Recipes and Ratings EDA

Authors: Jason Gu, Ethan Deng

Project Overview

This is a data science project on investigating if there is a coorelation between the protein content and average rating and if there is a coorelation between the protein content and cooking time of the recipe. The dataset used to investigate the topic can be find here, and is originally scrapped from this source.

Table of Contents

Introduction:

Recently there have been more bodybuilding and strength influencers on the rise, leading to an increase in gym culture and people striving to improve their physique. With this in mind, it’s important to eat high-protein foods to build muscle after a hard workout, so in our project, we’re curious to find out if recipes that are high in protein are also the ones that people seem to like more. We’re also interested in seeing if the time it takes to cook these protein-rich meals affects how much people enjoy them. After all, we all want delicious food that’s also good for our muscles, but if it takes too long to make, we might not be that keen on cooking it.

The dataset we are working with is from food.com and contains recipes and reviews that have been collected since 2008. This dataset is divided into two data frames, recipes and ratings. We are mainly interested in the recipes data frame, where we will be looking at the nutrition and cooking time. However, we will merge the two data frames to get the average ratings for each recipe and use that for our analysis.

The recipe data frame has 83782 rows, meaning that there are 83782 unique recipes. Meanwhile, the reviews data frame has 731927 rows, where each review is from a person that submitted a review of a recipe from the recipes data frame.

This is a description of what the recipes dataframe contains (83782 rows):

Column Desciption
‘name’ Recipe name
‘id’ Recipe ID
‘minutes’ Minutes to prepare recipe
‘submitted’ User ID who submitted this recipe
‘tags’ Food.com tags for recipe
‘nutrition’ Nutrition information in this form [calries (#), total fat (PDV), sugar (PDV), sodium (PDV), protein (PDV), saturated fat (PDV), carbohydrates (PDV)]; PDV stands for “percentage of daily value”
‘n_steps’ Number of steps in the recipe
‘steps’ Step by step instructions to follow
‘description’ A description of what the recipe makes

This is a description of what the reviews dataframe contains (731927 rows):

Column Desciption
‘user_id’ User ID
‘recipe_id’ Recipe ID
‘date’ Date of interaction
‘rating’ Rating (1-5)
‘review’ Review text

Data Cleaning

  1. We merged the two data frames on the ‘recipe_id’ column from ‘reviews’ and the ‘id’ column from ‘recipes’ to assign each rating from the reviews data frame onto each recipe.

  2. We grouped by the ‘recipe_id’s and took the mean of the ratings for all reviews on each recipe to get an average rating for each recipe.

  3. We assigned this series of average ratings onto a new column in the recipes data frame.

  4. We also had to convert the nutrition column from a string into a list. This then makes it possible to extract the grams of protein from that column and add a new column called ‘protein’ to easily identify how much protein is in each recipe.

  5. There were some recipes that had no average rating (or an average rating of 0, which are invalid) and some recipes that didn’t have a description, so we got rid of those rows and saved it to a new dataframe called recipes_nona to better examine the data that we do have. There were about 2600 rows with NA values, but thankfully this didn’t impact the size of our data frame that much.

Here is what our recipes data frame now looks like with no ‘NA’ values, and some columns have been removed for an easier viewing experience on the variables of interest.

name id minutes contributor_id submitted nutrition average_rating protein
1 brownies in the world best ever 333281 40 985201 2008-10-27 [138.4, 10.0, 50.0, 3.0, 3.0, 19.0, 6.0] 4 3
1 in canada chocolate chip cookies 453467 45 1848091 2011-04-11 [595.1, 46.0, 211.0, 22.0, 13.0, 51.0, 26.0] 5 13
412 broccoli casserole 306168 40 50969 2008-05-30 [194.8, 20.0, 6.0, 32.0, 22.0, 36.0, 3.0] 5 22
millionaire pound cake 286009 120 461724 2008-02-12 [878.3, 63.0, 326.0, 13.0, 20.0, 123.0, 39.0] 5 20
2000 meatloaf 475785 90 2202916 2012-03-06 [267.0, 30.0, 12.0, 12.0, 29.0, 48.0, 2.0] 5 29

Univariate Analysis

Here we take a look at the distribution of how many grams of protein is in the recipes, the distribution average ratings, and the distribution of cooking time all on their own bar charts.

