With the rise of the internet, it's natural that many people have shifted away from cookbooks and classes to webpages where anyone can find a recipe for whatever they're craving in minutes.

Websites like food.com (where these datasets were scraped from by researchers Bodhisattwa Prasad Majumder Shuyang Li, Jianmo Ni, and Julian McAuley) contain endless assortments of recipes. Because of the less curated and structured nature of sites where users submit their own recipes, analyzing recipe data helps us see the big picture of what kinds of recipes are being submitted and whether they're suitable additions to a balanced diet.

As someone who avoids eating meat, the internet is a great tool for finding new recipes to try. Something that dwells in many minds of vegetarians and vegans is whether or not they're eating healthy amounts of protein. This goal of this project is to find out whether online vegetarian recipes are offering the same amounts of protein as non-vegetarian recipes. If they aren't, those who avoid meat may need to be careful to find additional ways to incorporate protein into their diets.

To explore this question, I have combined the aforementioned datasets of recipe posts and their comments into one dataframe containing 234429 rows and 18 columns, where each row represents a review of a recipe on food.com.

Some relevant columns of the dataset are as follows:

| Column name | Description | | tags | A list of categories the food belongs to. We use this list to determine whether recipes are vegetarian or not | | nutrition | A list of data about the macronutrients of the food. We use this column to find the protein and calories of a recipe |

To prepare to answer our question, the dataframe must be adapted into a useful form. The main components of this process were fixing the data types of the columns, extracting features useful to answering our question, and to check our dataframe for supsicious entries.

It is apparent after using the info() command that the submitted and date columns are not in datetime format. Also, the user_id, recipe_id, and rating columns are not stored as integers. These are easily adjusted to save space and improve clarity

Dealing with the data stored in tags, nutrition, and steps is more troublesome because the data is stored a text version of a list. By converting the data into sets of tags, ingredients, and steps, we start to see the bigger picture of what we are working with.

Below is a sample of tags in the tags column.

{'', '1-day-or-more', '15-minutes-or-less', '3-steps-or-less', '30-minutes-or-less', '4-hours-or-less', '5-ingredients-or-less', '60-minutes-or-less', 'Throw the ultimate fiesta with this sopaipillas recipe from Food.com.', 'a1-sauce', 'african', 'american', 'amish-mennonite', 'angolan', 'appetizers', 'apples', ... }

The tags column contains 549 unique tags, the steps column contains 840168 unique steps, and the ingredients column contains 11170 unique ingredients. Since there is so much variety in the steps and uniqueness columns, it is not worth examining them to find patterns in our dataset. The tags column is much more promising. If we were using this data to create a predictive model, a one-hot encoding of the tags column might be very useful data. For the purpose of a hypothesis test, this overcomplicates the process and clutters our dataframe. Instead of a one-hot encoding, we will create a new feature: is_vegetarian. is_vegetarian will be a boolean variable found by testing whether "vegetarian" or "vegan" is a tag present in each of the lists of tags.

Each element in the nutrients column contains a list of length six with the following structure: [calories, total_fat (percent daily value), sugar (percent daily value), protein (percent daily value), saturated fat (percent daily value), carbohydrates (percent daily value)] Since all the lists are the same length and each index corresponds to a feature, we can split this list into 6 new columns in our dataframe. We now have the feature protein_pdv corresponding to the percent of the daily recommended amount of protein in each recipe.

The protein_pdv column is essential for our analysis. Unfortunately, many entries of this column are 0, even when the corresponding recipe is something abundant in protein like a ham dish. A strategy to mark these false zeros as NaN values is required. Since there are also many recipes for different drinks or brines, which truly do have no protein, this is a difficult problem to solve. Luckily each recipe has a sizeable list of tags describing it. Some of these tags contain ingredients like ham, mushroom, lentils, tofu, or duck. By changing the values of protein_pdv to NaN for rows where protein_pdv is 0 and there is a tag signaling that there is protein in the dish, we can detect many false zeros.

Finally, since the number of comments any recipe has is irrelevant to its protein content, we should groupby recipe_id. If we don't, the recipes with more comments will be weighted more heavily in our analysis than those which have fewer comments. We can also drop columns not relevant to our analysis

The first 5 rows of the cleaned dataframe are displayed as follows.

