
Imagine this. You finished a long day of work and decide to pick up some groceries on the way home. After running some errands, you look at your watch: 9:00pm. To give yourself some rest, you decide to grab dinner at a fast-food joint. Sound familiar? I bet.
We all live incredibly busy lives. Although we all know that Fast Food is not necessarily the most healthiest option, a lot of people still utilize these facilities due to their immense convenience. We tend to bundle all of these chain restaurants as being equally unhealthy as the next. However, looking into the specific nutritional facts is key to distinguishing them and making the right choice for a healthier meal. In this case study, I focus on two very popular fast-food restaurants, McDonald’s and Taco Bell, and answer the age-old question:
Eating from which restaurant would be the healthier choice in the long-run?
Simulating the System
I first grabbed the menu’s from both restaurants and labelled each item as either an entree, drink, side, dessert, sauce, or dressing. For McDonalds information, I pulled from a dataset on Kaggle and for Taco Bell, I created the dataset myself based on a nutrition facts website I found. I kept drinks that were unique to each restaurant and discarded the rest from the analysis. In other words, drinks such as Coke, Sprite, etc. were removed from both datasets as I only consider Food items that are trademark to the restaurant. The scope of this analysis encompasses lunch and dinner menu items only.
I then created four distinct simulations in which a customer would purchase meals from each restaurant, the key difference being the definition of the word "meal".
Simulation 1: A customer purchasing one entree alone
Simulation 2: A customer purchasing one entree and a drink
Simulation 3: A customer purchasing one entree, a drink, and a side
Simulation 4: A customer purchasing one entree, a drink, a side, and a dessert
To make the analysis even more realistic, I created stipulations within certain menu items for both restaurants. If a salad were to be randomly picked as a side item, the script randomly picks a salad dressing to go along with the meal. If chicken nuggets or chicken strips were picked as an entree item, then the script randomly selects a sauce to go with it as well. For Taco Bell entrees, I made sure each simulation randomly selects two sauces to go along with each entree item.
For each simulation, meals following these combinations were sampled 10,000 times. From this, clear distinctions were able to be made between between the facilities. Let us first consider the simplest case in which a customer orders one entree alone. From simulation 1, I created the following plot:

Note that the average calories, calories from fat, cholesterol, and sodium are quite similar between the two facilities. I was curious if this trend carries over for all simulations, leading me to compare the averages for these features for all simulations run. The short answer is no. I created this plot which shows us the results.

We see that stark differences can be made in nutritional features across trials. Simulation 1 is in fact the only trial that resulted in seemingly similar results for both restaurants. This means that the drinks, sides, and desserts in the restaurants exhibit higher variance in nutritional qualities. The previously mentioned features are quite higher for McDonald’s than for Taco Bell. To assess if these differences are mathematically significant, I ran a non-parametric test (a Mann-Whitney U Test) for all simulations. Predictably, I obtained very low p-values for all trials, indicating a significant difference between the nutritional features displayed above for the two restaurants. I did not expect a significant difference for Simulation 1, however.
Let’s take a closer look at Simulation 4, which encompasses a full-course meal. In my opinion, this should be the trial that we place the most emphasis on. If we take a snapshot of how the nutritional features compare from one meal to another for the first 500 samples, we would see the following:

As one can see, the calories from fat, cholesterol, trans fats, and saturated fats are generally higher for a McDonalds meal. To gain some quantitative measure regarding how much higher some of these features are for McDonalds, let us observe how the ECDF’s differ for the calories from fat and cholesterol for each meal in Simulation 4.

As we can see, approximately 37% of meals at McDonalds have greater than 600 calories from fat, the maximum value for a Taco Bell meal. Furthermore, around 60% of Taco Bell meals fall between 220 and 410 calories from fat whereas 60% of McDonalds meals fall between 420 and 650 calories from fat. Additionally, around 77% of Taco Bell meals have less than 400 calories from fat whereas only around 18% of meals at McDonalds have the same quality.
From the righthand plot, one can see that all Taco Bell meals fall short of approximately 90 milligrams of cholesterol. On the other hand, only 18% of McDonalds meals fall under this same cholesterol level. In fact, 30% of McDonalds meals have greater than 180 milligrams of cholesterol – double the possible maximum cholesterol value of a Taco Bell meal.
So What Does This All Mean?
Before we make a brisk conclusion, let us consider the meanings of the features explored in this analysis and the overarching results obtained. Each simulation with 10,000 samples yielded substantial and significant nutritional differences between the two restaurants. Specifically, we observed that McDonalds has significantly higher values for all features in all simulations conducted. Is this necessarily a bad thing?
Based on Harvard T.H Chan School of Public Health, trans fats are the worst types of fat to consume due to their negative effects on our blood vessels and heart. High intake of this type of fat can result in insulin resistance, diabetes, and many other complications. According to a MayoClinic article, the maximum suggested calories obtained from saturated fats is 10% of your daily total calories. It is typical for an individual to eat around 2,000 calories a day, which gives a cap of 200 calories from fats to remain "healthy". Assuming you are eating at a fast-food place, you will likely exceed this threshold. However, the likelihood that you will triple or quadruple it with one full-course meal at McDonalds is far more likely than doing so at Taco Bell.
According to an article by the US Food and Drug Administration, having high sodium diets can cause heart disease as well as an increased risk for stroke. They state that the recommended daily amount of sodium intake is less than 2,300 milligrams. Based on Simulation 4, McDonalds surpasses that value with one meal whereas Taco Bell stays around 1,500 milligrams on average. Lastly, higher levels of cholesterol can cause clogging of our blood vessels due to fatty deposits. From the Simulation 4 snapshot and ECDF plots we saw that McDonalds meals on average have a significantly higher amount of cholesterol than do Taco Bell meals.
Of course, the definitions I ascribed to the word "meal" in addition to the conditional additions of dressings/sauces in this study will give rise to algorithmic bias within my simulations. It would be a good idea to run even more simulations with different conditions to add even more realism into the analysis. Nevertheless, I believe that my current results are quite insightful!
All in all, the results of my analysis point to a crystal clear conclusion: Taco Bell is the healthier option in the long run.
If you enjoyed this article and are interested in more content like this, you can follow me on Medium. The code for this project can be found on my Github here. Thanks for reading!