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<title>Box plot에 좀더 많은 정보를 담아보자</title>

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<h1>Box plot에 좀더 많은 정보를 담아보자</h1>

<p>데이터 분석할 때 무엇을 가장 먼저 하세요?</p>

<p>저는 우선 데이터의 분포 및 도수를 확인합니다. 데이터의 형태와 종류에 따라 사용할 수 있는 분석 방법이 정해지기 때문이죠. 이상치의 확인 때문이기도 합니다.

개인적으로 데이터의 분포를 확인할 때 Box plot을 즐겨 사용하는데요. </p>

<p>Box plot 정확히 상자와 수염 그림(box and whisker plot)은 두 개 이상의 집단의 상대적 비교를 위해서 각 집단의 최대값(max)과 최소값(min) 그리고 중앙값(자료를 크기순으로 나열했을 때 가운데 위치하는 값: median) 및 사분위수(자료를 크기 순서에 따라 늘어놓은 자료를 4등분 했을 때 위치하는 값을 의미함) 제 1사분위수(아래에서 25% 백분위점에 위치하는 수: Q1), 제 3사분위수(아래에서 75% 백분위점에 위치하는 수: Q3)등 다섯 숫자를 요약하여 그래프로 나타내는 방법으로 <a href="http://en.wikipedia.org/wiki/John_Tukey">John W. Tukey</a>가 제안한 탐색적 데이터 분석 방법입니다. </p>

<p>Box plot에서 상자 안의 직선은 중위수를 의미하고 상자의 양쪽 끝은 두 개의 사분위수를 그리고 상자의 양쪽에 이상치를 제외한 최대 및 최소값을 잇는 수염을 직선으로 그려줌으로써 데이터의 전체적 분포 양상을 쉽게 파악할 수 있습니다. </p>

<p>보통 R에서 Box plot을 그리면 아래와 같은 결과를 얻을 수 있습니다. 만약 2개의 Group(A, B)과 3가지의 처리(trt1, trt2, trt3) 변수에 대해 두 번 이상 값을 측정했다면 </p>

<pre><code class="r">mydf &lt;- read.csv(&quot;../data/sample.csv&quot;, head = T)

boxplot(Value ~ Trt + Group, data = mydf)

<p><img src="data:image/png;base64,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alt="plot of chunk unnamed-chunk-1"/> </p>

<p>그런데 어느 고갱님께서 좀더 많은 정보를 그래프에 넣을 수 있겠냐고 문의(라 쓰고 명령이라 읽습니다) 하시기에:</p>

<li>산술 평균 </li>

<li>각 사분위수로 부터 1.5IRQ ~ 3IRQ 사이의 이상치는 +, 3IRQ 보다 크거나 작은 이상치는 *: 단, IQR=Q3-Q1</li>

<li><a href="http://wp.me/p1u7fk-8n">각 범주에 해당하는 관측치 수</a></li>

<li>각 범주의 라벨</li>

<p>을 넣어보았습니다. </p>

<pre><code class="r"># 각 Group, trt에 대한 최소값 Q1, 평균, 중위수, Q3, 최대값 계산

summary.tab &lt;- aggregate(mydf[&quot;Value&quot;], mydf[c(&quot;Group&quot;, &quot;Trt&quot;)], summary)

summary.tab &lt;- cbind(summary.tab[, 1:2], as.data.frame(summary.tab$Value))

IQR.tab &lt;- aggregate(mydf[&quot;Value&quot;], mydf[c(&quot;Group&quot;, &quot;Trt&quot;)], IQR)

summary.tab &lt;- merge(summary.tab, IQR.tab, by = c(&quot;Group&quot;, &quot;Trt&quot;))

names(summary.tab) &lt;- c(&quot;Group&quot;, &quot;Trt&quot;, &quot;Min&quot;, &quot;Q1&quot;, &quot;Median&quot;, &quot;Mean&quot;, &quot;Q3&quot;,

