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<html>
<head>
<meta charset="utf-8" />
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<title>Course Documents</title>
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<div class="toc-content col-xs-12 col-sm-8 col-md-9">
<div id="header">
<h1 class="title toc-ignore">Course Documents</h1>
</div>
<p><br></p>
<div id="class-slides-and-documents" class="section level1">
<h1>Class Slides and Documents</h1>
<p>Class slides and documents will be posted here.</p>
<div id="week-1" class="section level2">
<h2>Week 1</h2>
<div id="sept.-5" class="section level3">
<h3>Sept. 5</h3>
<p><a href="sta305-19sept5-class1_posted.pdf">Class slides</a></p>
<p><a href="sta305-19sept5-class1-inclass.pdf">Class slides - in
class</a></p>
</div>
</div>
<div id="week-2" class="section level2">
<h2>Week 2</h2>
<div id="sept.-10" class="section level3">
<h3>Sept. 10</h3>
<p><a href="class2-10sept19.pdf">Class slides</a></p>
<p><a href="class2-10sept19-inclass.pdf">Class slides - inclass</a></p>
</div>
<div id="sept.-12" class="section level3">
<h3>Sept. 12</h3>
<p><a href="class3slides-12sept2019.pdf">Class slides</a></p>
<p><a href="class3slides-12sept2019-inclass.pdf">Class slides - in
class</a></p>
</div>
</div>
<div id="week-3" class="section level2">
<h2>Week 3</h2>
<div id="sept.-17" class="section level3">
<h3>Sept. 17</h3>
<p><a href="class4slides-17sept19.pdf">Class slides</a></p>
<p><a href="class4slides-17sept19-inclass.pdf">Class slides -
inclass</a></p>
</div>
<div id="sept.-19" class="section level3">
<h3>Sept. 19</h3>
<p><a href="sta305-2019sept19-class5.pdf">Class slides</a></p>
<p><a href="sta305-2019sept19-class5-inclass.pdf">Class slides -
inclass</a></p>
<p>Live coding demo from class examined each line from the R code
below.</p>
<pre class="r"><code>library(BHH2)
data(shoes.data)
shoes.data
diff <- shoes.data$matA-shoes.data$matB
N <- 2^(10) # number of treatment assignments
res <- numeric(N) #vector to store results
LR <- list(c(-1,1)) # difference is multiplied by -1 or 1 # generate all possible treatment assign
trtassign <- expand.grid(rep(LR, 10))
for (i in 1:N) {
res[i] <- mean(as.numeric(trtassign[i,])*diff) }
trtassign[1:2,]
trtassign
dim(trtassign)
meandiff <- mean(diff)
res <= meandiff
sum(res <= meandiff)</code></pre>
</div>
</div>
<div id="week-4" class="section level2">
<h2>Week 4</h2>
<div id="sept.-24" class="section level3">
<h3>Sept. 24</h3>
<p><a href="sta305-2019sept24-class6.pdf">Class slides</a></p>
<p><a href="sta305-2019sept24-class6-inclass.pdf">Class slides
-inclass</a></p>
</div>
<div id="sept.-26" class="section level3">
<h3>Sept. 26</h3>
<p><a href="sta305-2019sept26-class7.pdf">Class slides</a></p>
<p><a href="sta305-2019sept26-class7-inclass.pdf">Class slides
-inclass</a></p>
</div>
</div>
<div id="week-5" class="section level2">
<h2>Week 5</h2>
<div id="oct.-1" class="section level3">
<h3>Oct. 1</h3>
<p><a href="sta305-2019oct1-class8.pdf">Class slides</a></p>
<p><a href="sta305-2019oct1-class8-inclass.pdf">Class slides -
inclass</a></p>
</div>
</div>
<div id="week-6" class="section level2">
<h2>Week 6</h2>
<div id="oct.-8" class="section level3">
<h3>Oct. 8</h3>
<p>Midterm test #1</p>
</div>
<div id="oct.-10" class="section level3">
<h3>Oct. 10</h3>
<p><a href="sta305-10oct2019-class9.pdf">Class slides</a></p>
<p><a href="sta305-10oct2019-class9-inclass.pdf">Class slides -
inclass</a></p>
<div id="background-on-angrist-and-lavy-study" class="section level4">
<h4>Background on Angrist and Lavy Study</h4>
<p><a href="https://en.wikipedia.org/wiki/Maimonides%27_rule">Wikepia
article on Maimonides’ Rule</a></p>
<p><a href="https://economics.mit.edu/files/8273">Using Maimonides’ Rule
to Estimate the Effect of Class Size on Scholastic Achievement</a></p>
</div>
</div>
</div>
<div id="week-7" class="section level2">
<h2>Week 7</h2>
<div id="oct.-15" class="section level3">
<h3>Oct. 15</h3>
<p><a href="sta305-15Oct2019-class10.pdf">Class slides</a></p>
<p><a href="sta305-15Oct2019-class10-inclass.pdf">Class slides
-inclass</a></p>
</div>
<div id="oct.-17" class="section level3">
<h3>Oct. 17</h3>
<p><a href="sta305-17Oct2019-class11.pdf">Class slides</a></p>
<p><a href="sta305-17Oct2019-class11-inclass.pdf">Class slides -
inclass</a></p>
<p>The data used in class from <a
href="https://wwwn.cdc.gov/nchs/nhanes/nhefs/default.aspx/">NHEFS
Survey</a> is available <a href="nhefshw2dat.csv">nhefshw2dat.csv</a>.
The R code to read the data into an R data frame, and create the
covariates used in the analyses done in class is below.</p>
<pre class="r"><code># Read the data into a data frame
#
nhefshwdat <- read.csv("nhefshw2dat.csv")
# Define the variables used in the propensity score model
#
years1 <- mean(nhefshwdat$age[nhefshwdat$qsmk == 1])
years0 <- mean(nhefshwdat$age[nhefshwdat$qsmk == 0])
male1 <- 100 * mean(nhefshwdat$sex[nhefshwdat$qsmk == 1] == 0)
male0 <- 100 * mean(nhefshwdat$sex[nhefshwdat$qsmk == 0] == 0)
white1 <- 100 * mean(nhefshwdat$race[nhefshwdat$qsmk == 1] == 0)
white0 <- 100 * mean(nhefshwdat$race[nhefshwdat$qsmk == 0] == 0)
university1 <- 100 * mean(nhefshwdat$education.code[nhefshwdat$qsmk == 1] == 5)
university0 <- 100 * mean(nhefshwdat$education.code[nhefshwdat$qsmk == 0] == 5)
kg1 <- mean(nhefshwdat$wt71[nhefshwdat$qsmk == 1])
kg0 <- mean(nhefshwdat$wt71[nhefshwdat$qsmk == 0])
cigs1 <- mean(nhefshwdat$smokeintensity[nhefshwdat$qsmk == 1])
cigs0 <- mean(nhefshwdat$smokeintensity[nhefshwdat$qsmk == 0])
smoke1 <- mean(nhefshwdat$smokeyrs[nhefshwdat$qsmk == 1])
smoke0 <- mean(nhefshwdat$smokeyrs[nhefshwdat$qsmk == 0])
noexer1 <- 100 * mean(nhefshwdat$exercise[nhefshwdat$qsmk == 1] == 2)
noexer0 <- 100 * mean(nhefshwdat$exercise[nhefshwdat$qsmk == 0] == 2)
inactive1 <- 100 * mean(nhefshwdat$active[nhefshwdat$qsmk == 1] == 2)
inactive0 <- 100 * mean(nhefshwdat$active[nhefshwdat$qsmk == 0] == 2)</code></pre>
</div>
</div>
<div id="week-8" class="section level2">
<h2>Week 8</h2>
<div id="oct.-22" class="section level3">
<h3>Oct. 22</h3>
<p><a href="sta305-class12-22oct19.pdf">Class slides</a></p>
<p><a href="sta305-class12-22oct19-inclass.pdf">Class slides
-inclass</a></p>
<p>Data from the blood coagualtion study is <a
href="tab0401.dat">here</a>, and can be read into an R data frame using
the floowing code:</p>
<pre class="r"><code>tab0401 <- read.table("tab0401.dat", header=TRUE, quote="\"")
head(tab0401) # print first 6 rows of data frame</code></pre>
<pre><code>## run diets y
## 1 20 A 62
## 2 2 A 60
## 3 11 A 63
## 4 10 A 59
## 5 5 A 63
## 6 24 A 59</code></pre>
</div>
<div id="oct.-24" class="section level3">
<h3>Oct. 24</h3>
<p><a href="sta305-oct24-2019-class13.pdf">Class slides</a></p>
<p><a href="sta305-oct24-2019-class13-inclass.pdf">Class slides -
inclass</a></p>
<p><a href="sta305-inclassproblem-24Oct2019.pdf">In class
problem</a></p>
</div>
</div>
<div id="week-9" class="section level2">
<h2>Week 9</h2>
<div id="oct.-29" class="section level3">
<h3>Oct. 29</h3>
<p><a href="sta305-class14-29oct2019.pdf">Class slides</a></p>
<p><a href="sta305-class14-29oct2019-inclass.pdf">Class slides -
inclass</a></p>
</div>
<div id="Oct31" class="section level3">
<h3>Oct. 31</h3>
<p><a href="sta305-class15-31oct2019.pdf">Class slides</a></p>
<p>Data files: <a href="pilotplant.xlsx">pilotplant.xlsx</a>; <a
href="tab0502.dat">tab0502.dat</a>; <a
href="tab0503.dat">tab0503.dat</a></p>
<p><a href="sta305-class15-31oct2019-inclass.pdf">Class slides -
inclass</a></p>
</div>
</div>
<div id="week-10" class="section level2">
<h2>Week 10</h2>
<div id="nov.-12" class="section level3">
<h3>Nov. 12</h3>
<p><a href="sta305-class16-7Nov2019.pdf">Class slides</a></p>
<p><a href="sta305-class16-7nov2019-inclass.pdf">Class slides
-inclass</a></p>
</div>
