R Lesson 23: US Mapmaking with R (pt. 2)-Coloring the Map with Geographic Data

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Hello everybody,

Michael here, and first of all, Happy New Year! I bet you’re glad that 2020 is finally behind us!

Now, for my first post of 2021, I will continue my lesson on US Mapmaking with R that I started before the holidays. This time, I will cover how to fill in the map based on certain geographic data. Also, before you start coding along, make sure to install the usmap package.

Now, let’s upload our first data set (I’ll use two data sets for this lesson) to R. Here’s the file for the data:

This is a simple dataset showing the amount of COVID-19 cases and deaths in each state (excluding DC) as of January 13, 2021. However, this data-frame needs one more column-FIPS (representing the FIPS code of each state). Here’s how to add the FIPS column to this data-frame:

> file$fips <- fips(file$ï..state)
> str(file)
'data.frame':   50 obs. of  4 variables:
 $ ï..state: chr  "Alabama" "Alaska" "Arizona" "Arkansas" ...
 $ Cases   : int  410995 50816 641729 262020 2815933 366774 220576 67173 1517472 749417 ...
 $ Deaths  : int  5760 225 10673 4186 31105 5326 6536 994 23754 11803 ...
 $ fips    : chr  "01" "02" "04" "05" ...

In this example, I used the fips function to retrieve all of the FIPS codes for each state. I then stored the results of this function in a variable called file$fips, which attaches the fips variable to the existing file data-frame. Once I ran the str(file) command again, I see that the fips variable has been added to the file data-frame.

Now, let’s plot a basic US map with the COVID case data-this time, let’s focus on cases:

plot_usmap(data=file, values="Cases")

In order to create a US map plot of COVID cases, all I needed to do was to indicate the data (which is the data-frame file) and the values (Cases enclosed in double quotes).

As you can see, the map plot above is colored in varying shades of blue to represent a state’s cumulative COVID case count-the lighter the blue, the more cumulative cases a state had. California is the colored with lightest shade of blue, as they had over 2 million cumulative cases as of January 13, 2021. On the other hand, Vermont is colored with the darkest shade of blue, as they were the only state with fewer than 10,000 COVID cases as of January 13, 2021.

The map plot above looks good, but what if you wanted to change the color or scale? Here’s how to do so (and add a title in the process)-also keep in mind that if you want to update the color, scale, and title for the map plot, remember to install the ggplot2 package:

 plot_usmap(data=file, values="Cases") + labs(title="US COVID cases in each state 1-13-21") + scale_fill_continuous(low = "lightgreen", high = "darkgreen", name = "US COVID cases", label = scales::comma) + theme(legend.position = "right")

In this example, I still created a US plot map from the Cases column in the dataset, but I changed the color scale-and in turn color-of the map plot to shades of green (where the greater of COVID cases in a state, the darker the shade of green that state is colored). I also changed the scale name to US COVID cases and labels to scales::comma, which displays the numbers on the scale as regular numbers with thousands separators (not the scientific notation that was displayed on the previous example’s scale.

After modifying the coloring and scale of the map plot, I also added a title with the labs function and used the theme function to place the legend to the right of the map plot.

Now I will create another map, this time using the Deaths column as the values. Here’s the code to do so:

 plot_usmap(data=file, values="Deaths") + labs(title="US COVID deaths in each state 1-13-21") + scale_fill_continuous(low = "yellow1", high = "yellow4", name = "US COVID deaths", label = scales::comma) + theme(legend.position = "right")

In this example, I used the same code from the previous example, except I replaced “cases” with “deaths” and colored the map in yellow-scale (the more deaths a state had, the darker the shade of yellow). As you can see, California, Texas, and New York have the darkest shades of yellow, which meant that they led the nation in COVID-19 deaths on January 13, 2021. However, unlike with COVID cases, New York led the nation in COVID deaths, not California (New York had just under 40,000 COVID deaths while California had roughly 31,000).

Now, let’s try creating a state map (broken down by county) with COVID data. For these next examples, I’ll create a county map of the state of Tennessee’s COVID cases and deaths-similar to what I did in the previous two examples.

First, let’s upload the new dataset to R. Here’s the file for the dataset:

Just like the previous dataset, this dataset also has data regarding COVID cases & deaths, except this time it’s broken down by counties in the state of Tennessee (and the data is from January 22, 2021, not January 13).

Now, before we start creating the map plots, we need to retrieve the county FIPS codes for each of the 95 Tennessee counties. Here’s the code to do so:

> file2$fips <- fips(file2$ï..county, state="TN")
> str(file2)
'data.frame':   95 obs. of  4 variables:
 $ ï..county: chr  "Davidson County" "Shelby County" "Knox County" "Hamilton County" ...
 $ Cases    : int  81141 79388 40804 36652 33687 21776 18551 14836 14674 12811 ...
 $ Deaths   : int  679 1169 434 337 294 142 232 149 160 216 ...
 $ fips     : chr  "47037" "47157" "47093" "47065" ...

To retrieve the FIPS codes for counties, you would follow the same syntax as you would if you were retrieving FIPS codes for states. However, you also need to specify the state where the counties in the dataset are located-recall that from the previous lesson R Lesson 22: US Mapmaking with R (pt. 1) that there are several counties in different states that have the same name (for instance, 12 states have a Polk County, including Tennessee).

Now that we have the county FIPS codes, let’s start plotting some maps! Here’s the code to plot the map of Tennessee counties with COVID case data by county:

plot_usmap(regions="counties", data=file2, values="Cases", labels=TRUE, include=c("TN")) + labs(title="Tennessee county COVID cases 1-22-21") + scale_fill_continuous(low = "orange1", high = "orange4", name = "Tennessee county COVID cases", label = scales::comma) + theme(legend.position = "right")

Now, the code to create a state map plot broken down by county is nearly identical to the code used to create a map plot of the whole US with a few differences. Since you are plotting a map of an individual state, you need to specify the state you are plotting in the include parameter’s vector (the state is TN in this case). Also, since you are breaking down the state map by county, specify that regions are counties (don’t use county since you’re plotting all counties in a specific state, not just a single county).

