Overview of the M&M ANOVA Experiment
A professor asked six groups of students in an Elementary Statistics course to collect ten bags of M&M’s, open them, and count the number of candies of different colors in each bag. Thus, each of the six groups had data on how many Red, Orange, Yellow, Green, Blue, and Brown candies were in each bag: of course, these data differed between groups since a producer does not put identical amounts in each bag. The professor summarized the data from all six groups in a table that counted the total amount of candy in each bag for each group. This allowed us to see that Group #3’s data was much lower than the other groups, and an error was determined: the students in this group used the wrong package size for the other groups.
The professor then calculated the average number of candies for each group, SSW, and the sum of SSW and SSB. This gave him an F-statistic for the data, which showed that not all the packs were taken from the same population because the value was above the critical level. In other words, the packages that the students used were produced in different series.
Assessment of ANOVA Assumptions
In conducting the ANOVA, the professor assumed that the dependent variable (number of candies) was continuous and that the independent variable (student group) was categorical and had more than two groups. The professor also found outliers in group #3 data, and the independence of the observations was maintained. However, the normality of the distribution and homogeneity of variance were not checked, which are some of the most critical assumptions.
Interpretation of ANOVA Results
I initially thought the professor would use ANOVA to test for differences in the candy of different colors. Still, he used it to determine the origin of samples from populations, which was unexpected. However, the fact that the packages were taken from different production series is unsurprising because many packages and different groups of students were used. Since the professor did not use an ANOVA to determine color differences, it is impossible to say whether one of the candy colors was greater than the others.
Comparison with Another ANOVA Study
Another source suggests using an ANOVA to determine the effect of a particular type of fertilizer on yield (Bevans, 2022). The author found a statistically significant difference (F(2) = 9.073, p <.001), which means that fertilizer type did affect yield. In other words, unlike Winters (2015), Bevans (2022) obtained significant results and was able to reject the null hypothesis.
References
Bevans, R. (2022). One-way ANOVA | When and how to use it (with examples). Scribbr. Web.
Winters, B. (2015). M&M ANOVA. Redneck Math. Web.