Engineering Statistics Project
CONCLUSIONS
EXECUTIVE SUMMARY
This experimentation aimed to determine the cereal, milk, and milk volume that produced the greatest sound level initially (over the first fifteen seconds) and sustainably (over ninety seconds). We performed baseline tests and 12 single variable trials with three replications to obtain statistically significant sound level data. We tested for the response variables, initial and sustained sound level, as a result of changes to factors including type of cereal, type of milk, and volume of milk. The factor levels tested were Rice Krispies, Cheerios, Cookie Crisps, 2% cow milk, almond milk, 1/2 cup of milk, and 3/4 cup of milk.
Our data collection took place over a three hour time period in a quiet room to obtain the most accurate, un-confounded data. We used an iPhone app, DecibelX, to record the sound level (in decibels) produced by the bowl of cereal with milk over a 90 second time period. Averaging the response variables of each trial allowed us to simplify the data and cancel outliers that may have occurred during replication of the experiment.
Using the averaged response variable, we could go into further statistical and design of experiment analysis. Statistical analysis proved that the average sound level of each cereal were significantly different. Most notably, Rice Krispies cereal was significantly greater than Cheerios (p = 1.02E-10 < 0.05) and Cookie Crisps (p = 3.50E-12 < 0.05). Design of Experiment analysis provided another view of the statistically significant data, showing where the average response variable from each factor level compared to each other. The graphs also demonstrated which factor had the greatest change in response variable between levels; the factor with the greatest slope on its interaction graph likely has the greatest effect on the response variable of the experiment. In this case, DOE means plots display that the cereal factor has the greatest effect on its initial and sustained sound level, while the volume of milk added plays little to no role in the sound level produced. According to factor level interaction plots, Rice Krispies with almond milk had the greatest initial sound level and Rice Krispies with 2% milk has the greatest sustained sound level.
The optimal cereal and milk combination for greatest initial sound level:
Cereal: Rice Krispies
Milk: Almond
Volume of Milk: 1/2 cup or 3/4 cup
The optimal cereal and milk combination for greatest sustained sound level:
Cereal: Rice Krispies
Milk: 2% milk
Volume of Milk: 1/2 cup or 3/4 cup
This information will be useful in enjoying a quiet morning simply listening the the gentle snap, crackle, pop emmitted from a bowl of cereal. We have disproven our hypothesis that Rice Krispies in a 1/2 cup of 2% milk will produce the most sound. In fact, Rice Krispies in a 1/2 cup of almond milk will produce the greatest initial sound level while Rice Krispies in a 1/2 cup of 2% milk will produce the greatest sustained sound level.
INDIVIDUAL CONCLUSIONS
ISAIAH BRYNER
There were many results that could be pulled from our data as we analyzed our results. Some were predicted in our hypothesis, such as which controllable input factors affected the sound level of the cereal. However, some findings were rather interesting because they were unexpected. For example, we did not expect there to be too much of a significant difference between the sound levels of Cheerios and Cookie Crisp over an initial or sustained amount of time. However, these two cereals were very significantly different in sound level within their trial run combinations.
Figure 1 represents the magnitude of the p-values between each cereal type. This was for the purpose of understanding how much the sound levels between each type of cereal differed; the larger the p-value (such as Cheerios [CH] and Cookie Crisp [CC]) the less certain we are that their sound levels were different. It also peaked my interest because there didn’t seem to be too noticeable of a difference in sound level between Cookie Crisp and Cheerios, but it turns out that statistically there was.
Figure 1: Initial sound level p-values between the three types of cereal, representing an interesting find and comparison between these significant differences.
INDIVIDUAL CONCLUSIONS
MEGHAN SAMPSON
After analyzing factors affecting the initial and sustained sound levels produced by a bowl of cereal, we could conclude that almond milk caused a significantly greater initial sound level in Rice Krispies than 2% dairy milk did. Though this was surprising, the most surprising aspect of this discovery was that almond milk produced a lower initial sound level in the other cereals, Cheerios and Cookie Crisps, than the 2% milk. Even stranger, 2% milk caused a higher sustained sound level in the Rice Krispies. I expected that almond milk would have a similar effect on each cereal, helping produce a higher sound level than its counterpart. Additionally, I believed that the trend of greater sound from almond milk in Rice Krispies would continue across initial and sustained sound levels. Since this was not the case in our experimental data, I turned my curiosity into a new graph comparing the trend of sound level over time in a ½ cup of each respective milk type when combined with a cup of Rice Krispies.
Figure 2 below demonstrates a visible difference in the trend lines of sound level over time in each milk type. Almond milk remains the loudest factor level in the cereal, (following the aqua trend line) until the sound levels of almond milk and 2% milk equal each other. This equivalency occurs approximately 32 seconds after combining the milk and cereal, based on the trend line equation derived in Excel and documented in Figure 2 below. After 32 seconds, interestingly, 2% milk has a greater sound level (following the yellow trend line) than almond milk. Because 2% milk has a sound level greater than that of almond milk for almost 2/3 of our data collection time, it averages out to have the greater overall sustained sound level. Further research could be conducted to determine whether the ingredients and structure of the cereal or the chemistry of the milk is the most significant contributor to this difference between cereals and in Rice Krispies over time.
Figure 2: Traditional vary x, vary y distribution demonstrating the sound level of almond and 2% milk over time with a 1/2 cup of each milk combined with one cup of Rice Krispies
CLOSING REMARKS
Rice Krispies are the loudest way to start your morning, in terms of cereals. No matter the preferred type of amount of milk added to a cup of cereal, Rice Krispies will always be the snappiest cereal initially and over a longer stretch of time. If looking to increase the initial crackle with statistical significance, adding any volume of almond milk to your bowl of Rice Krispies will produce the greatest sound level over the first fifteen seconds in comparison to other cereal and milk combinations. The next time you wake up to the smiling sun streaming into your windows in the morning, take a few minutes to quietly enjoy the gentle, steady popping of a cup of Rice Krispies with a half cup of almond milk.