  • You don’t need to add the county name labels to the map-I just thought that it would be a nice addition to the map plot.

In this example, I colored the map plot in orange-scale (meaning that the more cases of COVID in a county, the darker the shade of orange will be used). As you can see, the four counties with the darkest shades of orange are Davidson, Shelby, Knox, and Hamilton counties, meaning that these four counties had the highest cumulative case count as of January 22, 2021. These four counties also happen to be where Tennessee’s four major cities-Nashville, Memphis, Knoxville, and Chattanooga-are located.

Now let’s re-create the plot above, except this time let’s use the Deaths variable for values (and change the color-scale as well):

plot_usmap(regions="counties", data=file2, values="Deaths", labels=TRUE, include=c("TN")) + labs(title="Tennessee county COVID deaths 1-22-21") + scale_fill_continuous(low = "turquoise1", high = "turquoise4", name = "Tennessee county COVID deaths", label = scales::comma) + theme(legend.position = "right")

In this example, I used the same code from the previous example, except I used Deaths for the values and replaced the word “cases” with “deaths” on both the legend scale and title of the map plot. I also used turquoise-scale for this map plot rather than orange-scale.

An interesting difference between this map plot and the Tennessee COVID cases map plot is that, while the four counties that led in case counts (Hamilton, Knox, Shelby, and Davidson) also led in deaths, Shelby County is actually darker on the map than Davidson county, which implies that Shelby County (where Memphis is located) led in COVID deaths (Davidson County led in cases).

Thanks for reading, and can’t wait to share more great programming and data analytics content in 2021 with you all!

Michael

R Lesson 22: US Mapmaking with R (pt. 1)

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Hello everybody,

Michael here, and today’s post (which is my last post for 2020) will be a lesson on basic US mapmaking with R. Today we’ll only focus on US mapmaking with R, but don’t worry, I intend to do a global mapmaking with R post later on.

Before we get started mapmaking, install these two packages to R-ggplot2 and usmap. Once you get these two packages installed, write this code and see the output:

plot_usmap(regions = "states") + labs(title="US States") + theme(panel.background = element_rect(color="black", fill = "lightblue"))

As you can see, we have created a basic map of the US (with Alaska and Hawaii), complete with a nice blue ocean.

However, this isn’t the only way you can plot a basic map of the US. The regions parameter has four different options for plotting the US map-states (which I just plotted), state, counties, and county.

Let’s see what happens when we use the state option:

plot_usmap(regions = "state", include=c("TN")) + labs(title="Tennessee") + theme(panel.background = element_rect(color="black", fill = "lightblue"))

In this example, I used the state option for the regions parameter to create a plot of the state of Tennessee (but left everything else unaltered).

How did I manage to get a plot of a single state? The plot_usmap function has several optional parameters, one of which is include. To plot the state of Tennessee, I passed a vector to the include parameter that consisted of a single element-TN.

  • Whenever you want to plot a single state (or several states), don’t type in the state’s full name-rather, use the state’s two-letter postal code.
  • Another parameter is exclude, which allows you to exclude certain states from a multi-state map plot (I’ll discuss multi-state map plots later).

Awesome! Now let’s plot our map with the counties option:

plot_usmap(regions = "counties") + labs(title="US Counties") + theme(panel.background = element_rect(color="black", fill = "lightblue"))

This map looks just like the first map, except it shows all of the county lines in each state.

Last but not least, let’s plot our map with the county option:

plot_usmap(regions = "county", include=c("Davidson County")) + labs(title="Davidson County") + theme(panel.background = element_rect(color="black", fill = "lightblue"))

In this example, I attempted to create a plot of Davidson County, TN, but that didn’t work out. The plot didn’t work because, even though I told R to include Davidson County in the plot, R didn’t know which state Davidson County was in, as there are two counties named Davidson in the US-one in Tennessee and another in North Carolina.

This shows you that using the county name alone when using the county argument for the regions parameter won’t work, since there are often multiple counties in different states that share the same name-the most common county name in the US is Washington County, which is shared by 31 states.

So, how do I correctly create a county plot in R? First, I would need to retrieve the county’s FIPS code.

To give you some background, FIPS stands for Federal Information Processing Standards and FIPS codes are 2- or 5-digit codes that uniquely identify states or counties. State FIPS codes have 2-digits and county FIPS codes have 5 digits; the first two digits of a county FIPS code are the corresponding state’s FIPS code. Here’s an example of county FIPS codes using the two Davidson Counties I discussed earlier:

> fips(state="TN", county="Davidson")
[1] "47037"
> fips(state="NC", county="Davidson")
[1] "37057"

In this example, I printed out the county FIPS codes for the two Davidson Counties. The FIPS code for Davidson County, TN is 47307 because Tennessee’s FIPS code is 47. Similarly, the FIPS code for Davidson County, NC is 37057 because North Carolina’s FIPS code is 37.

Now that we know the FIPS code for Davidson County, TN, we can create a plot for the county. Here’s the code to do so:

plot_usmap(regions = "county", include=c(fips(state="TN", county="Davidson"))) + labs(title="Davidson County, TN") + theme(panel.background = element_rect(color="black", fill = "lightblue"))

When I create a map plot of an individual US county, I get the shape of the county.

  • A more efficient way to write the code for this plot would have been plot_usmap(regions = "county", include=c(fips) + labs(title="Davidson County, TN") + theme(panel.background = element_rect(color="black", fill = "lightblue")) where fips would be stored as a variable with the value fips <- fips(state="TN", county="Davidson") .

So how can we get a map of several US counties, or rather, a state map broken down by counties? Here’s the code to do so:

plot_usmap(regions = "counties", include=c("TN")) + labs(title="Tennessee's 95 counties") + theme(panel.background = element_rect(color="black", fill = "lightblue"))

To create a state map broken down by counties, set regions to counties and set the include parameter to include the state you want to plot (TN in this case). As you can see, I have created a map plot of the state of Tennessee that shows all 95 county boundaries in the state.

What if you wanted to plot several states at once? Well, the usmap packages has built-in region parameters that create a plot of certain US regions (as defined by the US Census Bureau), which consist of several states. The regions you can plot include:

  • .east_north_central-Illinois, Indiana, Michigan, Ohio, and Wisconsin
  • .east_south_central-Alabama, Kentucky, Mississippi, and Tennessee
  • .midwest_region-any state in the East North Central and the West North Central regions
  • .mid_atlantic-New Jersey, New York, and Pennsylvania
  • .mountain-Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah, and Wyoming
  • .new_england-Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont
  • .northeast_region-any state in the New England or Mid-Atlantic regions
  • .north_central_region-any state in the East and West North Central regions
  • .pacific-Alaska, California, Hawaii, Oregon, and Washington
  • .south_atlantic-Delaware, Florida, Georgia, Maryland, North Carolina, South Carolina, Virginia, Washington DC, and West Virginia
  • .south_region-any state in the South Atlantic, East South Central, and West South Central regions
  • .west_north_central-Iowa, Kansas, Minnesota, Missouri, Nebraska, North Dakota, and South Dakota
  • .west_region-any state in the Mountain and Pacific regions
  • .west_south_central-Arkansas, Oklahoma, Louisiana, and Texas

Let’s plot out a simple region map for the .east_south_central region. Here’s the code to do so:

 plot_usmap(include = .east_south_central) +  labs(title="East South Central US", size=10) + theme(panel.background = element_rect(color="black", fill = "lightblue"))

Simple enough, right? All I did was set the include parameter to .east_south_central.

  • Remember to always include a dot in front of the region name so R reads the region name as one of the built-in regions in usmap; if you don’t include the dot, R would read the region name as a simple String, which will generate errors in your code.

Now let’s break up the region map by counties. Here’s the code to do so:

plot plot_usmap(regions = "counties", include = .east_south_central) +  labs(title="East South Central US", size=10) + theme(panel.background = element_rect(color="black", fill = "lightblue"))

To show all of the county lines in a specific region, simply set the regions parameter to counties. Also (and you probably noticed this already), if you don’t set a value for the regions parameter, regions defaults to states.

OK, so I’ve covered the basics of US map plotting with the usmap package. But did you know you can display state and county names on the map plot? Here’s the code to add state name labels to a map plot of the whole US:

 plot_usmap(regions = "states", labels=TRUE) + labs(title="US States") + theme(panel.background = element_rect(color="black", fill = "lightblue"))

The code I used to create this map plot is almost identical to the code I used to create the first map plot with one major exception-I included a labels parameter and set it to TRUE. If the labels parameter is set to true, the state label name will be displayed on each state (the label name being the state’s 2-letter postal code).

Now let’s display county names on a map, using the state map of Tennessee. Here’s the code to do so:

 plot_usmap(regions = "counties", labels=TRUE, include=c("TN")) + labs(title="Tennessee's 95 counties") + theme(panel.background = element_rect(color="black", fill = "lightblue"))

As you can see, by setting labels to TRUE, I was able to include all of Tennessee’s county names on the map (and most of them fit quite well, though there are a few overlaps).

Thanks for reading,

Michael

Also, since this is my last post of 2020, thank you all for reading my content this year. I know it’s been a crazy year, but hope you all learned something from my blog in the process. Have a happy, healthy, and safe holiday season, and I’ll see you all in 2021 with brand new programming content (including a part 2 to this lesson)!

R Lesson 17: ANOVA Part 1

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Hello everybody,

It’s Michael, and today I will be discussing ANOVA in R. ANOVA is a statisical technique in R that stands for analysis of variance. ANOVA is used to analyze data in R by comparing the means of subsets in the data. There are two types of ANOVA-one way and two way-the first of which I’ll discuss in this post. I’ll discuss two-way ANOVA in my next post.

Here’s the dataset-US Cities.

This dataset contains information about 150 randomly selected US cities (three for each state) such as population and climate. As always let’s load our file into R and learn more about our data:

There are 150 observations of 11 variables. Here’s a detailed breakdown of each variable:

  • City-the name of the US city
    • The reason R says City only displays 149 levels, despite there being 150 cities is because I used “Jackson” twice  (for Jackson, Mississippi and Jackson, Wyoming).
  • State-I used the state’s postal code here, rather than the state’s name. For instance, Alaska is AK, Alabama is AL, and so on.
  • Population-the city’s population; I tried to get the most recent data possible, but in some cases, I had to rely on data from the 2010 US Census.
  • January.High and January.Low-The city’s high & low temperatures for the month of January, respectively.
  • July.High and July.Low-The city’s high & low temperatures for the month of July, respectively.
    • I chose January and July to get a gauge of a city’s climate since they are the coldest and hottest months of the year, respectively.
  • Time.Zone-the time zone where the city is located. I used single letters to represent each time zone, which are as follows:
    • A-Alaska (the state has its own time zone)
    • H-Hawaii (the one other state with its own time zone)
    • E-Eastern
    • C-Central
    • M-Mountain
    • P-Pacific
  • Elevation-How many feet a city is above sea level.
    • There is one negative number in the dataset-(-6)-which corresponds to New Orleans. This means that New Orleans is the only city in this dataset that is below sea level.
  • Landlocked-Whether or not the city is located in a landlocked state-0 means the state isn’t landlocked while 1 means the state is landlocked.
  • Founded-the year a city was founded/settled. Sometimes I used the settlement year if I couldn’t find the year a city was founded.

