\end{array}\]</span></p></li>
</ol>
</div>
-<div id="twitter-users-and-news-part-i" class="section level1">
-<h1>5.8 Twitter users and news, Part I</h1>
+<div id="twitter-users-news-i" class="section level1">
+<h1>5.8 Twitter users & news I</h1>
<p>The general formula for a confidence interval is <span class="math inline">\(point~estimate~±~z^*\times~SE\)</span>. Where <span class="math inline">\(z^*\)</span> corresponds to the z-score for the desired value of <span class="math inline">\(\alpha\)</span>.</p>
<p>To estimate the interval from the data described in the question, identify the three different values. The point estimate is 45%, <span class="math inline">\(z^* = 2.58\)</span> for a 99% confidence level (that’s the number of standard deviations around the mean that ensure that 99% of a Z-score distribution is included), and <span class="math inline">\(SE = 2.4\%\)</span>. With this we can plug and chug:</p>
<p><span class="math display">\[52\% ± 2.58 \times 2.4\%\]</span> And that yields: <span class="math display">\[95\% CI = (45.8\%, 58.2\%)\]</span></p>
<p>Which means that from this data we are 99% confident that between 45.8% and 58.2% U.S. adult Twitter users get some news through the site.</p>
</div>
-<div id="twitter-users-and-news-part-ii" class="section level1">
-<h1>5.10 Twitter users and news, Part II</h1>
+<div id="twitter-users-news-ii" class="section level1">
+<h1>5.10 Twitter users & news II</h1>
<ol style="list-style-type: lower-alpha">
<li><p>False. See the answer to exercise 5.8 above. With <span class="math inline">\(\alpha = 0.01\)</span>, we can consult the 99% confidence interval. It includes 50% but also goes lower. A null hypothesis of <span class="math inline">\(p=0.50\)</span> would not be rejected at this level.</p></li>
<li><p>False. The standard error of the sample proportion does not contain any information about the proportion of the population included in the sample. It estimates the variability of the sample proportion.</p></li>
## 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 %>%
group_by(subject_race) %>%
filter(!is.na(subject_race)) %>%
+ 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
+## <fct> <int> <dbl>
+## 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 %>%
+ group_by(subject_race) %>%
+ filter(!is.na(subject_race), !is.na(search_conducted)) %>%
+ summarize(
+ across(search_conducted, sum)
+ )</code></pre>
+<pre><code>## # A tibble: 5 x 2
+## subject_race search_conducted
+## <fct> <int>
+## 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 %>%
+ group_by(subject_race) %>%
+ filter(!is.na(subject_race) & !is.na(search_conducted)) %>%
+ 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
+## <fct> <int> <dbl>
+## 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 %>%
+ group_by(subject_race) %>%
+ filter(!is.na(subject_race) & !is.na(search_conducted)) %>%
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
)
)
) %>%
<pre><code>## # A tibble: 5 x 5
## subject_race n_stops prop_total_stops search_conducted… search_conducted_o…
## <fct> <int> <dbl> <int> <dbl>
-## 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>
```
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.
-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:
-```{r tidyverse crosstabs}
+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 `subject_race`.
+```{r tidyverse stops by subject_race}
ilstops %>%
group_by(subject_race) %>%
filter(!is.na(subject_race)) %>%
summarize(
n_stops = n(),
prop_total_stops = round(n() / nrow(ilstops), digits=3),
+ )
+```
+In that block I first make a call to `group_by()` to tell R that I want it to run subsequent commands on the data "grouped" within the categories of `subject_race`. Then I pipe the grouped data to `summarize()`, 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.
+
+What about counting up the number and proportion of searches within each group? One way to think about that is as another call to `summarize()` (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 (`search_conducted` in this case) can be accomplished with the `across()` function.
+
+In general, the `across()` function seems to usually be made within a call to another verb like `summarize()` or `mutate()`. The syntax for `across()` is similar to these others. It requires two things: (1) at least one variable to summarize across (`search_conducted` here) and (2) the outputs I want.
+
+In this particular case, I'll use it to calculate the within group sums of `search_conducted`. Notice that I also filter out the missing values from `search_conducted` before I call `summarize` here.
+```{r }
+ilstops %>%
+ group_by(subject_race) %>%
+ filter(!is.na(subject_race), !is.na(search_conducted)) %>%
+ summarize(
+ across(search_conducted, sum)
+ )
+```
+If I want `across()` to calculate more than one summary, I need to provide it a list of things (in a `name = value` format sort of similar to `summarize()` or `mutate()`).
+
+```{r}
+ilstops %>%
+ group_by(subject_race) %>%
+ filter(!is.na(subject_race) & !is.na(search_conducted)) %>%
+ summarize(
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
)
)
- ) %>%
- arrange(desc(n_stops))
+ )
```
+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 `arrange()` and `desc()`. I can also insert my earlier summary statistics for the number and proportions of stops by group back into the table.
-Notice the use of `across()` within a call to `summarize()` provides one way to calculate conditional summariy info. I also use a nested call to `arrange()` and `desc()` at the end to sort my results in descending order by one of the columns.
+```{r}
+ilstops %>%
+ group_by(subject_race) %>%
+ filter(!is.na(subject_race) & !is.na(search_conducted)) %>%
+ summarize(
+ n_stops = n(),
+ prop_total_stops = round(n() / nrow(ilstops), digits=3),
+ across(
+ search_conducted,
+ list(
+ sum = sum,
+ over_n_stops = mean)
+ )
+ ) %>%
+ arrange(desc(n_stops))
+```
### Searches by `date`
projects / stats_class_2020.git / commitdiff