updating explanation of part I to address reasons for dropped observations

[stats_class_2020.git] / psets / pset3-worked_solution.html

diff --git a/psets/pset3-worked_solution.html b/psets/pset3-worked_solution.html
index 0970f3e2acd4ae783e0a76622318634588dcb236..20d0eae0c0bc8325c02365bf6b305b7a87a10c64 100644 (file)
--- a/psets/pset3-worked_solution.html
+++ b/psets/pset3-worked_solution.html
@@ -1786,18 +1786,73 @@ round(
 ##   other                   0.00 0.00
 ##   white                   0.64 0.51</code></pre>
 <p>Here the noteworthy comparisons again arise within the black and hispanic categories. Both groups account for a substantially larger proportion of stops resulting in searches vs. those that do not result in searches.</p>
 ##   other                   0.00 0.00
 ##   white                   0.64 0.51</code></pre>
 <p>Here the noteworthy comparisons again arise within the black and hispanic categories. Both groups account for a substantially larger proportion of stops resulting in searches vs. those that do not result in searches.</p>

-<p>For the sake of completeness/comparison, here’s a way to do similar cross-tabulations in single a chunk of tidyverse code. I include conditional proportions of all stops to facilitate comparison with some of the tables I created earlier as well:</p>
+<p>For the sake of completeness/comparison, here’s a way to do similar cross-tabulations in chunks of tidyverse code. This first bit summarizes the number of stops and proportion of total stops accounted for within each of the categories of <code>subject_race</code>.</p>

 <pre class="r"><code>ilstops %&gt;%
   group_by(subject_race) %&gt;%
   filter(!is.na(subject_race)) %&gt;%
 <pre class="r"><code>ilstops %&gt;%
   group_by(subject_race) %&gt;%
   filter(!is.na(subject_race)) %&gt;%

+  summarize(
+    n_stops = n(),
+    prop_total_stops = round(n() / nrow(ilstops), digits = 3),
+  )</code></pre>
+<pre><code>## # A tibble: 5 x 3
+##   subject_race           n_stops prop_total_stops
+##   &lt;fct&gt;                    &lt;int&gt;            &lt;dbl&gt;
+## 1 asian/pacific islander    4053            0.032
+## 2 black                    25627            0.202
+## 3 hispanic                 16940            0.133
+## 4 other                      335            0.003
+## 5 white                    80105            0.63</code></pre>
+<p>In that block I first make a call to <code>group_by()</code> to tell R that I want it to run subsequent commands on the data “grouped” within the categories of <code>subject_race</code>. Then I pipe the grouped data to <code>summarize()</code>, which I use to calculate the number of stops within each group (in this data that’s just the number of observations within each group) as well as the proportion of total stops within each group.</p>
+<p>What about counting up the number and proportion of searches within each group? One way to think about that is as another call to <code>summarize()</code> (since, after all, I want to calculate the summary information for searches within the same groups). Within the Tidyverse approach to things, this kind of summarizing within groups and within another variable (<code>search_conducted</code> in this case) can be accomplished with the <code>across()</code> function.</p>
+<p>In general, the <code>across()</code> function seems to usually be made within a call to another verb like <code>summarize()</code> or <code>mutate()</code>. The syntax for <code>across()</code> is similar to these others. It requires two things: (1) at least one variable to summarize across (<code>search_conducted</code> here) and (2) the outputs I want.</p>
+<p>In this particular case, I’ll use it to calculate the within group sums of <code>search_conducted</code>. Notice that I also filter out the missing values from <code>search_conducted</code> before I call <code>summarize</code> here.</p>
+<pre class="r"><code>ilstops %&gt;%
+  group_by(subject_race) %&gt;%
+  filter(!is.na(subject_race), !is.na(search_conducted)) %&gt;%
+  summarize(
+    across(search_conducted, sum)
+  )</code></pre>
+<pre><code>## # A tibble: 5 x 2
+##   subject_race           search_conducted
+##   &lt;fct&gt;                             &lt;int&gt;
+## 1 asian/pacific islander               68
+## 2 black                              1806
+## 3 hispanic                           1049
+## 4 other                                14
+## 5 white                              3010</code></pre>
+<p>If I want <code>across()</code> to calculate more than one summary, I need to provide it a list of things (in a <code>name = value</code> format sort of similar to <code>summarize()</code> or <code>mutate()</code>).</p>
+<pre class="r"><code>ilstops %&gt;%
+  group_by(subject_race) %&gt;%
+  filter(!is.na(subject_race) &amp; !is.na(search_conducted)) %&gt;%
+  summarize(
+    across(
+      search_conducted,
+      list(
+        sum = sum,
+        over_n_stops = mean
+      )
+    )
+  )</code></pre>
+<pre><code>## # A tibble: 5 x 3
+##   subject_race           search_conducted_sum search_conducted_over_n_stops
+##   &lt;fct&gt;                                 &lt;int&gt;                         &lt;dbl&gt;
+## 1 asian/pacific islander                   68                        0.0168
+## 2 black                                  1806                        0.0707
+## 3 hispanic                               1049                        0.0620
+## 4 other                                    14                        0.0419
+## 5 white                                  3010                        0.0376</code></pre>
+<p>I can clean this up a bit by using two functions to the output in descending order by one of the columns. I do this with a nested call to two functions <code>arrange()</code> and <code>desc()</code>. I can also insert my earlier summary statistics for the number and proportions of stops by group back into the table.</p>
+<pre class="r"><code>ilstops %&gt;%
+  group_by(subject_race) %&gt;%
+  filter(!is.na(subject_race) &amp; !is.na(search_conducted)) %&gt;%