Now let’s start the ANOVA. I will start with one-way ANOVA, which is just ANOVA using  one independent variable.

Here’s our model along with the model’s summary:

In this model, I used January.Low as a dependent variable and State as an independent variable. If you’re wondering what I’m trying to analyze, I’m looking the relationship between states and the pleasantness/misery of their winters. I used January.Low rather than January.Highbecause I felt that the former would be a better measure of how good/bad a state’s winter is.

Now, before I discuss the output below summary, let me explain the concepts of null hypothesis and alternative hypothesis, as they are important to one-way ANOVA. A null hypothesis states that there is NO statistical significance between the dependent and independent variable. In this case, the null hypothesis is that there is no statistically significant relationship between a state and the pleasantness/misery of their winters.This is the hypothesis that we are trying to disprove.

On the other hand, the alternative hypothesis is simply the opposite of the null hypothesis; this hypothesis states that there is a statistically significant relationship between our dependent variable (January.Low) and our independent variable (State).

Now let’s explain the output below summary. First of all, the Df stands for degrees of freedom, which represents the amount of values that are free to vary in a dataset. The Df for State is 49, which means that there are 49 values in State that may vary.

We got 49 degrees of freedom because there are 50 possible values for State. Degrees of freedom for a variable/dataset will always be equal to N-1, with N being either the number of possible values in a variable or number of observations in a dataset. Why do we always subtract by 1? Here’s why:

Let’s say we’re looking for a set a four numbers that add up to 100. Some possibilities include (15, 20, 25, 40) or (15, 18, 30, 37) or (15, 16, 30, 39). However, notice that only three of the four numbers in each set vary, while the fourth is fixed, since it will always be 15. Therefore, only three of the four numbers are free to vary.

The f-value is 17.46 which is highly significant, given that the corresponding p-value is much less than the benchmark* level of significance-0.01 or 1%. This means that there is a statistically significant relationship between a state and how good/bad their winters are.

  • The “benchmark level of significance” refers to the threshold where you should reject the null hypothesis. Remember that if the Pr(>f)-which refers to the p-value of your independent variable-is less than 0.01 for your independent variable, reject the null hypothesis.

The Sum Sq and Mean Sq columns, which represent sum of squares and mean of sqaures, respectively (for both the independent variable and the residuals(, aren’t important for our ANOVA analysis.

Now it’s time to analyze pair-wise differences. In this case, we are analyzing the pair-wise differences between states to see which state pair has the greatest winter temperature difference. To analyze pair-wise differences, let’s use Tukey’s HSD test, which stands for Tukey’s Honest Significance Test. Here’s how it works (and I couldn’t post a screenshot since the output is too long). By the way, the line to set up the Tukey’s HSD test is TukeyHSD(model, conf.level=0.99)-remember that we’re analyzing our data with a 99% confidence level:

