College Majors with Fewer Women tend to have Larger Pay Gaps

The Gender Pay Gap has become a key talking point for many in politics in the past few years. It is commonly quoted that women make only 77¢ for every $1 of their male counterparts. This statistic is calculated by taking the average salary of women and comparing it to the average salary of men. This does not control for job title, degree, regional difference, company size, or hours worked. After controlling for these factors, the gender pay gap drops from 77% to 98% (Payscale.com does a fantastic analysis and break down of the gender pay gap. I highly recommend you check it out.)

Using the salaries that controlled for these factors from the Payscale report, I decided to do further analysis on the pay gap. I wanted to know how the percentage of women in a field effected the pay difference between men and women. Since many companies try to hire equal amounts of men and women for similar roles and there are significantly fewer women in science and engineering, I assumed these few women would be able to demand a higher salary because of the scarcity. However, I found the opposite.

The interactive graphic below shows that college majors with fewer women tend to have higher differences in pay. (The graphics may be difficult to see on mobile, please switch to a desktop or use the mobile-friendly version)

Two of the largest outliers are Nursing and Accounting. Nursing has 92.3% women and men still make about $2400 more on average. Accounting has 52.1% women and a pay difference of +$2400 for men. One point of interest is elementary education where women make 1.4% more than men.

The following graph shows the same results as above, but instead of absolute difference in dollars, the commonly used metric of women's salaries as a percentage of men's salaries is plotted.



Any guess as to why this occurs would largely be speculative, but I imagine a “boy’s club” mentality could be to blame where men like to hire men and are willing to even pay more to do so.

The links to the data sources can be found below and as always, add any suggestions in the comments.

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Data Source:

[1] http://www.payscale.com/career-news/2009/12/do-men-or-women-choose-majors-to-maximize-income
[2] https://docs.google.com/spreadsheets/d/1FDrXUk4t-RQekuKotqMD7pyGFmylHip-xarOawcVvqk/edit#gid=0

A Look at Lynching in the United States

With the current racial tension within the United States and the Halloween season, I have seen many posts on Facebook showing black mannequins and other human-like figures hanging from trees. These images spark debate on whether these are directly racist acts or just distasteful mistakes. The comment sections are filled with pseudo-lynching-experts defending both sides.

So I decided to do an analysis on lynching within the United States. I found data on lynching from the Tuskegee Institute [1-2]. This data set contains information on lynchings from 1882-1962. I tried to find lynching statistics from before 1882 and found, during slavery, lynching Africans was fairly uncommon due to slave owners having a vested interest in keeping the slave alive.

The first bit of information I found shocking was whites made up 27% of lynching victims. However, the percentage of whites vs. blacks changes wildly from state to state. To understand this the percentage of black victims were plotted by state. As can be assumed, the deep south had the highest percentage of blacks followed by the rest of the south.

However, a look at the total number of lynchings showed states in the deep south did not offend evenly. Mississippi, Georgia, and Texas had the most lynchings (581, 531, and 493 respectfully) and then there was a large drop off to Louisiana and Alabama at 391 and 347. New Hampshire had zero lynchings and Delaware, Maine, and Vermont had one. New York and New Jersey only had two.

Over time, the number of people lynched has dropped to near zero. The next graph shows how lynching has decreased over time for whites and blacks. Black lynchings have about a 30 year lag behind the decrease of white lynchings.

In the first few years of the above chart, whites out number blacks in the number of lynchings. Below is a graph showing the percentage breakdown by year. Whites out number blacks for 4 years and then blacks out number whites for 60 years. In the last few years in the data set, whites exceed blacks. When taking into account how infrequent lynchings where in these last few years, two white people being lynched can account for 66.6% of lynchings.

I hope you learned something new, reading this analysis and as always, please feel free to add ideas for additional graphs or analysis in the comment section.