</div>
<div id="week-11" class="section level2">
<h2>Week 11</h2>
<div id="nov.-21" class="section level3">
<h3>Nov. 21</h3>
<p><a href="sta305-class17-21Nov2019.pdf">Class slides</a></p>
<p><a href="sta305-class17-21nov2019-inclass.pdf">Class slides -
inclass</a></p>
<p>A plot of the <span class="math inline">\(N(0,1)\)</span> and
Studentized range (comparing <code>k=4</code> means with
<code>df=20</code>) CDFs.</p>
<pre class="r"><code>p <- seq(-4, 6, by =0.01) # generate a sequence of points
plot(p, pnorm(p), type = "l", ylab = expression(P(X<= x)),
xlab = "x", col= "black",lty = 1,
main = "Comparison of Normal and Studentized Range CDFs"); # plot normal CDF
# add Studentized range cdf
points(p, ptukey(p,nmeans = 4, df = 20, lower.tail = T), col = "blue", type = "l", lty = 2);
# add plot legend
legend("topleft", col = c("black","blue"), lty = 1:2,
legend = c("Normal","Studentized, k = 4, df =20"))</code></pre>
<p><img src="coursedocs_files/figure-html/unnamed-chunk-4-1.png" width="672" /></p>
</div>
</div>
<div id="week-12" class="section level2">
<h2>Week 12</h2>
<div id="nov.-26" class="section level3">
<h3>Nov. 26</h3>
<p><a href="sta305-class18-26Nov2019.pdf">Class slides</a></p>
<p><a href="sta305-class18-26nov2019-inclass.pdf">Class slides
-inclass</a></p>
</div>
<div id="nov.-28" class="section level3">
<h3>Nov. 28</h3>
<p><a href="sta305-class19-2019nov28.pdf">Class slides</a></p>
<p><a href="sta305-class19-2019nov28-inclass.pdf">Class slides
-inclass</a></p>
</div>
</div>
<div id="week-13" class="section level2">
<h2>Week 13</h2>
<div id="dec.-3" class="section level3">
<h3>Dec. 3</h3>
<p><a href="sta305-class20-2019dec3.pdf">Class slides</a></p>
<p><a href="sta305-class20-2019dec3-inclass.pdf">Class slides
-inclass</a></p>
</div>
<div id="calculating-standard-errors-in-2k-factorial-designs"
class="section level3">
<h3>Calculating Standard Errors in <span
class="math inline">\(2^k\)</span> Factorial Designs</h3>
<p>Consider the data from a replicated <span
class="math inline">\(2^3\)</span> design from class 14.</p>
<table>
<thead>
<tr class="header">
<th align="right">run</th>
<th align="right">T</th>
<th align="right">C</th>
<th align="right">K</th>
<th align="right">y</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">6</td>
<td align="right">-1</td>
<td align="right">-1</td>
<td align="right">-1</td>
<td align="right">59</td>
</tr>
<tr class="even">
<td align="right">2</td>
<td align="right">1</td>
<td align="right">-1</td>
<td align="right">-1</td>
<td align="right">74</td>
</tr>
<tr class="odd">
<td align="right">1</td>
<td align="right">-1</td>
<td align="right">1</td>
<td align="right">-1</td>
<td align="right">50</td>
</tr>
<tr class="even">
<td align="right">5</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">-1</td>
<td align="right">69</td>
</tr>
<tr class="odd">
<td align="right">8</td>
<td align="right">-1</td>
<td align="right">-1</td>
<td align="right">1</td>
<td align="right">50</td>
</tr>
<tr class="even">
<td align="right">9</td>
<td align="right">1</td>
<td align="right">-1</td>
<td align="right">1</td>
<td align="right">81</td>
</tr>
<tr class="odd">
<td align="right">3</td>
<td align="right">-1</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">46</td>
</tr>
<tr class="even">
