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b:head_first_statistics:visualization [2022/09/14 11:10] – hkimscilb:head_first_statistics:visualization [2025/09/08 08:22] (current) – [Histogram Modality] hkimscil
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 | 999  | 2  | | 999  | 2  |
  
 +{{:b:head_first_statistics:pasted:20240904-082648.png}}
  
 in R . . . .  in R . . . . 
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 hist(dat, breaks=5) hist(dat, breaks=5)
 </code> </code>
 +{{:b:head_first_statistics:pasted:20240904-082258.png}}
  
 +<code>
 +dat.iq <- rnorm(1000, 100, 15)
 +head(dat.iq)
 +tail(dat.iq)
 +head(dat.iq, n=12)
 +tail(dat.iq, n=12)
 +
 +mean(dat.iq)
 +sd(dat.iq)
 +
 +hist(dat.iq)
 +hist(dat.iq, breaks=30, col='lightblue')
 +
 +set.seed(101)
 +dat.iq <- rnorm(1000, 100, 15)
 +head(dat.iq)
 +tail(dat.iq)
 +head(dat.iq, n=12)
 +tail(dat.iq, n=12)
 +
 +mean(dat.iq)
 +sd(dat.iq)
 +
 +hist(dat.iq)
 +hist(dat.iq, breaks=30, col='lightblue')
 +</code>
 ====== Scatter plot ====== ====== Scatter plot ======
 <code> <code>
Line 138: Line 165:
    pch=19)</code>    pch=19)</code>
  
-{{:c:ps1-1:2019:pasted:20190909-075028.png}}+{{:b:head_first_statistics:pasted:20240904-083016.png}}
  
 explanatory (설명) variable at x axis explanatory (설명) variable at x axis
Line 146: Line 173:
  
 Drawing a line among the data. Drawing a line among the data.
 +
 <code># Add fit lines <code># Add fit lines
 abline(lm(mpg~wt), col="red") # regression line (y~x) abline(lm(mpg~wt), col="red") # regression line (y~x)
-lines(lowess(wt,mpg), col="blue") # lowess line (x,y)</code> +</code> 
-{{:c:ps1-1:2019:pasted:20190909-075639.png}}+{{:b:head_first_statistics:pasted:20240904-083157.png}}
  
 +Outlier에 대한 주의
 +[{{:pearson-6.png? |}}]
 +<WRAP clear />
  
-A bit more fancy line  
-<code># Enhanced Scatterplot of MPG vs. Weight 
-# by Number of Car Cylinders 
-library(car) 
-scatterplot(mpg ~ wt | cyl, data=mtcars, 
-   xlab="Weight of Car", ylab="Miles Per Gallon", 
-   main="Enhanced Scatter Plot", 
-   labels=row.names(mtcars))</code> 
-{{:c:ps1-1:2019:pasted:20190909-080032.png}} 
  
-Line can be: +====== Presentation ====== 
 +For a very good example, see 
 +https://www.gapminder.org/answers/how-does-income-relate-to-life-expectancy/ 
 +  * Life expectancy data: {{:life.exp.csv}}
  
-**__관계의 방향 (direction)__** +<WRAP clear/> 
-^  관계의 방향  ^^  +====== Histogram skewedness ====== 
-| {{:r.positive.png}}  | {{:r.negative.png}}  |+<WRAP column half> 
 +<code> 
 +#### 
 +# left-skewed distribution 
 +# 1. 
 +set.seed(1) 
 +data <- rbeta(500, shape1 = 10, shape2 = 2) 
 +hist(data, probability = TRUE,  
 +     main = "Histogram with Left-skewed data", 
 +     xlab = "Value", ylab = "Density",  
 +     col = "lightblue", border = "white")
  
 +# 2.
 +# install.packages("fitdistrplus") 
 +library(fitdistrplus)
  
-**__관계의 모양 (shape)__** +fit <- fitdist(data, "beta") 
-^  관계의 모양  ^^  +alpha_est <- fit$estimate["shape1"] 
-| {{:r.positive.png}}  | {{:r.curvepositive.png}}  |+beta_est <- fit$estimate["shape2"]
  