Here above we had to remove some outliers in the protein and time columns because there were some recipes with ridiculously unreal amounts of protein and time taken, which were clearly not real recipes. We excluded the outliers by only including values within 2 standard deviations within the mean. But as we can see, most recipes have a fairly low amount of protein and take about 30-50 minutes to prepare, and as the amount of protein in a recipe increases, they appear less frequently. Also we can see that most recipe ratings are a 4 and above

Bivariate Analysis

Here we look at two scatter plots to see the relationship between protein and average ratings among the recipes. As well as protein and cooking time.

When looking at the scatter plot of Protein vs Average Rating, there isn’t much of a relationship between the two variables, but we can see that most recipes have a high average rating and low protein, as most of the dots are clumped into the top left

When looking at the scatter plot of Protein vs Average Rating, there also isn’t much of a relationship, but it is clear that most recipes have a shorter cooking time and lower protein.

Interesting Aggregates

Here we are aggregating the recipes by average rating, and seeing how the amount of protein and cooking time vary among each rating group.

(‘rating_group’, ‘’) (‘protein’, ‘mean’) (‘protein’, ‘median’) (‘protein’, ‘std’) (‘minutes’, ‘mean’) (‘minutes’, ‘median’) (‘minutes’, ‘std’)
1-2 27.2464 14 28.8051 60.6933 40 76.5207
2-3 30.5448 19 30.0176 62.3437 40 81.769
3-4 31.0934 20 29.7814 58.9369 35 78.132
4-5 28.6202 17 29.3303 54.5229 35 70.8765

Here we can get a better look at how protein and cooking time vary between the ratings groups. From this table, there seems to be little to no differences for protein among the rating groups, as they fluctuate minimally. However, it is pretty clear that the recipes in the 4-5 rating group have the lowest mean, meadian, and standard deviation of cooking time. This makes sense because most people would rather not spend a longer time cooking if they don’t have to.

rating_group 0-30 30-60 60-120 120+
1-2 22.6831 26.9227 32.3457 39.287
2-3 24.2185 32.2783 33.6454 46.0409
3-4 25.2867 33.1707 36.7743 42.1723
4-5 22.7715 31.8557 34.2425 39.7874

In this table, we can see that as the cooking time increases for the recipe, the protein also increases. This makes sense because typically a longer cooking time means a bigger portion of food being prepared. However, within the cooking times, it seems that foods with a 2-3 or 3-4 rating have a little more protein than ratings between 1-2 and 4-5. What we can deduce from this is that protein may be slightly less favorable for most people.

NMAR Analysis

We understand that “Not Missing at Random” (NMAR) indicates that there is a relationship between the propensity of a value to be missing and its value. We think that the missingness in the average_rating is potentially NMAR. We believe that the missingness in average_rating has to do with the length of the recipe. The longer it takes to finish the recipe, it is potentially less likely for the recipe to be made, causing the recipe to have fewer ratings or even missing ratings. Furthermore, we believe that it is more likely for recipes that are either really good or really bad to receive ratings. It is possible that the missing ratings are due to the fact that people did not feel anything special about the recipe. Due to the fact that there may exist a cause-and-effect relationship to these missing values, NMAR would therefore be a valid indication.

Missingness dependency

We wanted to test if there is a correlation between the missingness in average_rating in comparison to the minutes (the minutes it takes to cook a certain recipe). The average_rating values are likely to be missing because there were no reviews for these recipes. One of the reasons is that we did a left merge with recipes and reviews to get the average rating column, where recipes are on the left, so recipes that had no reviews left for them were calculated to be NaN. Based on what we can see below in the plot, as well as our permutation test, there appears to be a correlation between the cooking time and the missingness of the average_rating column.