   summarize(
     n_stops = n(),
     prop_total_stops = round(n() / nrow(ilstops), digits = 3),
     across(
       search_conducted,
       list(
   summarize(
     n_stops = n(),
     prop_total_stops = round(n() / nrow(ilstops), digits = 3),
     across(
       search_conducted,
       list(

-        sum = ~ sum(.x, na.rm = TRUE),
-        over_n_stops = ~ round(mean(.x, na.rm = TRUE), digits = 3)
+        sum = sum,
+        over_n_stops = mean

       )
     )
   ) %&gt;%
       )
     )
   ) %&gt;%


@@ -1805,12 +1860,11 @@ round(
 <pre><code>## # A tibble: 5 x 5
 ##   subject_race    n_stops prop_total_stops search_conducted… search_conducted_o…
 ##   &lt;fct&gt;             &lt;int&gt;            &lt;dbl&gt;             &lt;int&gt;               &lt;dbl&gt;
 <pre><code>## # A tibble: 5 x 5
 ##   subject_race    n_stops prop_total_stops search_conducted… search_conducted_o…
 ##   &lt;fct&gt;             &lt;int&gt;            &lt;dbl&gt;             &lt;int&gt;               &lt;dbl&gt;

-## 1 white             80105            0.63               3010               0.038
-## 2 black             25627            0.202              1806               0.071
-## 3 hispanic          16940            0.133              1049               0.062
-## 4 asian/pacific …    4053            0.032                68               0.017
-## 5 other               335            0.003                14               0.042</code></pre>
-<p>Notice the use of <code>across()</code> within a call to <code>summarize()</code> provides one way to calculate conditional summariy info. I also use a nested call to <code>arrange()</code> and <code>desc()</code> at the end to sort my results in descending order by one of the columns.</p>
+## 1 white             80043            0.63               3010              0.0376
+## 2 black             25548            0.201              1806              0.0707
+## 3 hispanic          16914            0.133              1049              0.0620
+## 4 asian/pacific …    4049            0.032                68              0.0168
+## 5 other               334            0.003                14              0.0419</code></pre>

 </div>
 <div id="searches-by-date" class="section level3">
 <h3>Searches by <code>date</code></h3>
 </div>
 <div id="searches-by-date" class="section level3">
 <h3>Searches by <code>date</code></h3>


@@ -2181,6 +2235,8 @@ sapply(groups, gen_subgroup_prop)</code></pre>
 <p>Again, many possible things worth mentioning here, so I’ll provide a few that stand out to me.</p>
 <ul>
 <li>The generalizability of analysis focused on one state during one 6 year period is limited.</li>
 <p>Again, many possible things worth mentioning here, so I’ll provide a few that stand out to me.</p>
 <ul>
 <li>The generalizability of analysis focused on one state during one 6 year period is limited.</li>

+<li>Working with a random <span class="math inline">\(1\%\)</span> sample of the full dataset means that our results here could diverge from those we would find in an analysis of the full population of traffic stops in unpredictable ways. That said, even the very small sample is quite big and once you’ve read <em>OpenIntro</em> §5 you’ll have some tools to estimate standard errors and confidence intervals around the various results from this analysis.<br />
+</li>

 <li>The data seem very prone to measurement errors of various kinds. In particular, I suspect the race/ethnicity classifications provided by officers are subject to some biases that are hard to identify and might also shift over time/region. The prevalence of missing values during the first two years of the dataset illustrate one aspect of this and may impact estimates of raw counts and proportions.<br />
 </li>
 <li>While the comparisons across racial/ethnic groups and between the traffic stops/searches and baseline population proportions illustrates a number of suggestive patterns, conclusive interpretation or attribution of those patterns to any specific cause or causes is quite difficult in the absence of additional information or assumptions. For one example, see my comments regarding statistical independence and the possible explanations in SQ2 above.</li>
 <li>The data seem very prone to measurement errors of various kinds. In particular, I suspect the race/ethnicity classifications provided by officers are subject to some biases that are hard to identify and might also shift over time/region. The prevalence of missing values during the first two years of the dataset illustrate one aspect of this and may impact estimates of raw counts and proportions.<br />
 </li>
 <li>While the comparisons across racial/ethnic groups and between the traffic stops/searches and baseline population proportions illustrates a number of suggestive patterns, conclusive interpretation or attribution of those patterns to any specific cause or causes is quite difficult in the absence of additional information or assumptions. For one example, see my comments regarding statistical independence and the possible explanations in SQ2 above.</li>