-**__관계의 정도 (힘)__** +# 3. 
-^  관계의 정도 (힘)  ^^  +curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est), 
-| [{{:r.StrengthA.png|Figure_4-1}}]  | [{{:r.StrengthB.png|Figure 4-2}}]  | +      add = TRUE, col = "red", lwd = 2) 
-| [{{:r.StrengthC.png|Figure_4-3}}]  | [{{:r.StrengthD.png|Figure 4-4}}]  | +</code> 
-<WRAP clear /> +</WRAP>
-Pearson's r 의 의미 +
-__Relations, not cause-effect__ +
-[{{:r_eg.15.6.png?250 |Figure 6. Correlation And Causation}}] 상관관계 계수는 단순히 두 변인 (x, y) 간의 관계가 있다는 것을 알려줄 뿐, 왜 그 관계가 있는지는 설명하지 않는다. 바꿔 말하면, 충분한 r 값을 구했다고 해서 이 값이 두 변인 간의 '''원인'''과 '''결과'''의 관계를 말한다고 이야기 하면 __안된다__. 예를 들면 아이스크림의 판매량과 성범죄가 서로 상관관계에 있다고 해서, 전자가 후자의 원인이라고 단정할 수 있는 근거는 없다. 이는 연구자의 논리적인 판단 혹은 이론적인 판단에 따른다.  +
-<WRAP clear />+
  
-__Interpretation with limited range__ +<WRAP column half> 
-[{{:r_eg.15.71.png?250 |Figure_7._Correlation_And_Range}}]  +{{:b:head_first_statistics:pasted:20250903-074821.png}} 
-[{{:r_eg.15.7b1.png?250 |Figure_7._Correlation_And_Range}}]  +</WRAP> 
-데이터의 [[Range]]에 대한 판단에 신중해야 한다. 왜냐 하면, 데이터의 어느 곳을 자르느냐에 따라서 r 값이 심하게 변하기 때문이다.  +<WRAP clear/> 
-<WRAP clear /> +<WRAP column half> 
-__Outliers__ +<code> 
-[{{:r_eg.15.8a.png?250 |Figure_7._Correlation_And_Extreme_Data}}]  +set.seed(1) 
-[{{:r_eg.15.8b.png?250 |Figure_7._Correlation_And_Extreme_Data}}]  +data <- rbeta(500, shape1 = 10, shape2 = 10) 
-위의 설명과 관련하여, 만약에 아주 심한 Outlier가 존재한다면 두 변인 간의 상관관계에 심한 영향을 준다. +hist(data, probability = TRUE,  
-[{{:pearson-6.png?300 |}}]+     main = "Histogram with Normal Distribution Data", 
 +     xlab = "Value", ylab = "Density",  
 +     col = "lightblue", border = "white")
  
-make it sure that there is __no data entry error__. +# 2. 
-{{:r.crime.scatterplot.for.single.by.state.jpg}}+# install.packages("fitdistrplus")  
 +library(fitdistrplus)
  
 +fit <- fitdist(data, "beta")
 +alpha_est <- fit$estimate["shape1"]
 +beta_est <- fit$estimate["shape2"]
  
-<WRAP clear />+# 3. 
 +curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est), 
 +      add = TRUE, col = "red", lwd = 2) 
 +</code> 
 +</WRAP>
  
-see  +<WRAP column half> 
-https://www.gapminder.org/answers/how-does-income-relate-to-life-expectancy/ +{{:b:head_first_statistics:pasted:20250903-074830.png}} 
-  * Life expectancy data: {{:life.exp.csv}}+</WRAP>
  
 +<WRAP clear/>
 +<WRAP column half>
 <code> <code>
-le <- as.data.frame(read.csv("http://commres.net/wiki/_media/life.exp.csv", header=T)) +## 
-colnames(le)[1] <- "c.code" # not really necessary. But, sometimes imported first characters are broken. +# right-skewed distribution 
-lea <- le$X2017 +# 1.  
-leb <- lea[complete.cases(lea)] +set.seed(1) 
-hist(leb, color="grey")+data <- rbeta(500, shape1 = 2, shape2 = 10) 
 +hist(data, probability = TRUE,  
 +     main = "Histogram with Right-skewed Distribution", 
 +     xlab = "Value", ylab = "Density",  
 +     col = "lightblue", border = "white") 
 + 
 +# install.packages("fitdistrplus")  
 +library(fitdistrplus) 
 + 
 +fit <- fitdist(data, "beta") 
 +alpha_est <- fit$estimate["shape1"] 
 +beta_est <- fit$estimate["shape2"] 
 + 
 +#  
 +curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est), 
 +      add = TRUE, col = "red", lwd = 2)
 </code> </code>
 +</WRAP>
 +<WRAP column half>
 +{{:b:head_first_statistics:pasted:20250903-082513.png}}
 +</WRAP>
 +<WRAP clear/>
  
