589 |
5 | 0.2049 | 0.1232319 |
The chart below shows the sugar content means by shelf.
The following plot shows the collected data in a box plot with a dot plot on top. It appears that there are not any major differences between shelf and sugar content. A hypothesis test and multiple comparison procedure (seen below) confirm this observation.
Hypothesis Test: Test Statistic Method
Steps in the Test Statistic Method
(1) Ho: µ1 = µ2 = µ3= µ4= µ5
Ha: At least one pair of means is unequal. This means that the sugar (g) to serving size (g) ratio means are not equal among all shelve pairs.
(2)Test statistic: F = 1.1346
Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
Factor(Shelf) | 4 | 0.06572 | 0.016431 | 1.1346 | 0.3524 |
Residuals | 45 | 0.65168 | 0.014482 |
(3) Critical Value: F.10,4,45 = 2.074151
(4) Since 2.074151 > 1.1346, do not reject Ho.
(5) There is not sufficient evidence to conclude that any of the sugar content means are different on any shelf.
Multiple Comparison Procedure: HSD
Factor level means
Shelf | Mean |
1 | 0.2619 |
2 | 0.3169 |
3 | 0.2786 |
4 | 0.2558 |
5 | 0.2049 |
Tukey multiple comparisons of means in R results
Comparison | Diff | Lower | Upper | P Adj |
2-1 | 0.055178524 | -0.08144894 | 0.19180598 | 0.8423564 |
3-1 | 0.016591147 | -0.12003631 | 0.15321861 | 0.9979629 |
4-1 | -0.005912775 | -0.14254024 | 0.13071469 | 0.9999657 |
5-1 | -0.056865698 | -0.19349316 | 0.07976176 | 0.8273658 |
3-2 | -0.038587377 | -0.17521484 | 0.09804008 | 0.9515074 |
4-2 | -0.0610913 | -0.19771876 | 0.07553616 | 0.7871265 |
5-2 | -0.112044222 | -0.24867168 | 0.02458324 | 0.2456542 |
4-3 | -0.022503922 | -0.15913138 | 0.11412354 | 0.9933753 |
5-3 | -0.073456845 | -0.21008431 | 0.06317062 | 0.6527179 |
5-4 | -0.050952923 | -0.18758038 | 0.08567454 | 0.8769284 |
Mean comparison plot by shelf: Experimentwise error rate = 0.10
5 4 1 3 2
Conclusions:
The test statistic method and the HSD multiple comparison procedure indicate that there is not a difference in mean sugar content among any of the shelves. The sugar content of boxed cereals does not appear to have a relationship. Ashley Johnson
ashley.johnson419@gmail.com