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Data Link and Notes:

[1] - http://law2.umkc.edu/faculty/projects/ftrials/shipp/lynchingsstate.html
[2] - http://law2.umkc.edu/Faculty/projects/ftrials/shipp/lynchingyear.html

Launching @BestOfData

[Image Credit: Gizmodo]

Since starting HallwayMathlete, many of my friends started having an interest in data visualization and all around data journalism. They have asked for suggestions on other websites to get top quality stories told through data analysis. The easiest answer is: FiveThirtyEight. However, there are many smaller blogs that turn out fantastic quality material, but in low volume. These smaller websites tend not to have Twitters, Facebook Pages, or other venues for fans to follow their most recent work.

For this reason, I am launching @BestOfData. Best of Data is an aggregation of the best smaller data journalism blogs on the web. Currently, Best of Data automatically pulls from a list of my favorite blogs and I will manual add other articles I find interesting.

The complete list of website automatically populating @BestOfData:
FlowingData.com
HowMuch.net
RandalOlson.com/Blog
Priceonomics.com
InformationIsBeautiful.net
ToddwSchneider.com
Insidesamegrain.com

Any websites you think I should add to this list? Please add them in the comments.

If you are not a Twitter user (you should really have a Twitter), the list of articles can be found at BestOfData.org.

Which is the best Pokemon in Pokemon GO?

Below are interactive graphics that display the average max CP of each Pokemon by trainer level. The first graph is of only the top Pokemon in Pokemon GO. The final graph shows all Pokemon and the following graphs are grouped by type.

Tips:

• If you want to know which Pokemon a line represents, place your mouse on the line and the information will be displayed. 
• To remove lines from the plot click the Pokemon's name in the legend.
• To see a graph in greater detail, click and drag over the region you wish to observe. 

Note: The graphics look better on desktop.

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Top Pokemon
Best Pokemon:
1. Mewtwo 

2. Dragonite 

3. Mew 

4. Moltres 

5. Zapdos 

6. Snorlax 

7. Arcanine 

8. Lapras 

9. Articuno 

10. Exeggutor 

11. Vaporeon 

12. Gyarados 

13. Flareon 

14. Muk 

15. Charizard 

Top Pokemon Currently Available In-Game 

1. Dragonite 

2. Snorlax 

3. Arcanine 

4. Lapras 

5. Exeggutor 

6. Vaporeon 

7. Gyarados 

8. Flareon 

9. Muk 

10. Charizard 

Some interesting notes, Blastoise and Venusaur both are not in the top pokemon; this is surprising for many who played the Gameboy Games because the starter pokemon were always some of the most powerful. Also, Dragonite and Charizard are the only top 10 pokemon who have three evolution forms. All others are two evolutions besides, Snorlax and Lapras.

After trainer level 30 the CP limit for each Pokemon grows at a slower rate than previous levels.

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All Pokemon

Magikarp is all the way at the bottom and by far the worst Pokemon in Pokemon GO.

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By Type 

• Bug 
• Dragon 
• Electric 
• Fairy 
• Fighting 
• Fire 
• Flying 
• Ghost 
• Grass 
• Ground 
• Ice 
• Normal 
• Poison 
• Psychic 
• Rock 
• Steel 
• Water

The data for the above plots comes from Serebii.net. In the following weeks, Hallway Mathlete will post a web-scraping tutorial showing how the data was gathered.

Analyzing the Annual Republicans vs. Democrats Congressional Baseball Game

Every year, the United States Congress takes a break from blocking each others bills and plays a charity baseball game. The best part, the teams are broken down by party lines, Republicans vs. Democrats. The tradition started in 1909 by Representative John Tener of Pennsylvania, a former professional baseball player. Last week was the annual game and Republicans were able to break a 7 year winning streak by the Democrats.

Below the net wins over the series is shown. The higher on the y axis the more Republican wins and the lower on the y axis the more Democrat wins. From this graph it is fairly obvious that each party has had long winning streaks. The gray dots represent years when the game was not held or I could not find any information about the game. In 1935, 1937, 1938, 1939, and 1941, games were held between members of congress and the press.

The following graph displays the points scored by each team over time. In the early years of the series, the games had much higher total scores than more recent years.

Next the point differentials were explored. The point differential is the difference between the scores of the two teams. Many of the closest games were held in the late seventies through the nineties. This time period also saw few winning streaks because the competition was fairly even between the parties.