&quot;Max&quot;, &quot;IQR&quot;)

summary.tab$IQR15 &lt;- summary.tab$IQR * 1.5

summary.tab$IQR30 &lt;- summary.tab$IQR * 3

# Lower Inner Fence (Q1 - 1.5 * IQR)

summary.tab$Lower.IF &lt;- with(summary.tab, Q1 - IQR15)

# Lower Outer Fence (Q1 - 3 * IQR)

summary.tab$Lower.OF &lt;- with(summary.tab, Q1 - IQR30)

# Upper Inner Fence (Q3 + 1.5 * IQR)

summary.tab$Upper.IF &lt;- with(summary.tab, Q3 + IQR15)

# Upper Outter Fence (Q3 + 3 * IQR)

summary.tab$Upper.OF &lt;- with(summary.tab, Q3 + IQR30)

# 각 범주별 관측치수 구하기

n.obs &lt;- aggregate(mydf[&quot;Value&quot;], mydf[c(&quot;Trt&quot;, &quot;Group&quot;)], length)

xlabel &lt;- paste(&quot;N=&quot;, n.obs$Value, sep = &quot;&quot;)

# Boxplot 그리기

at &lt;- c(1:3, 5:7)

labels &lt;- c(&quot;trt1&quot;, &quot;trt2&quot;, &quot;trt3&quot;)

boxplot(Value ~ Trt, data = mydf, subset = Group == &quot;A&quot;, axes = F, outline = F,

xlim = c(0, 8), at = c(1:3), ylim = c(0, max(mydf$Value)))

boxplot(Value ~ Trt, data = mydf, subset = Group == &quot;B&quot;, axes = F, outline = F,

xlim = c(5, 7), add = T, at = c(5:7))

# y축

axis(2)

# x축에 관측치 수, N=??, 표시

axis(1, at = at, labels = xlabel, las = 1, cex.axis = 0.8)

# Group 라벨

mtext(c(&quot;Group A&quot;, &quot;Group B&quot;), side = 1, line = 3, at = c(2, 6))

# trt 라벨

mtext(labels, side = 3, at = at, cex = 0.9)

# Box plot에 평균치 표시

points(at, summary.tab$Mean, cex = 1.2, pch = 19)

box()

# Inner Fence와 Outter Fence의 이상치 그리기

nn &lt;- 1

for (i in c(&quot;A&quot;, &quot;B&quot;)) {

for (j in c(&quot;trt1&quot;, &quot;trt2&quot;, &quot;trt3&quot;)) {

sub.df &lt;- subset(mydf, Group == i &amp; Trt == j)

Outer.Fence &lt;- sub.df$Value &gt; summary.tab$Upper.OF[nn] | sub.df$Value &lt;

summary.tab$Lower.OF[nn]

Inner.Fence &lt;- (sub.df$Value &lt;= summary.tab$Upper.OF[nn] &amp; sub.df$Value &gt;

summary.tab$Upper.IF[nn]) | (sub.df$Value &gt;= summary.tab$Lower.OF[nn] &amp;

sub.df$Value &lt; summary.tab$Lower.IF[nn])

indicator &lt;- ifelse(Inner.Fence, TRUE, FALSE)

if (sum(indicator) &gt; 0) {

points(rep(at[nn], sum(indicator)), sub.df$Value[which(indicator)],

pch = 3)

}

indicator &lt;- ifelse(Outer.Fence, TRUE, FALSE)

if (sum(indicator) &gt; 0) {

points(rep(at[nn], sum(indicator)), sub.df$Value[which(indicator)],

pch = 8)

}

nn &lt;- nn + 1

}

}

<p><img 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alt="plot of chunk unnamed-chunk-2"/> </p>

<p>결과 R 코드는 복잡해 졌지만, 확실히 그래프만으로 알 수 있는 정보의 양은 늘었네요. 조금 더 일반화시켜서 함수로 만들어 놓고 필요할 때마다 유용하게 쓰게 될 것 같습니다. </p>

<p>예제에 사용한 데이터 및 R 코드는 <a href="https://github.com/mitrad/Boxplot">여기</a>에서 받을 수 있습니다. </p>