-[{{:c:ps1-1:2019:pasted:20190909-110252.png|Life expectancy in 2017}}]+====== Histogram Modality====== 
 +<WRAP column half> 
 +Unimodal  
 +<code> 
 +### unimodal data  
 +set.seed(1) 
 +d.1 <- rnorm(500, 10, 2) 
 +hist(d.1, breaks = 30, probability = T, 
 +     main = "Hist with Unimodal distrib", 
 +     xlab = "Value", ylab = "Density",  
 +     col = "lightblue", border = "black") 
 +lines(density(d.1),  
 +      col = "darkred", lwd = 2) 
 +</code> 
 +</WRAP>
  
-[{{:c:ps1-1:2019:pasted:20190909-104759.png|Distribution of temperature}}]+<WRAP column half> 
 +{{:b:head_first_statistics:pasted:20250903-083409.png}} 
 +</WRAP>
  
-[{{:c:ps1-1:2019:pasted:20190909-111117.png|skewness}}]+<WRAP clear/>
  
-[{{:c:ps1-1:2019:pasted:20190909-111001.png|modality}}]+Bimodal distribution 
 +<WRAP column half> 
 +<code> 
 +### bimodal data  
 +set.seed(1) 
 +d.1 <- rnorm(500, 10, 2) 
 +d.2 <- rnorm(500, 20, 2) 
 +d.all <- c(d.1, d.2) 
 +hist(d.all, breaks = 30, probability = T, 
 +     main = "Hist with bimodal distrib", 
 +     xlab = "Value", ylab = "Density",  
 +     col = "lightblue", border = "black") 
 +lines(density(d.all),  
 +      col = "darkred", lwd = 2) 
 +</code> 
 +</WRAP> 
 + 
 +<WRAP column half> 
 +{{:b:head_first_statistics:pasted:20250903-083524.png}} 
 +</WRAP> 
 +<WRAP clear/>
  
-box plot+<WRAP column half> 
 +<code> 
 +### multi-modal data  
 +# Parameters for the first normal distribution (Mode 1) 
 +m.1 <- 50 
 +sd.1 <- 5 
 + 
 +# Parameters for the second normal distribution (Mode 2) 
 +m.2 <- 100 
 +sd.2 <- 15 
 + 
 +m.3 <- 160 
 +sd.3 <- 6 
 + 
 +# Mixing proportion for Mode 1 
 +prop.1 <- 0.3 
 +# Mixing proportion for Mode 2 
 +prop.2 <- 0.6 # This is 1 - prop1 
 +# Mixing proportion for Mode 2 
 +prop.3 <- 1.0 # This is 1 - prop1 
 + 
 +# Number of samples to generate 
 +n.sam <- 1000 
 + 
 +# Create an empty vector to store the combined samples 
 + 
 +mm.dist <- numeric(n.sam) 
 +set.seed(1) 
 +for (i in 1:n.sam) { 
 +  # Randomly choose which distribution to sample from 
 +  tmp <- runif(1) 
 +  if (tmp < prop.1) { 
 +    mm.dist[i] <- rnorm(1, mean = m.1, sd = sd.1) 
 +  } else if (tmp < prop.2) { 
 +    mm.dist[i] <- rnorm(1, mean = m.2, sd = sd.2) 
 +  } else { 
 +    mm.dist[i] <- rnorm(1, mean = m.3, sd = sd.3) 
 +  } 
 + 
 +} 
 + 
 +hist(mm.dist, breaks = 30,  
 +     main = "Multimodal Distribution",  
 +     xlab = "Value", ylab = "Density",  
 +     freq = FALSE, probability = T, 
 +     col = "lightblue", border = "black") 
 +lines(density(mm.dist),  
 +      col = "darkred", lwd = 2) 
 + 
 +</code> 
 +</WRAP> 
 +<WRAP column half> 
 +{{:b:head_first_statistics:pasted:20250908-082219.png}} 
 +</WRAP> 
 +<WRAP clear/> 
 + 
 + 
 +====== box plot ====== 
 +<WRAP column half>
 <code> <code>
 # Boxplot of MPG by Car Cylinders # Boxplot of MPG by Car Cylinders
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     ylab="Miles Per Gallon")     ylab="Miles Per Gallon")
 </code> </code>
-{{:c:ps1-1:2019:pasted:20190909-111438.png}}+</WRAP>
  
 +<WRAP column half>
 +{{:c:ps1-1:2019:pasted:20190909-111438.png}}
 +</WRAP>
 +<WRAP clear/>
 +====== see also ======
 +https://r-graph-gallery.com/
  
b/head_first_statistics/visualization.1663121403.txt.gz · Last modified: 2022/09/14 11:10 by hkimscil
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