<td align="right">7</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">79</td>
</tr>
<tr class="odd">
<td align="right">13</td>
<td align="right">-1</td>
<td align="right">-1</td>
<td align="right">-1</td>
<td align="right">61</td>
</tr>
<tr class="even">
<td align="right">4</td>
<td align="right">1</td>
<td align="right">-1</td>
<td align="right">-1</td>
<td align="right">70</td>
</tr>
<tr class="odd">
<td align="right">16</td>
<td align="right">-1</td>
<td align="right">1</td>
<td align="right">-1</td>
<td align="right">58</td>
</tr>
<tr class="even">
<td align="right">10</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">-1</td>
<td align="right">67</td>
</tr>
<tr class="odd">
<td align="right">12</td>
<td align="right">-1</td>
<td align="right">-1</td>
<td align="right">1</td>
<td align="right">54</td>
</tr>
<tr class="even">
<td align="right">14</td>
<td align="right">1</td>
<td align="right">-1</td>
<td align="right">1</td>
<td align="right">85</td>
</tr>
<tr class="odd">
<td align="right">11</td>
<td align="right">-1</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">44</td>
</tr>
<tr class="even">
<td align="right">15</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">81</td>
</tr>
</tbody>
</table>
<p>The factorial effects for <code>T</code> <code>C</code>
<code>K</code> are twice the regression coefficients: <span
class="math inline">\(2\hat \beta_i\)</span>. So, the standard error of
the factorial estimates are</p>
<p><span class="math display">\[s.e.(2\hat \beta_i)=\sqrt
{Var(2\hat\beta_i)}=\sqrt
{4Var(\hat\beta_i)}=2\sqrt{Var(\hat\beta_i)}=2s.e.(\hat
\beta_i)\]</span></p>
<pre class="r"><code>fact.mod <- lm(y ~ T*C*K, data = tab0503)
summary(fact.mod)</code></pre>
<pre><code>##
## Call:
## lm(formula = y ~ T * C * K, data = tab0503)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.00 -1.25 0.00 1.25 4.00
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.425e+01 7.071e-01 90.863 2.40e-13 ***
## T 1.150e+01 7.071e-01 16.263 2.06e-07 ***
## C -2.500e+00 7.071e-01 -3.536 0.007670 **
## K 7.500e-01 7.071e-01 1.061 0.319813
## T:C 7.500e-01 7.071e-01 1.061 0.319813
## T:K 5.000e+00 7.071e-01 7.071 0.000105 ***
## C:K 7.216e-16 7.071e-01 0.000 1.000000
## T:C:K 2.500e-01 7.071e-01 0.354 0.732810
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.828 on 8 degrees of freedom
## Multiple R-squared: 0.9763, Adjusted R-squared: 0.9555
## F-statistic: 47.05 on 7 and 8 DF, p-value: 7.071e-06</code></pre>
<p>For example, the factorial estimate for <code>T</code> is <span
class="math inline">\(2\times 11.5 = 23\)</span>, and the standard error
of the factorial estimates are: <span class="math inline">\(2 \times
.7071=1.412\)</span>. Confidence intervals for the factorial estiamtes
are:</p>
<pre class="r"><code>2*confint(fact.mod)</code></pre>
<pre><code>## 2.5 % 97.5 %
## (Intercept) 125.238818 131.761182
## T 19.738818 26.261182
## C -8.261182 -1.738818
## K -1.761182 4.761182
## T:C -1.761182 4.761182
## T:K 6.738818 13.261182
## C:K -3.261182 3.261182
## T:C:K -2.761182 3.761182</code></pre>
<p>See <a href="#Oct31">Oct. 31 slides - class 14</a>.</p>
</div>
</div>
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<br> <br>
<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.
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