A Fun ANOVA: Does Milk Affect the Fluffiness of Pancakes?
by Iván Alfonso, guest blogger
I'm a huge fan of hot cakes—they are my favorite dessert ever. I’ve been cooking them for over 15 years, and over that time I’ve noticed many variation in textures, flavor, and thickness. Personally, I like fluffy pancakes.
There are many brands of hotcake mix on the market, all with very similar formulations. So I decided to investigate which ingredients and inputs may influence the fluffiness of my pancakes.
Potential factors could include the type of mix used, the type of milk used, the use of margarine or butter (of many brands), the amount of mixing time, the origin of the eggs, and the skill of the person who prepares the pancakes.
Instead of looking at all of these factors, I focused on the type of milk used in the pancakes. I had four types of milk available: whole milk, light, low fat, and low protein.
My goal was to determine if these different milk formulations influence fluffiness (thickness). Is the whole milk the best for fluffy hotcakes? Does skim milk works the same way as the whole milk? Can I be sure that the use of light milk will result in hot cakes that are less smooth?
I sorted the four formulations as shown in the diagram below:
I used the the same amounts of milk, flour (one brand), salt and margarine for each batch of hotcakes I cooked.
The response variable was the thickness of the cooked pancakes. I prepared 6 pancakes for each type of milk, which gives me a total of 8 pancakes. I randomized the cooking order to minimize bias. I also prepared each batch by myself—if my sister or mother had helped with some lots, it would be a potential source of variation.
To measure the fluffiness, I inserted a stick into the center of each hotcake until the bottom, marked the stick with a pencil, then measured the distance to the mark in millimeters with a ruler.
After a couple of hours of cooking hotcakes, making measurements, and recording the data on a worksheet, I started to analyze my data with Minitab.
Analysis of Variance (ANOVA)
My goal was to assess the variation in thickness or fluffiness between different batches of hot cakes, so the most appropriate statistical technique was analysis of variance, or ANOVA. With this analysis I could visualize and compare the formulations based on my response variable, the thickness in millimeters, and see if there were statistically significant differences between them. I used a 0.05 significance value.
As soon as I had my data in a Minitab worksheet, I started to check it for the assumptions of ANOVA. First, I needed to see if the data followed a normal distribution, so I went straight to Statistics > Basic Statistics > Normality Test. Minitab produced the following graph:
My data passed both the Kolmogorov-Smirnov and Anderson-Darling normality tests. This was a relief—since my data had a normal distribution, I didn’t need to worry about ANOVA’s assumptions of normality.
Traditional ANOVA also has an assumption of equal variances; however, I knew that even if my data didn’t meet this assumption, I could proceed using the method called Welch’s ANOVA, which accommodates unequal variances. But when I ran Bartlett’s test for equal variances, and even the more stringent Levene test, my data passed.
With confirmation that my data met the assumptions, I proceeded to perform the ANOVA and create box-and-whisker graphs.
Here's the Minitab output for the ANOVA:
The ANOVA revealed that there were indeed statistically significant differences (p = 0.009) among my four batches of hotcakes.
Minitab’s output also included grouping information using Tukey’s method of multiple comparisons for 95% confidence intervals:
The Tukey analysis shows that low-fat milk and light items do not show a significant difference in fluffiness. However, the batches made with whole milk and low protein did significantly differ from each other.
The box-and-whisker diagram makes the results of the analysis easier to visualize:
It is clear from the graph that hotcakes produced with whole milk had the most fluffiness, and those made with low protein milk had the least fluffiness. There was not a big difference between the fluffiness of hotcakes made with light milk and lowfat milk.
Which Milk Should You Use for Fluffy Pancakes?
Based on this analysis, I recommend using whole milk for fluffier hotcakes. If you want to avoid fats and sugars in milk, low fat milk is a good choice.
I always use lowfat milk, but the analysis indicates that light milk offers a good alternative for people following a strict no-fat diet.
It’s important to note that for this analysis, I only compared formulations that used the same brand of pancake mix and the same amounts of salt and butter. But there are other factors to consider! My next pancake experiment will use design of experiments (DOE) to compare milk types, different brands of flour, and margarine with and without salt, to see how all of these factors together affect the fluffiness of pancakes.
About the Guest Blogger:
Iván Alfonso is a biochemical engineer and statistics professor at the Autonomous University of Campeche, Mexico. Alfonso holds a master's degree in marine chemistry and has worked extensively in data analysis and design of experiments in basic and advanced sciences like chemistry and epidemiology.
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