The observed statistic here was 117.34 and the p-value was 0.0369. Seeing that the p-value is below 0.05, this means that there is a correlation between the cooking time and the missingness of the average_rating column. This makes sense because recipes that take a long time to cook are less likely to be made and therefore won’t have a rating left for them. This means that the data is NMAR because the missingness of a rating is dependent on the cooking time for the recipe. Therefore the missingness of average rating is dependent on the cooking time.

The observed statistic here was 1.29 and the p-value was 0.1936. For this chart we can see that the p-value is quite high (around 0.2), which means that the amount of protein a recipe has does not coorelate with whether or not there is a rating for the recipe. The negative values simply indicate that in that permutation, the group with missing ratings had a lower mean protein level than the group with ratings. This conclusion sense because whether or not a recipe has more or less protein shouldn’t stop someone from giving the recipe a rating. Therefore the missingness of average rating is NOT dependent on the amount of protein.

Hypothesis Testing

Permutation Test for correlation between protein content and average rating:

In order to credibly answer our research question, where we are testing whether there exists a correlation between the rating of a recipe and the protein content of a recipe, we must test for a correlation between protein content and average rating using permutation testing:

Null Hypothesis (H0): There is no correlation between the protein content of a recipe and the average rating of a recipe.

Alternative Hypothesis (Ha): There is a correlation between the protein content of a recipe and the average rating of a recipe.

Test Statistics: For the purpose of finding the correlation between the average rating of a recipe and its protein content, we would simply utilize our merged data frame ‘recipe_nona’ to have already categorized columns as our testing variables. The specific columns we focused upon from ‘recipe_nona’ are the ‘protein’ column and the ‘average_rating’ column. Therefore, since we are trying to determine a linear correlation between two variables within the same data set, we utilized Pearson correlation coefficient as our test statistics.

Significance Level: To ensure the accuracy of our findings and conclusions on our research question, we chose to use a significance level of 5% for this permutation test.

The plot below showcases the coorelation from permutation testing of our test statics in 10000 permutations

Observed Pearson correlation: -0.02273678966808098 P-value from the permutation test: 0.0 From the plot above, we can see that our p-value of 0 from the test that is less than our significance level of 0.05. Hence, we reject our null hypothesis.

Permutation Test for correlation between protein content and cooking time:

In order to credibly answer our research question, where we are testing whether there exists a correlation between the cooking time of a recipe and the protein content of a recipe, we must test for a correlation between protein content and cooking time using permutation testing:

Null Hypothesis (H0): There is no correlation between the protein content of a recipe and the cooking time of a recipe.

Alternative Hypothesis (Ha): There is a correlation between the protein content of a recipe and the cooking time of a recipe.

Test Statistics: For the purpose of finding the correlation between the cooking time of a recipe and its protein content, we would simply utilize our merged data frame ‘recipe_nona’ to have already categorized columns as our testing variables. The specific columns we focused upon from ‘recipe_nona’ are the ‘protein’ column and the ‘minutes’ column. Therefore, since we are trying to determine a linear correlation between two variables within the same data set, we utilized Pearson correlation coefficient as our test statistics.

Significance Level: To ensure the accuracy of our findings and conclusions on our research question, we chose to use a significance level of 5% for this permutation test.

The plot below showcases the coorelation from permutation testing of our test statics in 10000 permutations

Observed Pearson correlation: 0.18592457955173802 P-value from the permutation test: 0.0 From the plot above, we can see that our p-value of 0 from the test that is less than our significance level of 0.05. Hence, we reject our null hypothesis.

Conclusion:

Given the tests conducted above and the results generated above, we conclude that our observed data in the merged ‘recipe_nona’ ’dataset indicates that there is a very weak negative correlation between the amount of protein in food and the rating of the food. Moreover, there is also a very weak positive correlation between the amount of protein and the minutes to prepare the food. Therefore, we reject that there is a correlation between the protein content of a recipe and the average rating of a recipe; we also reject that there is a correlation between the protein content of a recipe and the cooking time of a recipe.

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