diff lwr upr p adj
AL-AK 34.33333333 15.0921361 53.574530535 0.0000000
AR-AK 26.90000000 7.6588028 46.141197201 0.0000048
AZ-AK 42.16666667 22.9254695 61.407863868 0.0000000
CA-AK 43.03333333 23.7921361 62.274530535 0.0000000
CO-AK 16.86666667 -2.3745305 36.107863868 0.0650303
CT-AK 18.80000000 -0.4411972 38.041197201 0.0145141
DE-AK 25.06666667 5.8254695 44.307863868 0.0000350
FL-AK 48.80000000 29.5588028 68.041197201 0.0000000
GA-AK 33.16666667 13.9254695 52.407863868 0.0000000
HI-AK 61.10000000 41.8588028 80.341197201 0.0000000
IA-AK 10.23333333 -9.0078639 29.474530535 0.9446692
ID-AK 13.10000000 -6.1411972 32.341197201 0.5202584
IL-AK 13.83333333 -5.4078639 33.074530535 0.3867198
IN-AK 16.80000000 -2.4411972 36.041197201 0.0681855
KS-AK 18.13333333 -1.1078639 37.374530535 0.0249778
KY-AK 22.23333333 2.9921361 41.474530535 0.0006339
LA-AK 39.13333333 19.8921361 58.374530535 0.0000000
MA-AK 18.06666667 -1.1745305 37.307863868 0.0263343
MD-AK 23.90000000 4.6588028 43.141197201 0.0001185
ME-AK 13.50000000 -5.7411972 32.741197201 0.4457807
MI-AK 15.26666667 -3.9745305 34.507863868 0.1844181
MN-AK 5.33333333 -13.9078639 24.574530535 1.0000000
MO-AK 20.20000000 0.9588028 39.441197201 0.0043056
MS-AK 36.26666667 17.0254695 55.507863868 0.0000000
MT-AK 12.33333333 -6.9078639 31.574530535 0.6652421
NC-AK 28.03333333 8.7921361 47.274530535 0.0000014
ND-AK -2.43333333 -21.6745305 16.807863868 1.0000000
NE-AK 11.63333333 -7.6078639 30.874530535 0.7858266
NH-AK 11.86666667 -7.3745305 31.107863868 0.7478742
NJ-AK 23.30000000 4.0588028 42.541197201 0.0002188
NM-AK 21.06666667 1.8254695 40.307863868 0.0019407
NV-AK 26.66666667 7.4254695 45.907863868 0.0000062
NY-AK 19.76666667 0.5254695 39.007863868 0.0063352
OH-AK 19.10000000 -0.1411972 38.341197201 0.0112786
OK-AK 24.00000000 4.7588028 43.241197201 0.0001069
OR-AK 32.00000000 12.7588028 51.241197201 0.0000000
PA-AK 20.33333333 1.0921361 39.574530535 0.0038167
RI-AK 20.50000000 1.2588028 39.741197201 0.0032794
SC-AK 32.90000000 13.6588028 52.141197201 0.0000000
SD-AK 7.70000000 -11.5411972 26.941197201 0.9996197
TN-AK 25.93333333 6.6921361 45.174530535 0.0000138
TX-AK 36.00000000 16.7588028 55.241197201 0.0000000
UT-AK 16.70000000 -2.5411972 35.941197201 0.0731639
VA-AK 27.16666667 7.9254695 46.407863868 0.0000036
VT-AK 7.56666667 -11.6745305 26.807863868 0.9997438
WA-AK 30.73333333 11.4921361 49.974530535 0.0000001
WI-AK 7.83333333 -11.4078639 27.074530535 0.9994447
WV-AK 21.60000000 2.3588028 40.841197201 0.0011709
WY-AK 10.26666667 -8.9745305 29.507863868 0.9423542
AR-AL -7.43333333 -26.6745305 11.807863868 0.9998304
AZ-AL 7.83333333 -11.4078639 27.074530535 0.9994447
CA-AL 8.70000000 -10.5411972 27.941197201 0.9954754
CO-AL -17.46666667 -36.7078639 1.774530535 0.0418707
CT-AL -15.53333333 -34.7745305 3.707863868 0.1572874
DE-AL -9.26666667 -28.5078639 9.974530535 0.9866689
FL-AL 14.46666667 -4.7745305 33.707863868 0.2858501
GA-AL -1.16666667 -20.4078639 18.074530535 1.0000000
HI-AL 26.76666667 7.5254695 46.007863868 0.0000056
IA-AL -24.10000000 -43.3411972 -4.858802799 0.0000964
ID-AL -21.23333333 -40.4745305 -1.992136132 0.0016592
IL-AL -20.50000000 -39.7411972 -1.258802799 0.0032794
IN-AL -17.53333333 -36.7745305 1.707863868 0.0398126
KS-AL -16.20000000 -35.4411972 3.041197201 0.1029146
KY-AL -12.10000000 -31.3411972 7.141197201 0.7075040
LA-AL 4.80000000 -14.4411972 24.041197201 1.0000000
MA-AL -16.26666667 -35.5078639 2.974530535 0.0984460
MD-AL -10.43333333 -29.6745305 8.807863868 0.9297498
ME-AL -20.83333333 -40.0745305 -1.592136132 0.0024125
MI-AL -19.06666667 -38.3078639 0.174530535 0.0116018
MN-AL -29.00000000 -48.2411972 -9.758802799 0.0000005
MO-AL -14.13333333 -33.3745305 5.107863868 0.3368657
MS-AL 1.93333333 -17.3078639 21.174530535 1.0000000
MT-AL -22.00000000 -41.2411972 -2.758802799 0.0007960
NC-AL -6.30000000 -25.5411972 12.941197201 0.9999977
ND-AL -36.76666667 -56.0078639 -17.525469465 0.0000000
NE-AL -22.70000000 -41.9411972 -3.458802799 0.0003998
NH-AL -22.46666667 -41.7078639 -3.225469465 0.0005039
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NH-NE 0.23333333 -19.0078639 19.474530535 1.0000000
NJ-NE 11.66666667 -7.5745305 30.907863868 0.7805710
NM-NE 9.43333333 -9.8078639 28.674530535 0.9823527
NV-NE 15.03333333 -4.2078639 34.274530535 0.2108675
NY-NE 8.13333333 -11.1078639 27.374530535 0.9987715
OH-NE 7.46666667 -11.7745305 26.707863868 0.9998117
OK-NE 12.36666667 -6.8745305 31.607863868 0.6590833
OR-NE 20.36666667 1.1254695 39.607863868 0.0037030
PA-NE 8.70000000 -10.5411972 27.941197201 0.9954754
RI-NE 8.86666667 -10.3745305 28.107863868 0.9936474
SC-NE 21.26666667 2.0254695 40.507863868 0.0016077
SD-NE -3.93333333 -23.1745305 15.307863868 1.0000000
TN-NE 14.30000000 -4.9411972 33.541197201 0.3107477
TX-NE 24.36666667 5.1254695 43.607863868 0.0000730
UT-NE 5.06666667 -14.1745305 24.307863868 1.0000000
VA-NE 15.53333333 -3.7078639 34.774530535 0.1572874
VT-NE -4.06666667 -23.3078639 15.174530535 1.0000000
WA-NE 19.10000000 -0.1411972 38.341197201 0.0112786
WI-NE -3.80000000 -23.0411972 15.441197201 1.0000000
WV-NE 9.96666667 -9.2745305 29.207863868 0.9608524
WY-NE -1.36666667 -20.6078639 17.874530535 1.0000000
NJ-NH 11.43333333 -7.8078639 30.674530535 0.8160859
NM-NH 9.20000000 -10.0411972 28.441197201 0.9881374
NV-NH 14.80000000 -4.4411972 34.041197201 0.2399005
NY-NH 7.90000000 -11.3411972 27.141197201 0.9993331
