Is there a significant difference in income between men and women? Does the difference vary depending on other factors (e.g., education, profession, criminal history, marriage status, etc.)?
To analyze this question, we’ll use the National Longitudinal Survey of Youth, 1997 cohort data set. This dataset is comprised of about 9000 youth who were initially interviewed in 1997, and then were interviewed more times in the following years. The dataset seeks to produce a longitudinal study of respondents transition from teenage to adult years. This gives us an opportunity to look at how income and gender intersect with other factors, particularly from the teenage years.
Note: The most recent survey data is from 2011. Any references to “last year” refer to the year prior to the survey, 2010.
First we should know the count of respondents, broken down by gender. We have 4385 females and 4599 males in the survey.
Next we’ll look at the mean income from last year, broken down by gender.
We can see here already that the average income from last year for women is lower than it is for men, by $7913.75, or that women are making 79.13% of what men make, on average. We’ll go into more detail about the statisitical significance of the difference later.
If we look at boxplots of income broken down by gender, we see that the interquartile range for women is lower than that of men, in addition to the lower mean. The outliers for the top earning women catch up with the outliers for the top earning men.
Note: At this point in the data summary we are excluding the top coded values. The rationale and further analysis regarding top coded values will be explained later in the report.
Now that we’ve looked at the data and observed a difference, we can run a t-test to find the statistical signifigance of this difference.
## ## Welch Two Sample t-test ## ## data: survey$income.lastyr by survey$gender ## t = -11.449, df = 5230, p-value < 2.2e-16 ## alternative hypothesis: true difference in means is not equal to 0 ## 99 percent confidence interval: ## -9694.893 -6132.607 ## sample estimates: ## mean in group female mean in group male ## 29997.82 37911.57
At a 95% confidence interval, we find a p-value of 0, indicating that the difference in the means of male and female income are not attributable to random chance.
So, to begin, we can say that yes, there is a significant difference in income between men and women. We will now consider the impact of other factors.
The mean income from last year, broken down by gender and race, can give us a starting off point for exploring other factors that may contribute to the wage gap. This table displays average income by gender by race, followed by the absolute and then percentage difference for each race in the survey. We can see that the gender wage gap exists for all racial catergories in the survey, though, by varying amounts. Looking at the boxplots, there appears to be less of a difference between the income means by gender for Blacks than for other races. There’s a large difference in the means for mixed race people, but there are also only 83 respondends coded as mixed race, making up only 0.92% of the survey. This low sample size makes it difficult to make inferences about this group.
|Female||Male||Abs Diff||% Diff|
Now we can also look at mean income by gender and industry. Again we see women making less, on average, than men across most of the categories.
The mean income for women is actually greater than men for
acs special codes. Similarly to what we saw in the breakdowns by race, though, it is worth nothing that only
acs special codes made up only 10 of respondants, which may mean that a singular or small number of outliers may be skewing this data.
|Female||Male||Abs Diff||% Diff|
|agr forest fish||21946.15||38904.76||16958.608||56.41|
|other public services||23123.93||28496.95||5373.027||81.15|
|entertain accom food||20168.33||23842.41||3674.081||84.59|
|fin insure real estate||35392.19||41608.47||6216.283||85.06|
|edu health social||30128.16||33902.60||3774.441||88.87|
|acs special codes||36500.00||21333.33||-15166.667||171.09|
If we look at boxplots of the distribution of income by gender and industry, we can make some other important observations. It appears that the sample of female active duty military is very small, and if we look at the data we can find it’s actually only 1. The lower quartile for men in the
utilities are above the upper quartile for women in those industries, while for
agr forest fish the quartiles don’t even overlap. The differences seem smaller for
entertain accom food, and
edu health social.
When bringing in and intially coding the data, I excluded missing values from numeric variables. While we can possibly make some assumptions about someone who, for example, did not know their income from last year, when analyzing and computing numeric values it is very difficult to do something with those assumptions.
Unfortuantely, we were missing last year’s income data for 40.98% of respondents. While that is unfortately a large percentage of our dataset, it still leaves 5302 respondents, which is a large sample size. The same goes for
industry, where we were missing 31.37%, but still have 6166 answers to analyze.
This does introduce a limit into the data, but for the most part the number of missing values was not too great.
For categorical values, things like
valid skip and
non-interview were coded into the analysis as
NA, while in most cases for categorical values
don't know were coded in as such. The
dont know values were ignored for some values where they comprised a small sample, but were analyzed further where they comprised a more signifigant proportion of responses.
For the most part, I removed topcoded values.
One instance where it made a difference was in looking at average income of men and women by industry. The averages by industry were displayed above in the data summary. The table below displays the industry, then mean female and male salary and the absolute difference and percent difference for means, all excluding topcoded values, followed by the absolute and percent differences if you include the topcoded values. The final column finds the difference in percentage points between the means that included the topcoded values and those that did not. This table is sorted by the final column.
|Female||Male||Excld Diff||Excld % Diff||W Diff||W % Diff||Differences|
|fin insure real estate||35392.19||41608.47||6216.283||85.06||5987.251||85.22||-0.16|
|agr forest fish||21946.15||38904.76||16958.608||56.41||16958.608||56.41||0.00|
|acs special codes||36500.00||21333.33||-15166.667||171.09||-15166.667||171.09||0.00|
|entertain accom food||20168.33||23842.41||3674.081||84.59||6803.854||82.92||1.67|
|edu health social||30128.16||33902.60||3774.441||88.87||4674.081||86.82||2.05|
|other public services||23123.93||28496.95||5373.027||81.15||6256.523||78.71||2.44|
Focusing only on the
Differences column we can see that some industries –
info comm and
construction in particular at -8.89% and 8.03% respectively, followed by
mining – have high differences depending on the inclusion or exclusion of the topcoded values. The next question is how big of a difference it makes to our analysis that these values are different.
Construction workers make up 4.79% of the respondents, which is a fair amount, while the number of respondants for other industries comprise a small portion of our sample.
Unexpected Variables That Had No Connection & Other Relationships
I had expected to find a difference between drug use and income by gender, but it was not very different.
I also thought there may be a difference income by gender based on household income growing up, that wealthier households would possibly set men up to be wealthier to a greater extent than women. However, it appears that greater income as a teenager means greater income as an adult but the difference by gender stays about steady, as seen in this graph below. In order to do this analysis I had to exclude some low, negative household income values that I think may be been erroneously entered.
Based on my finding that there is a relationship between weight and the income gap (more below) I suspected there may be a relationship between how respondents evaluated their own weight and income. However, we don’t see much difference across different answers to this question other than for men who consider themselves very underweight compared to women in the same catergory.