# Lab 7, October 31

Solutions

## Tidy data

Reference: R4DS Chapter 12

Data are “tidy” if each row is an observation and each column is a variable.

Here’s an example using population counts for Michigan counties in the past five years. The data are available on Canvas.

``````head(cpop <- read_csv('county-pop-2016.csv'))
``````
``````## # A tibble: 6 x 8
##    County respop72010 respop72011 respop72012 respop72013 respop72014
##     <chr>       <int>       <int>       <int>       <int>       <int>
## 1  Alcona       10890       10776       10609       10573       10439
## 2   Alger        9565        9550        9495        9495        9424
## 3 Allegan      111502      111550      111929      112415      113778
## 4  Alpena       29539       29339       29208       29012       28932
## 5  Antrim       23499       23385       23336       23219       23244
## 6  Arenac       15853       15617       15495       15412       15324
## # ... with 2 more variables: respop72015 <int>, respop72016 <int>
``````

This datset is not tidy because the columns are not variables—the population in each year is spread across multiple columns. The column names actually contain values of the variable `year`.

Imagine trying to plot the population of Washtenaw county over time using `ggplot`:

``````filter(cpop, County=='Washtenaw')
``````
``````## # A tibble: 1 x 8
##      County respop72010 respop72011 respop72012 respop72013 respop72014
##       <chr>       <int>       <int>       <int>       <int>       <int>
## 1 Washtenaw      345568      349071      351299      354573      358980
## # ... with 2 more variables: respop72015 <int>, respop72016 <int>
``````

You would not be able to display the year on the x-axis. We need a variable for the year and a variable for the population count.

The `gather` function will move the column names into a `year` variable and store the population counts in a single column.

`gather` requires these three parameters:

• The columns that contain values, not variables (the `respop####` columns).
• The name of the column whose values are the column names from the previous step (`year` in this case).
• The name of the variable whose values are spread across the columns (`count`, for population counts)

Putting this together,

``````(cpop <-
cpop %>%
gather(contains('respop'),
key = 'year', value = 'count'))
``````
``````## # A tibble: 581 x 3
##     County        year  count
##      <chr>       <chr>  <int>
##  1  Alcona respop72010  10890
##  2   Alger respop72010   9565
##  3 Allegan respop72010 111502
##  4  Alpena respop72010  29539
##  5  Antrim respop72010  23499
##  6  Arenac respop72010  15853
##  7  Baraga respop72010   8842
##  8   Barry respop72010  59081
##  9     Bay respop72010 107688
## 10  Benzie respop72010  17512
## # ... with 571 more rows
``````

The `contains()` function selects all columns whose names contain the specified string. The resulting `year` column is of `character` type. The final step would be to extract the numeric year from the strings `respop72010`, `respop72011`, etc. (Below I use the `str_replace` function from the `stringr` package.)

``````library(stringr)
cpop <-
mutate(cpop, year = as.numeric(str_replace(year, fixed('respop7'), '')))
``````

Now we could plot population counts over time, for example:

``````filter(cpop, County=='Washtenaw')
``````
``````## # A tibble: 7 x 3
##      County  year  count
##       <chr> <dbl>  <int>
## 1 Washtenaw  2010 345568
## 2 Washtenaw  2011 349071
## 3 Washtenaw  2012 351299
## 4 Washtenaw  2013 354573
## 5 Washtenaw  2014 358980
## 6 Washtenaw  2015 360847
## 7 Washtenaw  2016 364709
``````

The `spread` function does the opposite of `gather`:

``````spread(cpop, key='year', value = 'count')
``````
``````## # A tibble: 83 x 8
##     County `2010` `2011` `2012` `2013` `2014` `2015` `2016`
##  *   <chr>  <int>  <int>  <int>  <int>  <int>  <int>  <int>
##  1  Alcona  10890  10776  10609  10573  10439  10333  10352
##  2   Alger   9565   9550   9495   9495   9424   9347   9219
##  3 Allegan 111502 111550 111929 112415 113778 114661 115548
##  4  Alpena  29539  29339  29208  29012  28932  28791  28704
##  5  Antrim  23499  23385  23336  23219  23244  23133  23144
##  6  Arenac  15853  15617  15495  15412  15324  15280  15122
##  7  Baraga   8842   8818   8708   8682   8623   8546   8503
##  8   Barry  59081  58970  59068  59134  59283  59393  59702
##  9     Bay 107688 107498 107091 106910 106232 105557 104747
## 10  Benzie  17512  17431  17389  17400  17511  17436  17572
## # ... with 73 more rows
``````

## Exercise: University of Michigan Enrollment

Using data from the Registrar, I created two files containing University of Michigan enrollment counts by race/ethnicity and sex. Download these files from our Canvas page.