OH-NH 7.23333333 -12.0078639 26.474530535 0.9999117
OK-NH 12.13333333 -7.1078639 31.374530535 0.7015694
OR-NH 20.13333333 0.8921361 39.374530535 0.0045717
PA-NH 8.46666667 -10.7745305 27.707863868 0.9972766
RI-NH 8.63333333 -10.6078639 27.874530535 0.9960707
SC-NH 21.03333333 1.7921361 40.274530535 0.0020022
SD-NH -4.16666667 -23.4078639 15.074530535 1.0000000
TN-NH 14.06666667 -5.1745305 33.307863868 0.3476397
TX-NH 24.13333333 4.8921361 43.374530535 0.0000931
UT-NH 4.83333333 -14.4078639 24.074530535 1.0000000
VA-NH 15.30000000 -3.9411972 34.541197201 0.1808481
VT-NH -4.30000000 -23.5411972 14.941197201 1.0000000
WA-NH 18.86666667 -0.3745305 38.107863868 0.0137286
WI-NH -4.03333333 -23.2745305 15.207863868 1.0000000
WV-NH 9.73333333 -9.5078639 28.974530535 0.9718711
WY-NH -1.60000000 -20.8411972 17.641197201 1.0000000
NM-NJ -2.23333333 -21.4745305 17.007863868 1.0000000
NV-NJ 3.36666667 -15.8745305 22.607863868 1.0000000
NY-NJ -3.53333333 -22.7745305 15.707863868 1.0000000
OH-NJ -4.20000000 -23.4411972 15.041197201 1.0000000
OK-NJ 0.70000000 -18.5411972 19.941197201 1.0000000
OR-NJ 8.70000000 -10.5411972 27.941197201 0.9954754
PA-NJ -2.96666667 -22.2078639 16.274530535 1.0000000
RI-NJ -2.80000000 -22.0411972 16.441197201 1.0000000
SC-NJ 9.60000000 -9.6411972 28.841197201 0.9769993
SD-NJ -15.60000000 -34.8411972 3.641197201 0.1510067
TN-NJ 2.63333333 -16.6078639 21.874530535 1.0000000
TX-NJ 12.70000000 -6.5411972 31.941197201 0.5963928
UT-NJ -6.60000000 -25.8411972 12.641197201 0.9999917
VA-NJ 3.86666667 -15.3745305 23.107863868 1.0000000
VT-NJ -15.73333333 -34.9745305 3.507863868 0.1390297
WA-NJ 7.43333333 -11.8078639 26.674530535 0.9998304
WI-NJ -15.46666667 -34.7078639 3.774530535 0.1637665
WV-NJ -1.70000000 -20.9411972 17.541197201 1.0000000
WY-NJ -13.03333333 -32.2745305 6.207863868 0.5329043
NV-NM 5.60000000 -13.6411972 24.841197201 0.9999999
NY-NM -1.30000000 -20.5411972 17.941197201 1.0000000
OH-NM -1.96666667 -21.2078639 17.274530535 1.0000000
OK-NM 2.93333333 -16.3078639 22.174530535 1.0000000
OR-NM 10.93333333 -8.3078639 30.174530535 0.8811182
PA-NM -0.73333333 -19.9745305 18.507863868 1.0000000
RI-NM -0.56666667 -19.8078639 18.674530535 1.0000000
SC-NM 11.83333333 -7.4078639 31.074530535 0.7534555
SD-NM -13.36666667 -32.6078639 5.874530535 0.4702642
TN-NM 4.86666667 -14.3745305 24.107863868 1.0000000
TX-NM 14.93333333 -4.3078639 34.174530535 0.2229925
UT-NM -4.36666667 -23.6078639 14.874530535 1.0000000
VA-NM 6.10000000 -13.1411972 25.341197201 0.9999991
VT-NM -13.50000000 -32.7411972 5.741197201 0.4457807
WA-NM 9.66666667 -9.5745305 28.907863868 0.9745346
WI-NM -13.23333333 -32.4745305 6.007863868 0.4951198
WV-NM 0.53333333 -18.7078639 19.774530535 1.0000000
WY-NM -10.80000000 -30.0411972 8.441197201 0.8957091
NY-NV -6.90000000 -26.1411972 12.341197201 0.9999730
OH-NV -7.56666667 -26.8078639 11.674530535 0.9997438
OK-NV -2.66666667 -21.9078639 16.574530535 1.0000000
OR-NV 5.33333333 -13.9078639 24.574530535 1.0000000
PA-NV -6.33333333 -25.5745305 12.907863868 0.9999974
RI-NV -6.16666667 -25.4078639 13.074530535 0.9999988
SC-NV 6.23333333 -13.0078639 25.474530535 0.9999983
SD-NV -18.96666667 -38.2078639 0.274530535 0.0126238
TN-NV -0.73333333 -19.9745305 18.507863868 1.0000000
TX-NV 9.33333333 -9.9078639 28.574530535 0.9850575
UT-NV -9.96666667 -29.2078639 9.274530535 0.9608524
VA-NV 0.50000000 -18.7411972 19.741197201 1.0000000
VT-NV -19.10000000 -38.3411972 0.141197201 0.0112786
WA-NV 4.06666667 -15.1745305 23.307863868 1.0000000
WI-NV -18.83333333 -38.0745305 0.407863868 0.0141163
WV-NV -5.06666667 -24.3078639 14.174530535 1.0000000
WY-NV -16.40000000 -35.6411972 2.841197201 0.0899896
OH-NY -0.66666667 -19.9078639 18.574530535 1.0000000
OK-NY 4.23333333 -15.0078639 23.474530535 1.0000000
OR-NY 12.23333333 -7.0078639 31.474530535 0.6835500
PA-NY 0.56666667 -18.6745305 19.807863868 1.0000000
RI-NY 0.73333333 -18.5078639 19.974530535 1.0000000
SC-NY 13.13333333 -6.1078639 32.374530535 0.5139523
SD-NY -12.06666667 -31.3078639 7.174530535 0.7133999
TN-NY 6.16666667 -13.0745305 25.407863868 0.9999988
TX-NY 16.23333333 -3.0078639 35.474530535 0.1006599
UT-NY -3.06666667 -22.3078639 16.174530535 1.0000000
VA-NY 7.40000000 -11.8411972 26.641197201 0.9998474
VT-NY -12.20000000 -31.4411972 7.041197201 0.6895908
WA-NY 10.96666667 -8.2745305 30.207863868 0.8772854
WI-NY -11.93333333 -31.1745305 7.307863868 0.7365647
WV-NY 1.83333333 -17.4078639 21.074530535 1.0000000
WY-NY -9.50000000 -28.7411972 9.741197201 0.9803441
OK-OH 4.90000000 -14.3411972 24.141197201 1.0000000
OR-OH 12.90000000 -6.3411972 32.141197201 0.5582869
PA-OH 1.23333333 -18.0078639 20.474530535 1.0000000
RI-OH 1.40000000 -17.8411972 20.641197201 1.0000000
SC-OH 13.80000000 -5.4411972 33.041197201 0.3924661
SD-OH -11.40000000 -30.6411972 7.841197201 0.8209066
TN-OH 6.83333333 -12.4078639 26.074530535 0.9999790
TX-OH 16.90000000 -2.3411972 36.141197201 0.0635003
UT-OH -2.40000000 -21.6411972 16.841197201 1.0000000
VA-OH 8.06666667 -11.1745305 27.307863868 0.9989634
VT-OH -11.53333333 -30.7745305 7.707863868 0.8012360
WA-OH 11.63333333 -7.6078639 30.874530535 0.7858266
WI-OH -11.26666667 -30.5078639 7.974530535 0.8395194
WV-OH 2.50000000 -16.7411972 21.741197201 1.0000000
WY-OH -8.83333333 -28.0745305 10.407863868 0.9940553
OR-OK 8.00000000 -11.2411972 27.241197201 0.9991286
PA-OK -3.66666667 -22.9078639 15.574530535 1.0000000
RI-OK -3.50000000 -22.7411972 15.741197201 1.0000000
SC-OK 8.90000000 -10.3411972 28.141197201 0.9932164
SD-OK -16.30000000 -35.5411972 2.941197201 0.0962725
TN-OK 1.93333333 -17.3078639 21.174530535 1.0000000
TX-OK 12.00000000 -7.2411972 31.241197201 0.7250692
UT-OK -7.30000000 -26.5411972 11.941197201 0.9998897
VA-OK 3.16666667 -16.0745305 22.407863868 1.0000000
VT-OK -16.43333333 -35.6745305 2.807863868 0.0879728
WA-OK 6.73333333 -12.5078639 25.974530535 0.9999858
WI-OK -16.16666667 -35.4078639 3.074530535 0.1052106
WV-OK -2.40000000 -21.6411972 16.841197201 1.0000000
WY-OK -13.73333333 -32.9745305 5.507863868 0.4040725
PA-OR -11.66666667 -30.9078639 7.574530535 0.7805710
RI-OR -11.50000000 -30.7411972 7.741197201 0.8062496
SC-OR 0.90000000 -18.3411972 20.141197201 1.0000000
SD-OR -24.30000000 -43.5411972 -5.058802799 0.0000783
TN-OR -6.06666667 -25.3078639 13.174530535 0.9999992
TX-OR 4.00000000 -15.2411972 23.241197201 1.0000000
UT-OR -15.30000000 -34.5411972 3.941197201 0.1808481
VA-OR -4.83333333 -24.0745305 14.407863868 1.0000000
VT-OR -24.43333333 -43.6745305 -5.192136132 0.0000681
WA-OR -1.26666667 -20.5078639 17.974530535 1.0000000
WI-OR -24.16666667 -43.4078639 -4.925469465 0.0000899
WV-OR -10.40000000 -29.6411972 8.841197201 0.9324101
WY-OR -21.73333333 -40.9745305 -2.492136132 0.0010302
RI-PA 0.16666667 -19.0745305 19.407863868 1.0000000
SC-PA 12.56666667 -6.6745305 31.807863868 0.6216609
SD-PA -12.63333333 -31.8745305 6.607863868 0.6090496
TN-PA 5.60000000 -13.6411972 24.841197201 0.9999999
TX-PA 15.66666667 -3.5745305 34.907863868 0.1449218
UT-PA -3.63333333 -22.8745305 15.607863868 1.0000000
VA-PA 6.83333333 -12.4078639 26.074530535 0.9999790
VT-PA -12.76666667 -32.0078639 6.474530535 0.5837044
WA-PA 10.40000000 -8.8411972 29.641197201 0.9324101
WI-PA -12.50000000 -31.7411972 6.741197201 0.6342129
WV-PA 1.26666667 -17.9745305 20.507863868 1.0000000
WY-PA -10.06666667 -29.3078639 9.174530535 0.9552573
SC-RI 12.40000000 -6.8411972 31.641197201 0.6528992
SD-RI -12.80000000 -32.0411972 6.441197201 0.5773525
TN-RI 5.43333333 -13.8078639 24.674530535 1.0000000
TX-RI 15.50000000 -3.7411972 34.741197201 0.1605020
UT-RI -3.80000000 -23.0411972 15.441197201 1.0000000
VA-RI 6.66666667 -12.5745305 25.907863868 0.9999891
VT-RI -12.93333333 -32.1745305 6.307863868 0.5519339
WA-RI 10.23333333 -9.0078639 29.474530535 0.9446692
WI-RI -12.66666667 -31.9078639 6.574530535 0.6027260
WV-RI 1.10000000 -18.1411972 20.341197201 1.0000000
WY-RI -10.23333333 -29.4745305 9.007863868 0.9446692
SD-SC -25.20000000 -44.4411972 -5.958802799 0.0000304
TN-SC -6.96666667 -26.2078639 12.274530535 0.9999654
TX-SC 3.10000000 -16.1411972 22.341197201 1.0000000
UT-SC -16.20000000 -35.4411972 3.041197201 0.1029146
VA-SC -5.73333333 -24.9745305 13.507863868 0.9999999
VT-SC -25.33333333 -44.5745305 -6.092136132 0.0000263
WA-SC -2.16666667 -21.4078639 17.074530535 1.0000000
WI-SC -25.06666667 -44.3078639 -5.825469465 0.0000350
WV-SC -11.30000000 -30.5411972 7.941197201 0.8349684
WY-SC -22.63333333 -41.8745305 -3.392136132 0.0004272
TN-SD 18.23333333 -1.0078639 37.474530535 0.0230616
TX-SD 28.30000000 9.0588028 47.541197201 0.0000010
UT-SD 9.00000000 -10.2411972 28.241197201 0.9917758
VA-SD 19.46666667 0.2254695 38.707863868 0.0082348
VT-SD -0.13333333 -19.3745305 19.107863868 1.0000000
WA-SD 23.03333333 3.7921361 42.274530535 0.0002864
WI-SD 0.13333333 -19.1078639 19.374530535 1.0000000
WV-SD 13.90000000 -5.3411972 33.141197201 0.3753454
WY-SD 2.56666667 -16.6745305 21.807863868 1.0000000
TX-TN 10.06666667 -9.1745305 29.307863868 0.9552573
UT-TN -9.23333333 -28.4745305 10.007863868 0.9874204
VA-TN 1.23333333 -18.0078639 20.474530535 1.0000000
VT-TN -18.36666667 -37.6078639 0.874530535 0.0207147
WA-TN 4.80000000 -14.4411972 24.041197201 1.0000000
WI-TN -18.10000000 -37.3411972 1.141197201 0.0256479
WV-TN -4.33333333 -23.5745305 14.907863868 1.0000000
WY-TN -15.66666667 -34.9078639 3.574530535 0.1449218
UT-TX -19.30000000 -38.5411972 -0.058802799 0.0095084
VA-TX -8.83333333 -28.0745305 10.407863868 0.9940553
VT-TX -28.43333333 -47.6745305 -9.192136132 0.0000009
WA-TX -5.26666667 -24.5078639 13.974530535 1.0000000
WI-TX -28.16666667 -47.4078639 -8.925469465 0.0000012
WV-TX -14.40000000 -33.6411972 4.841197201 0.2956591
WY-TX -25.73333333 -44.9745305 -6.492136132 0.0000172
VA-UT 10.46666667 -8.7745305 29.707863868 0.9270184
VT-UT -9.13333333 -28.3745305 10.107863868 0.9894722
WA-UT 14.03333333 -5.2078639 33.274530535 0.3530942
WI-UT -8.86666667 -28.1078639 10.374530535 0.9936474
WV-UT 4.90000000 -14.3411972 24.141197201 1.0000000
WY-UT -6.43333333 -25.6745305 12.807863868 0.9999959
VT-VA -19.60000000 -38.8411972 -0.358802799 0.0073328
WA-VA 3.56666667 -15.6745305 22.807863868 1.0000000
WI-VA -19.33333333 -38.5745305 -0.092136132 0.0092399
WV-VA -5.56666667 -24.8078639 13.674530535 0.9999999
WY-VA -16.90000000 -36.1411972 2.341197201 0.0635003
WA-VT 23.16666667 3.9254695 42.407863868 0.0002504
WI-VT 0.26666667 -18.9745305 19.507863868 1.0000000
WV-VT 14.03333333 -5.2078639 33.274530535 0.3530942
WY-VT 2.70000000 -16.5411972 21.941197201 1.0000000
WI-WA -22.90000000 -42.1411972 -3.658802799 0.0003275
WV-WA -9.13333333 -28.3745305 10.107863868 0.9894722
WY-WA -20.46666667 -39.7078639 -1.225469465 0.0033807
WV-WI 13.76666667 -5.4745305 33.007863868 0.3982507
WY-WI 2.43333333 -16.8078639 21.674530535 1.0000000
WY-WV -11.33333333 -30.5745305 7.907863868 0.8303487