Since we are studying protein concentration in vegetarian vs. non-vegetarian food, it's important to view how protein content is distributed as a whole. One noticeable takeaway is that there are no obvious subgroups. If we saw two spikes in the graph it would suggest that there was a singular distinguishing factor that separates high-protein and low-protein food.

The natural first two variables to explore the relationship between are is_vegetarian and protein_pdv. By creating an overlayed histogram, we can see the distribution of protein in each type of food. The vegetarian food appears to be much more concentrated around the low-protein area of the graph.

To find correlating variables, I created a correlation matrix. The most notable correlation was between calories and protein_pdv with a correlation coefficient of about .6. When observing a scatter plot of calories vs. protein_pdv, this is not so obvious.

When the graph is also colored by is_vegetarian, it seems that vegetarian recipes contain less calories and less protein.

If we create a pivot table by grouping by the is_vegetarian column, we notice that there is a stark difference in the average protein in vegetarian foods and the average protein in non-vegetarian foods. Other macronutrients also differ by a large amount except for carbohydrates.

Both this pivot-table and the previous plot demonstrate that vegetarian recipes may contain both less protein and calories. This poses a problem for our analysis since most people eat only a certain amount of calories per day. If vegetarian recipes had less protein but vegetarians were eating more meals throughout the day, overall protein consumption could still be the same for vegetarians and non-vegetarians. To account for this, we will create a new column for our hypothesis test: protein_per_cal. By studying this variable we should get a better sense of how much protein vegetarians and non-vegetarians get over the course of an entire day.

There are no missing values in the is_vegetarian column, so the relevant column to analyze missing values in is protein_pdv.

Reflecting on the data-generating process, it's likely that the values in protein_pdv are either inputted by the users who submit their recipes or are generated by food.com.

If the values are inputted by the users, the missing values could stem from users who didn't feel the need to input nutritional information. Whether someone wanted to take the time to input nutritional information or not doesn't have any connection with how much protein is in a recipe, so in this situation the data is not NMAR.

If the values are generated by food.com, perhaps with an algorithm, then it's likely that missingness would be connected with how difficult it is to calculate the protein of a dish. Once again, there is no obvious connection between how difficult it is to calculate protein concentration of a dish and how much protein is in that dish, so we can conclude that data is not NMAR.

To test whether the missingness of protein depends on other columns, we can perform permutation tests. We will use the difference of means as our test statistic and have a significance level of 0.5.

Our first permutation test examines whether the missing values in protein_pdv are dependant on whether the food is vegetarian or not The null hypothesis assumes that the values in is_vegetarian when protein is missing and when protein is not missing come from the same distribution. Our p-value was .02, meaning we reject the null hypothesis and that my system of marking protein values as NaN was likely biased towards recipes containing meat.

The second permutation test was to test whether protein was missing conditionally on calorie count. Interestingly enough, our p-value was 0 and so once again we reject the null hypothesis, leading us to believe that protein is missing conditionally at random based on calorie count.

This plot shows how dramatically different the calorie distribution is depending on whether the protein_pdv data is missing.

The rejection of the null hypothesis in both of these tests makes sense since we've already seen some correlation between whether a recipe is vegetarian and its calorie count.

As a demonstration that this kind of permutation test fails to reject the null hypothesis when we test with a completely unrelated column, if we conduct the same test using id as our column, we find a p-value of .1.

It is now time to conduct our hypothesis test. Our null hypothesis is that the protein per calorie of vegetarian recipes on food.com is the same or greater than the protein per calorie of non-vegetarian recipes. Our alternative hypothesis is that vegetarian recipes on food.com have less protein per calorie than non-vegetarian recipes.

With more data and less variance, your significance level should become smaller. In our case, our dataset is quite large (83782 rows), and the variance of the protein_per_cal column is also quite low, so we will use a significance level of .01. We will create 1000 permutations during our test and use the difference of means as our test statistic.

The p-value from our permutation test is 0, even with 1000 iterations. In the above chart, the dark line on the vertical axis represents the observed difference in means. Hence we reject the null hypothesis, suggesting that vegetarian recipes likely contain less protein per calorie than non-vegetarian recipes. People nervous about obtaining enough protein throughout their day may need to take extra care to get protein from additional sources if they are relying completely on online recipes.