A histogram was formed to understand the distribution of point differences. The Democrats have some extremely large wins with three wins over 20 points and the Republicans have none. Another interesting finding is that only one game ended in a tie. This is surprising because the charity event does not have overtime so it is logical to think out of the 81 games played more than one would end in a tie.

Over the years, the annual game has been held at many different locations.  Each party has had different rates of success at each field. The winning percentage at each field was calculated to understand if either party has a home-field-advantage at any park. Langley High School is a bit of an outlier because it was selected as the location after two rain delays and only hosted one game. American League Park II and Georgetown Field were the first two stadiums to host the game and each only hosted one game. Memorial Stadium had the fourth fewest games with only four, but all other locations had nine or more games.

Ironically, RFK Stadium, named after the famous Democratic U.S. Senator, has given Republicans a strong home-field-advantage. Republicans have won 13 out of the 14 games played at the stadium. Democrats have seen similar success at Nationals Park; winning 7 out of the 9 games.

Currently, I am planning to update these graphs each year after the annual game. Please feel free to add ideas for additional graphs or analysis in the comment section.

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Notes:

1. The data came from https://en.wikipedia.org/wiki/Congressional_Baseball_Game#Game_results
2. Some of the stadiums were renamed over the years and the original data set contained both names. For the analysis, the same stadiums were combined with the most recent name.

Salaries of Presidential Primary Voters by Candidate and State

The data used in this post comes from FiveThirtyEight and are put into easy to understand graphics. The first graphic shows the average salary of supports of each candidate by state. The states are ranked by highest average salary, Maryland, to the state with the lowest salary, Mississippi. The red line shows the average salary for each state. The first obvious conclusion is that John Kasich supporters make about $5-10 thousand more than supporters of other candidates. Second, in low salary states Clinton and Sanders supporter's have similar salaries, but when looking at higher salary states, Clinton supporters' salaries are even with Trump and Cruz supporters' salaries.

The following plot shows the distribution of average salaries for each Presidential Candidate. Again we see similar trends as before with Kasich having a high average income and Clinton having a mix of low and high income supporters.

The last plot shows the relationship between the average salary of a state and the average salary of a candidate's supporters. The red line is a perfect 1 to 1 ratio and the closer a candidate is to the red line the closer the candidate's supporters are to having the same salary as the average person of that state. The reason for almost all the dots falling above the line is because people with below average salaries are less likely to vote.

If you have any suggestions for plots using this data, please share in the comment section.

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Note:

[1] All states are not included because all states have not held elections yet.

Introduction to Machine Learning with Random Forest

The purpose of this tutorial is to serve as a introduction to the randomForest package in R and some common analysis in machine learning.

Part 1. Getting Started

First step, we will load the package and iris data set. The data set contains 3 classes of 50 instances each, where each class refers to a type of iris plant. One class is linearly separable from the other 2; the latter are NOT linearly separable from each other.

install.packages('randomForest')
library(randomForest)
data(iris)
head(iris)

Part 2. Fit Model

Now that we know what our data set contains, let fit our first model. We will be fitting 500 trees in our forest and trying to classify the Species of each iris in the data set. For the randomForest() function, "~." means use all the variables in the data frame.

Note: a common mistake, made by beginners, is trying to classify a categorical variable that R sees as a character. To fix this, convert the variable to a factor like this randomForest(as.factor(Species) ~ ., iris, ntree=500)

fit <- randomForest(Species ~ ., iris, ntree=500)

The next step is to use the newly create model in the fit variable and predict the label.

results <- predict(fit, iris)
summary(results)

After you have the predicted labels in a vector (results), the predict and actual labels must be compared. This can be done with a confusion matrix. A confusion matrix is a table of the actual vs the predicted with the diagonal numbers being correctly classified elements while all others are incorrect.