In case you were wondering how many pairs are being analyzed, it’s 2450. How did I figure that out? Well, each state is paired up with every other state, so that makes for 49 possible pairings for each state, since states aren’t paired up with themselves. There are also 50 states with pairings, so multiply 49 by 50 to get 2450 pairings.

This table shows the pair-wise differences in average January low temperatures amongst pairs of states. The lwr and upr columns show the lower and upper 99% confidence bounds, respectively, for mean temperature differences between two states. The p adj column gives the p-values for each state pair adjusted for the number of comparisons made. Any p-value that is less than 0.01 means that the pair-wise difference is statistically significant. Some notably significant pair-wise differences include (rounded to two decimal places):

  • AZ-AK, Arizona-Alaska, 42.17
    • Makes sense. After all, Arizona is a dry desert, while Alaska is very close to the Arctic Circle
  • VT-HI, Vermont-Hawaii, -53.53
    • Vermont is in New England, which is known for cold winters, while Hawaii is made up of several islands that are situated on active volcanoes.
  • OR-MN, Oregon-Minnesota, 26.67
    • This one I found interesting, since both Oregon and Minnesota can get very cold winters, but if you live in Oregon, you’re likelier to experience rougher winters if you live west of the Cascade Mountains. Minnesota (and most of the Midwest for that matter) are known for their brutal winters.
  • LA-HI, Louisiana-Hawaii, -21.97
    • Another interesting observation, since neither state recieves plenty of snow (or gets very cold for that matter). Then again, Lousiana has lots of bayous, while Hawaii consists of several islands sitting on active volcanoes.

Thanks for reading, and stay tuned for my post on two-way ANOVA,

Michael