# Want a Raise? Move to a Smaller, Colder State?

I recently read an article about how the United States median household income has declined the last two years in a row. While that should make most of us as joyful as a vegetarian who just won a lifetime supply of beef jerky, there are some states that have median household incomes well above the norm.

So, any guesses as to which state is the best at over $70K, and which is the worst at nearly half that amount? Here's a hint: both states start with the letter M.

If you guessed Maryland and Mississippi, respectively, you’d be right.

The article then went on to list the top 5 states at both ends of the spectrum.

Perhaps temperature is on my mind because I recently had to bid farewell to my flip flops and reacquaint myself with my winter coat, but the first thing I noticed about this list was that all of the top states are going to be blanketed with snow in the upcoming months, while most of the not-so-rich states will be enjoying the warm sun for months to come.

And due to the fact that I was the proud owner of my very own true-to-scale U.S. States puzzle when I was a kid (thanks Mom and Dad), I also noticed that the highest-ranking states were generally smaller in size than the states with lower household incomes.

## Gathering Data for Further Analysis

I decided to dig deeper to find out if my observations regarding temperature and state size, and their relationship to household income, held true for *all* 50 states.

Using the U.S. Census Bureau web site, I collected data on the following variables for each of the 50 states:

- Median household income
- Percent of population below poverty line
- Unemployment rate
- Population
- State land size (square miles)
- Average winter temperature (December - February

You may have noticed that the Census Bureau reports the median, not the mean, household income. This is a good thing since the mean can be greatly influenced by outliers (Hello, Mr. Gates!).

In addition to collecting the data above, I also created a variable for population per square mile since there are states like Alaska (shown in blue) and Texas that are much bigger than every other state. Since Alaska is so gargantuan, it’s no surprise that this state has the least number of people per square mile. In fact, at 1.27 people per square mile, there are actually more caribou in Alaska than people. And in case you’re wondering, as I did, the most populated state happens to be New Jersey, at 1,189 people per square mile.

## Graphing the Data

The ultimate goal here is to prove whether or not I’m onto something with this idea that people in smaller, colder states are making more money. Like a good analyst, I used Minitab to first graph my data and found something rather interesting on one of the boxplots.

The boxplot for population per square mile reveals some outliers, nearly all of which rank among the richest states. Interesting! What top 5 state wasn’t an outlier for population per square mile? Alaska, of course, which at 1.27 is the minimum value on the graph.

Now, am I going to remove these outliers? Not a chance. They account for 10% of the entire dataset and belong with the rest of the population. And if I look at a scatterplot of income by population per square mile (not shown), I see a positive trend regardless of whether these observations are included or not, so they aren’t skewing the results even though the values are unusually large compared to the other states.

Also, depending on how you slice and dice the data, there are outliers everywhere…Alaska, Texas and California are much larger than most states; Hawaii is much warmer in the winter; etc.

## Analyzing the Data

After graphing the data to assess outliers and visually examine the relationship between the variables, I then ran a correlation analysis to evaluate the strength of the linear relationship between median household income and all of the other variables. Look what I found:

We can see that some of the p-values are statistically significant (using an alpha-level = 0.05), while others like state land size are not (p=0.383). Based on this nonsignificant p-value, it looks like my initial observation about smaller states making more money doesn't apply to the entire country.

However, my hypothesis regarding temperature was right on! The p-value for the correlation between income and average winter temperature is significant (p-value = 0.044). And since the correlation coefficient of -0.286 is negative, this tells us that as the average winter temperature increases, the median household income decreases.

The other two significant p-values are for %below poverty line, which makes sense, and population per square mile. The coefficient of 0.511 is positive, so this indicates that the more populous a state is, the higher the median household income.

In conclusion, there are statistically significant relationships between median household income and both population per square mile and average winter temperature (and %below poverty line). So if you want to make more money, I hope you find crowds and cold weather as appealing as a bigger paycheck!