# Confusion Matrix
 table(results, iris$Species) 

Now we can take the diagonal points in the table and sum them, this will give us the total correctly classified instances. Then dividing this number by the total number of instances will calculate the percentage of prediction correctly classified. <- -="" 1="" accuracy="" correctly_classified="" div="" error="" iris="" length="" pecies="" results="" style="overflow: auto;" table="" total_classified="">

# Calculate the accuracy  
correctly_classified <- table(results, iris$Species)[1,1] + table(results, iris$Species)[2,2] + table(results, iris$Species)[3,3] 
total_classified <- length(results)  
# Accuracy   
correctly_classified / total_classified   
# Error  
1 - (correctly_classified / total_classified)

Part 3. Validate Model 

The next step is to validate the prediction model. Validation requires splitting your data into two sections. First, the training set, which will be used to create the model. The second will be the test set and will test the accuracy of the prediction model. The reasoning for splitting the data is to allow a model to be created using one data set and then reserving some data, where the output is already known, to "test" the model accuracy. This more effectively estimates the accuracy of the model by not using the same data used to create the model and predict the accuracy.

# How to split into a training set   
rows <- nrow(iris) col_count <- c(1:rows)  
Row_ID <- sample(col_count, rows, replace = FALSE)   
iris$Row_ID <- Row_ID   
 
# Choose the percent of the data to be used in the training 
data training_set_size = .80   
#Now to split the data into training and test 
 index_percentile <- rows*training_set_size   
# If the Row ID is smaller then the index percentile, it will be assigned into the training set   
train <- iris[iris$Row_ID <= index_percentile,]   
# If the Row ID is larger then the index percentile, it will be assigned into the training set   
test <- iris[iris$Row_ID > index_percentile,]   
train_data_rows <- nrow(train)   
test_data_rows <- nrow(test)   
total_data_rows <- (nrow(train)+nrow(test)) train_data_rows / total_data_rows     
 
# Now we have 80% of the data in the training set  test_data_rows / total_data_rows     
# Now we have 20% of the data in the training set   
# Now lets build the randomforest using the train data set  
fit <- randomForest(Species ~ ., train, ntree=500) 

After the test set is predicted, a confusion matrix and accuracy must be calculated.

# Use the new model to predict the test set   
results <- predict(fit, test, type="response")   
# Confusion Matrix  
table(results, test$Species)  
# Calculate the accuracy   
correctly_classified <- table(results, test$Species)[1,1] + table(results, test$Species)[2,2] + table(results, test$Species)[3,3] total_classified <- length(results)   
# Accuracy   
correctly_classified / total_classified  
# Error  
1 - (correctly_classified / total_classified)

Part 4. Model Analysis 

After the model is created, understanding the relationship between variables and number of trees is important. R makes it easy to plot the errors of the model as the number of trees increase. This allows users to trade off between more trees and accuracy or fewer trees and lower computational time.

fit <- randomForest(Species ~ ., train, ntree=500)   
results <- predict(fit, test, type="response")  
 
# Rank the input variables based on their effectiveness as predictors   
varImpPlot(fit)   
# To understand the error rate lets plot the model's error as the number of trees increases  
plot(fit) 

Part 5. Handling Missing Values 

The last section of this tutorial involves one of the most time consuming and important parts of the data analysis process, missing variables. Very few machine learning algorithms can handle missing data in the data. However the randomForest package contains one of the most useful functions of all time, na.roughfix(). Na.roughfix() takes the most common factor in that column and replaces all the NAs with it. For this section we will first create some NAs in this data set and then replace them and run the prediction algorithm.

# Create some NA in the data.   
iris.na <- iris for (i in 1:4)  
iris.na[sample(150, sample(20)), i] <- NA   
 
# Now we have a dataframe with NAs   
View(iris.na)   
#Adding na.action=na.roughfix   
#For numeric variables, NAs are replaced with column medians.   
#For factor variables, NAs are replaced with the most frequent levels (breaking ties at random) 

iris.narf <- randomForest(Species ~ ., iris.na, na.action=na.roughfix) 

results <- predict(iris.narf, train, type="response")

Congratulations! You now know how to create machine learning models, fit data using those models, test the model’s accuracy and display it in a confusion matrix, how to validate the model, and quickly replace missing variables. All of these are the basic fundamental skills in machine learning!