Exploratory Data Analysis August 26, 2004
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1 Exploratory Data Analysis August 26, 2004 Exploratory Data Analysis p. 1/??
2 Agent Orange Case Study (SS: Ch 3) Dioxin concentrations in parts per trillion (ppt) for 646 Vietnam veterans and 97 veterans who did not serve in Vietnam. sample (nonrandom) of Vietnam vets who served during sample (nonrandom) of vets who served in the US and Germany between Dioxin measurements taken in 1987 Exploratory Data Analysis p. 2/??
3 Creting a Dataframe in R > vets = read.table("case0302.csv", header=t, sep=",") > names(vets) [1] "DIOXIN" "VETERAN" > attach(vets} Notes: 1. sep="," tells R that columns of data are separated by a comma (the csv format) 2. header=t tells R that the first line of the file contains variable names 3. the names function extracts the names variables and cases in a dataframe 4. the attach function allows us to refer to variables in the dataframe vets directly Exploratory Data Analysis p. 3/??
4 Graphical Views 1. Univariate: histograms, density curves, boxplots 2. Bivariate: scatter plots with trend lines, side-by-side boxplots 3. Several variables: scatter plot matrices, lattice or trellis plots, 3-dimensional plots, dynamic plots Exploratory Data Analysis p. 4/??
5 Histograms Default Number of Bins 50 Bins Density Density Dioxin Concentration (ppt) Dioxin Concentration (ppt) hist(y, prob=t,breaks=50,main="title", ylab="density",xlab="y") Exploratory Data Analysis p. 5/??
6 Estimating the Density Curve Default Settings for Histogram and Kernel Density Density Dioxin Concentration (ppt) dens = density(dioxin) lines(dens, lwd=2, col="orange") Exploratory Data Analysis p. 6/??
7 Kernel Density Estimation Default settings lead to a bumpy estimate. Are these real features or artifacts of the estimation procedure? density(y, bw, adjust, kernel, window) bw bandwidth controls amount of smoothing adjust actual bandwith is adjust*bw kernel, window smoothing kernel see help(density) for other options Reference: Silverman, B. W. (1986)Density Estimation. Chapman & Hall. Exploratory Data Analysis p. 7/??
8 Adjusting Bandwidth density(x = DIOXIN) density(x = DIOXIN, adjust = 1.25) Density Density Dioxin Concentration (ppt) Dioxin Concentration (ppt) density(x = DIOXIN, adjust = 1.5) density(x = DIOXIN, adjust = 2) Density Density Dioxin Concentration (ppt) Dioxin Concentration (ppt) Exploratory Data Analysis p. 8/??
9 Adding Locations of Data Use the rug function; rug(dioxin, lwd=2) density(x = DIOXIN, adjust = 1.25) Density Dioxin Concentration (ppt) Exploratory Data Analysis p. 9/??
10 Stem & Leaf Plots > stem(dioxin) The decimal point is at the // Exploratory Data Analysis p. 10/??
11 Stem & Leaf Plots Interpreting stem 0 is on the left leaf 0 is on the right of the indicates location of decimal place 15 cases with value < 2.0 (next stem/leaf) Advantages/Disadvantages + more detail - designed for small data sets - may not always fit on the page Exploratory Data Analysis p. 11/??
12 Boxplots Shows quartiles and outliers Box is based on upper (Q1) and lower (Q3) quartiles Line in box indicates median (Q2) Whiskers based on smallest/largest observation within 1.5*IQR of the box Points for all cases beyond whiskers outliers Good for showing outliers, skewness/symmetry Exploratory Data Analysis p. 12/??
13 Boxplot of Dioxin Default with Horizontal=T Dioxin Concentration (ppt) Dioxin Concentration (ppt) Exploratory Data Analysis p. 13/??
14 Side-by-Side Boxplots boxplot(dioxin ~ VETERAN, data=vets ) Dioxin Concentration (ppt) OTHER VIETNAM Exploratory Data Analysis p. 14/??
15 Formula Side-by-side boxplots are useful for showing distribution of a quantitative variable for each level of a qualitative variable boxplot(dioxin VETERAN, data=vets, ylab="dioxin Concentration (ppt)", main="boxplot(dioxin VETERAN, data=vets)" ) formula DIOXIN VETERAN creates a boxplot of dioxin for each level of VETERAN data specifies the dataframe to use Exploratory Data Analysis p. 15/??
16 Numerical Summaries means (average) mean standard deviations sd 5-point summary quantile (min, lower quartile, median, upper quartile, max) correlations cor summary learn to use the command apply and its relatives Exploratory Data Analysis p. 16/??
17 Points Empirical Rule: Bell-shaped data 95 % of the observations will be within ± 2 standard deviations of the mean. mean and standard deviation are sensitive to outliers symmetric data mean and median should be approximately equal Exploratory Data Analysis p. 17/??
18 Scatter Plots bivariate plot(x,y) plot(y x) all-possible pairwise scatter plots plot(dataframe) pairs(dataframe) Exploratory Data Analysis p. 18/??
19 Old Faithful Eruptions Variables Day (of eruption)in August interval (waiting time until the next eruption in minutes) duration (duration of current eruption in minutes) Exploratory Data Analysis p. 19/??
20 Summary > names(geyser) [1] "Day" "interval" "duration" > summary(geyser) Day interval duration Min. : 1.00 Min. :42.00 Min. : st Qu.: st Qu.: st Qu.:2.300 Median :16.00 Median :75.00 Median :4.000 Mean :12.30 Mean :71.01 Mean : rd Qu.: rd Qu.: rd Qu.:4.400 Max. :23.00 Max. :95.00 Max. :5.200 Exploratory Data Analysis p. 20/??
21 Pairs Plot Old Faithful Eruptions Day interval duration Exploratory Data Analysis p. 21/??
22 Adding a Smooth Trend The function lowess fits a one dimensional smooth trend to (x,y) pairs the function is in R package modreg, but builtin with newer versions of R Use library(modereg) to load it, if not available lines(lowess(duration, interval)) Exploratory Data Analysis p. 22/??
23 Adding a Smooth Trend Old Faithful Eruptions Waiting Time (mins) Duration (mins) Exploratory Data Analysis p. 23/??
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