The first file has enrollment counts for the years 2006–2015 and the second has the counts for 1995–2005. First import the files:

``````d15 <- read_csv('umich_enrollment15.csv')
``````

### Part 1

1. Familiarize yourself with how these data are formatted. Are the datasets “tidy”? I suggest running these commands:

``````names(d15)
names(d05)
count(d15, Level, Sex)
``````
2. The older data (`d05`) has fewer race/ethnicity categories. Use `mutate` to redefine the `Unknown` column in `d15` so that it combines the “Two or More”, “Hawaiian” and “Unknown” categories. Remove the columns for “Two or More” and “Hawaiian”.

3. The two data frames `d05` and `d15` should now have the same variables (columns). Run this command to “stack” the two datasets on top of each other:

``````d <- bind_rows(d15, d05)
``````
4. Create a data frame called `d_ut` with the undergraduate enrollment counts for men and women combined (filter the `Level` and `Sex` columns).

5. Compute the proportion of undergraduates in each race/ethnicity category. We can do this using `mutate_at`, which applies the same transformation to multiple columns. Run this command to complete this step:

``````d_ut <-
mutate_at(d_ut, vars(-Level, -Sex, -Year, -All), funs(. / All))
``````

This command selects all columns except `Level`, `Sex`, `Year` and `All`, and then divides each column by the value in `All`. You should now have a dataset like this:

``````head(d_ut)
``````
``````## # A tibble: 6 x 10
##           Level   Sex  Year   All     Asian      Black   Hispanic
##           <chr> <chr> <int> <int>     <dbl>      <dbl>      <dbl>
## 1 Undergraduate Total  2015 26353 0.1364171 0.04614275 0.04933025
## 2 Undergraduate Total  2014 26442 0.1350125 0.04409651 0.04572271
## 3 Undergraduate Total  2013 26329 0.1311482 0.04656462 0.04420981
## 4 Undergraduate Total  2012 26175 0.1290926 0.04691500 0.04305635
## 5 Undergraduate Total  2011 25752 0.1257766 0.04706431 0.04360826
## 6 Undergraduate Total  2010 25383 0.1231139 0.04782729 0.04597565
## # ... with 3 more variables: `Native American` <dbl>, White <dbl>,
## #   Unknown <dbl>
``````

Each column contains the percent undergraduate enrollment in one of the race/ethnicity categories. The `All` column still contains the count across all race/ethnicity categories, since it was unaffected by `mutate_at` from the previous step.

6. Use `gather` so that `d_ut` has a column called `reth`, containing the race/ethnicity category, and a column called `pct`, containing the percent enrollment in that category. Then create the following plot.

### Part 2

1. Now let’s focus on total enrollment by gender. Filter the `Level` variable to create a data frame called `d_t` containing just the total counts (remove the rows with undergraduate enrollment counts). Use `select` so that `d_t` only has three columns: `Sex`, `Year`, and `All` (the enrollment count across all race/ethnicity categories).

2. Compute the percent enrollment for each gender in each year. First use `spread` so we have separate columns for the male and female enrollment counts:

``````## # A tibble: 21 x 4
##     Year Females Males Total
##  * <int>   <int> <int> <int>
##  1  1995   15854 16836 32690
##  2  1996   15824 16537 32361
##  3  1997   16065 16689 32754
##  4  1998   16093 16549 32642
##  5  1999   16286 16654 32940
##  6  2000   16334 16504 32838
##  7  2001   16627 16578 33205
##  8  2002   16849 16591 33440
##  9  2003   16995 16521 33516
## 10  2004   17126 16809 33935
## # ... with 11 more rows
``````

Then `mutate` the `Females` and `Males` columns so they contain proportions instead of counts.

3. Now `gather` the result so there is a `Sex` column and a `pct` column.

``````## # A tibble: 42 x 4
##     Year Total     Sex       pct
##    <int> <int>   <chr>     <dbl>
##  1  1995 32690 Females 0.4849801
##  2  1996 32361 Females 0.4889837
##  3  1997 32754 Females 0.4904744
##  4  1998 32642 Females 0.4930151
##  5  1999 32940 Females 0.4944141
##  6  2000 32838 Females 0.4974115
##  7  2001 33205 Females 0.5007378
##  8  2002 33440 Females 0.5038577
##  9  2003 33516 Females 0.5070712
## 10  2004 33935 Females 0.5046707
## # ... with 32 more rows
``````
4. Finally, create this plot of the proportion of men and women at Michigan over time: