www.jjw3.com > stats.jjw3.com/math1431.htm > stats.jjw3.com/math1431/R_instructions.htm

john{dot}weber{at}gpc{dot}edu

Here are instructions on how to use R for statistics:

Introductory Instructions:

• Download R
  • http://www.r-project.org/ or http://sourceforge.net/projects/rportable/
  • NOTE: The two folders (R-Portable and work) and R-Start.exe link MUST be in root folder of USB drive.
• Start R-portable
  • Double-click R-Start.exe
  • NOTE: This will automatically load custom functions that will be used during the course.
• Find information about any functions
  • ?functionname
• Load saved work
  • load("name.Rdata")
• Load custom function
  • source("functionname.R")
• Load dataset in .csv file located in working directory (loads ALL variables and data and stores into newvarname)
  • newvarname = load.data("filename.csv")
• Identify all variables in dataset
  • names(newvarname)
• Load one variable from dataset and store into new variable
  • singlevarname = newvarname$var
• Load data into new variable
  • singlevarname = c(x1, x2, x3, etc) where x1, x2, x3, etc. are quantitative data; or
  • singlevarname = c("d1", "d2", "d3", etc) where "d1", "d2", "d3", etc. are qualitative data
• Repeat function several times
  • do(n)*function(arguments) where n is the number of repetitions
• Make comments within code
  • # this is a comment

Section 1.3: Simple Random Sampling

• sample(singlevarname, n, replace=F) where n is sample size

Section 1.4: Other Effective Sampling Methods

• Systematic sample
  • systematic(singlevarname, n) where n is sample size
• Stratified sample
  • stratified(varname, strataVarname, n) where varname is variable containing the population, strataVarname is the variable containing the levels (i.e., strata), and n is sample size

Section 2.1: Organizing Qualitative Data

• Construct frequency distribution
  • table(singlevarname)
• Construct relative frequency distribution
  • table(singlevarname)/length(singlevarname)

Section 2.1: Organizing Qualitative Data: The Popular Displays

• Construct frequency bar graph – note: the title and labels can be written in any order
  • barplot(table(singlevarname), xlab="variable name", ylab="frequency", main="Long Descriptive Title")
• Construct relative frequency bar graph – note: the title and labels can be written in any order
  • barplot(table(singlevarname)/length(singlevarname), xlab="variable name", ylab="relative frequency", main="Long Descriptive Title")
• Construct Pareto chart – note: the title and labels can be written in any order
  • pareto.chart(table(singlevarname), xlab="variable name", ylab="relative frequency", main="Long Descriptive Title")
• Construct side-by-side frequency bar graph – note: the title and labels can be written in any order
  • barplot(xtabs(~ levelvariable + singlevarname ), xlab="variable name", ylab="frequency", main="Long Descriptive Title", beside = TRUE, legend.text = levels(levelvariable), col = c("colorname1", "colorname2", etc.)

Section 2.2: Organizing Quantitative Data: The Popular Displays

• Construct histogram – note: the title and labels can be written in any order
  • hist(singlevarname, xlab="variable name", main="Long Descriptive Title")
• Construct relative frequency histogram – note: the title and labels can be written in any order
  • hist(singlevarname, freq=FALSE, xlab="variable name", ylab="relative frequency", main="Long Descriptive Title")
• Construct histogram with different starting value and classwidth – note: the title and labels can be written in any order
  • hist(singlevarname, xlab="variable name", main="Long Descriptive Title", breaks = c(b1, b2, b3, b4, etc)) where b1, b2, b3, etc. are lower/upper class limits
• Construct stemplot
  • stem(singlevarname, scale=value) note: use scale=10 to move decimal place one place to left in stemplot; use scale=100 to move decimal place two places to left in stemplot; use scale=0.1 to move decimal place one place to right in stemplot; etc.
• Construct back-n-back stemplot
  • stem.leaf.backback(var1, var2, back.to.back=T, unit=value, m=1) note: use unit=10 to move decimal place one place to left in stemplot; use unit=100 to move decimal place two places to left in stemplot; use unit=0.1 to move decimal place one place to right in stemplot; etc.

Section 3.1: Measures of Central Tendency

• [Arithmetic] Mean
  • sum(singlevarname)/length(singlevarname); or
  • mean(singlevarname)
• Median
  • median(singlevarname)

Section 3.2: Measures of Dispersion [a.k.a., Spread]

• Range
  • max(singlevarname) - min(singlevarname)
• Population Variance, σ²
  • sum((mean(singlevarname)-singlevarname)^2)/length(singlevarname)
• Sample Variance, s²
  • var(singlevarname)
• Population Standard Deviation, σ
  • sqrt(sum((mean(singlevarname)-singlevarname)^2)/length(singlevarname))
• Population Standard Deviation, σ
  • sigma(singlevarname)
• Sample Standard Deviation [a.k.a., sd], s
  • sqrt(var(singlevarname)); or
  • sd(singlevarname)
• Determine if data is normally-distributed
  • qqnorm(singlevarname)

Section 3.4: Measures of Positions and Outliers

• k^th percentile
  • qnorm(k, mean(singlevarname), sd(singlevarname))
• z-score – note: the xvalue is a number not a function here
  • z = (xvalue - mean(singlevarname))/sd(singlevarname)
• Q₁
  • quantile(singlevarname, 0.25, type=2)
• Q₃
  • quantile(singlevarname, 0.75, type=2)
• Interquartile range, IQR
  • quantile(singlevarname, 0.75, type=2) - quantile(singlevarname, 0.25, type=2); or
  • IQR(singlevarname, type=2)
• Lower fence for outliers
  • lowerfence = quantile(singlevarname, 0.25, type=2) - 1.5*IQR(singlevarname, type=2)
• Upper fence for outliers
  • upperfence = quantile(singlevarname, 0.75, type=2) + 1.5*IQR(singlevarname, type=2)
• Identify outliers below lower fence
  • singlevarname[singlevarname < lowerfence]
• Identify outliers above upper fence
  • singlevarname[singlevarname > upperfence]

Section 3.5: The Five Number Summary and Boxplots

• Five-number summary – note: mean is not a measure within the five-number summary
  • fivenum(singlevarname)
• Boxplot
  • boxplot(singlevarname, ylab="variable name", main="Long Descriptive Title") – note: use the argument horizontal=TRUE to change the orientation of the boxplot – make sure that you also switch the labels
• Multiple boxplots comparing different levels in variable
  • boxplot(singlevarname ~ levels, data=singlevarname, xlab="description of levels", ylab="variable name", main="Long Descriptive Title")
• Graph histogram and boxplot concurrently for same variable – note: after graphing close graphics window to reset window
  • attach(newvarname)
par(mfrow=c(2,1))
hist(singlevarname, xlab="variable name", ylab="frequency", main="Long Descriptive Title")
boxplot(singlevarname, xlab="variable name", horizontal=TRUE)
detach(newvarname)

Section 4.1: Scatter Diagram and Correlation

• Scatterplot
  • plot(xvarname, yvarname, xlab="x variable name", ylab="y variable name", main="Long Descriptive Title")
• Pearson linear correlation coefficient, r
  • cor(xvarname, yvarname, method="pearson", use="complete.obs") – note: use="complete.obs" removes any 'pair' of observations that has missing value(s)

Section 4.2: Least-Squares Regression

• Least-squares regression line (a.k.a., linear model)
  • lm(formula = yvarname ~ xvarname) – note: gives Intercept and coefficient of xvarname
• Plot scatterplot with least-squares regression line
  • plot(xvarname, yvarname, xlab="x variable name", ylab="y variable name", main="Long Descriptive Title")
abline(lm(formula = yvarname ~ xvarname))

Section 4.3: Coefficient of Determination

• Coefficient of determination, r²
  • (cor(xvarname, yvarname, method="pearson"))^2

Section 6.1: Discrete Random Variables

• Graph discrete probability histogram
  • Store x-values into variable: x = c(x1, x2, x3)
  • Store probabilities, p, into variable: p = c(p1, p2, p3)
  • barplot(x*p), xlab="variable name", ylab="probability", main="Long Descriptive Title")
• Compute mean (expected value) of a discrete random variable
  • Store x-values into variable: x = c(x1, x2, x3)
  • Store probabilities, p, into variable: p = c(p1, p2, p3)
  • sum(x*p)
• Compute variance of a discrete random variable
  • Store x-values into variable: x = c(x1, x2, x3)
  • Store probabilities, p, into variable: p = c(p1, p2, p3)
  • sum((x-sum(x*p))^2*p)
• Compute standard deviation of a discrete random variable
  • Store x-values into variable: x = c(x1, x2, x3)
  • Store probabilities, p, into variable: p = c(p1, p2, p3)
  • sqrt(sum((x-sum(x*p))^2*p))

Section 6.2: The Binomial Probability Distribution

• The number of combinations of r objects from n total objects
  • choose(n, r)
• Binomial probability of k successes from n trials with P(success) = p – note: order is not important
  • dbinom(k, prob=p, size=n)
• Cumulative binomial probability of a ≤ k ≤ b successes from n trials with P(success) = p
  • sum(dbinom(a:b, prob=p, size=n))
• Plot cumulative binomial probability of 0 ≤ k ≤ n successes from n trials with P(success) = p
  • barplot(dbinom(0:n, prob=p, size=n), names=0:n)

Section 7.1: Properties of the Normal Distribution

• Plot the normal curve with mean = m and sd = s
  • x = seq(-20,20,by=0.1)
y = dnorm(x, mean=m, sd=s)
plot(x, y)
• Find area under the normal curve with mean = m and sd = s to the left of x
  • pnorm(x, mean=m, sd=s)
• Find area under the normal curve with mean = m and sd = s to the right of x
  • pnorm(x, mean=m, sd=s, lower.tail=FALSE)
• Find area under the normal curve with mean = m and sd = s between a ≤ x ≤ b
  • pnorm(a, mean=m, sd=s) - pnorm(b, mean=m, sd=s)
• Plot a relative frequency histogram with Normal Curve
  • Store variable into x: x = singlevarname
  • Construct relative frequency histogram:
    hist(x, freq=FALSE, xlab="variable name", ylab="relative frequency", main="Long Descriptive Title")
  • Graph normal curve: curve(dnorm(x, mean=mean(x), sd=sd(x)), add=TRUE)

Section 7.2: The Standard Normal Distribution

• Find z_α given area = α to the right of z under a normal curve with mean = m and sd = s
  • qnorm(α, mean=m, sd=s, lower.tail=FALSE)
• Find the area [a.k.a., proportion, percentage, or probability] under the standard normal curve for z ≤ a
  • pnorm(a)
• Find the area [a.k.a., proportion, percentage, or probability] under the standard normal curve for z ≥ a
  • pnorm(a, lower.tail=FALSE)
• Find the area [a.k.a., proportion, percentage, or probability] under the standard normal curve for a ≤ z ≤ b
  • pnorm(b) - pnorm(a)

Section 7.3: Applications of the Normal Distribution

• Find the area [a.k.a., proportion, percentage, or probability] under the normal curve with mean = m and sd = s for x ≤ a
  • pnorm(a, mean=m, sd=s)
• Find the area [a.k.a., proportion, percentage, or probability] under the normal curve with mean = m and sd = s for x ≥ a
  • pnorm(a, mean=m, sd=s, lower.tail=FALSE)
• Find the area [a.k.a., proportion, percentage, or probability] under the normal curve with mean = m and sd = s for a ≤ x ≤ b
  • pnorm(b, mean=m, sd=s) - pnorm(a, mean=m, sd=s)
• Find the x^th percentile for normally-distributed variable with mean = m and sd = s
  • qnorm(x, mean=m, sd=s) where x is a decimal

Section 7.4: Assessing Normality

• qqnorm(singlevarname)

Section 9.1: The Logic in Constructing Confidence Intervals for a Population Mean

• How to find one-sample t confidence interval (using sample mean and σ)
  • zInterval(mean=samplemean, sd=population_sd, n=samplesize, conf.level=C-level) where C-Level is confidence level as a decimal; the arguments may be used in any order

Section 9.2: Confidence Intervals for a Population Mean

• How to find critical value, t_α
  • qt(1 – α, df) where α is area to the right; df = n – 1
• How to find one-sample t confidence interval (using sample mean and s)
  • load tInterval.R using source("tInterval.R")
  • then tInterval(mean=samplemean, sd=population_sd, n=samplesize, conf.level=C-level) where C-Level is confidence level as a decimal; the arguments may be used in any order
• How to find one-sample t confidence interval (using data)
  • t.test(data1, mu=mu_0, conf.level=C-Level) where data1 is variable containing data; mu_0 is population mean used in hypotheses; and C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]

Section 9.3: Confidence Intervals for a Polpulation Proportion

• How to find a one-sample confidence interval for population proportion using z-statistic
  • prop.test(x=number_of_successes, n=samplesize, p=p_0, conf.level=C-Level, alternative="two.sided") where x is the number of successes; n is sample size; p_0 is population proportion used in hypotheses; and C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]

Section 10.3: Hypothesis Test for a Population Mean – Population Standard Deviation Unknown

• How to perform one-sample hypothesis test for population mean using t-statistic (using data)
  • t.test(data1, mu=mu_0, conf.level=C-Level, alternative="two.sided") where data1 is variable containing data; mu_0 is population mean used in hypotheses; C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]; alternative is symbol used in alternate hypothesis: "less" for <, "greater" for >, "two.sided" for ≠

Section 10.4: Hypothesis Test for a Population Proportion

• How to perform one-sample hypothesis test for population proportion using z-statistic
  • prop.test(x=number_of_successes, n=samplesize, p=p_0, conf.level=C-Level, alternative="two.sided") where x is the number of successes; n is sample size; C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]; alternative is symbol used in alternate hypothesis: "less" for <, "greater" for >, "two.sided" for ≠

Section 11.1: Inferences about Two Means: Dependent Samples

• How to perform hypothesis test for matched-pairs design using t-statistic (using data)
  • t.test(data1, data2, paired=TRUE, conf.level=C-Level, alternative="two.sided") where data1 and data2 are variables containing data; C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]; alternative is symbol used in alternate hypothesis: "less" for <, "greater" for >, "two.sided" for ≠

Section 11.2: Inferences about Two Means: Independent Samples

• How to find two-sample t confidence interval (using data)
  • t.test(data1, data2, conf.level=C-Level) where data1 and data2 are variables containing data; C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]
• How to find pooled two-sample t confidence interval (using data)
  • t.test(data1, data2, conf.level=C-Level, var.equal) where data1 and data2 are variables containing data; C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]
• How to perform two-sample t-test (using data)
  • t.test(data1, data2, conf.level=C-Level, alternative="two.sided") where data1 and data22 are variables containing data; C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]; alternative is symbol used in alternate hypothesis: "less" for <, "greater" for >, "two.sided" for ≠
• How to perform pooled two-sample t-test (using data)
  • t.test(data1, data2, conf.level=C-Level, alternative="two.sided", var.equal) where data1 and data2 are variables containing data; C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]; alternative is symbol used in alternate hypothesis: "less" for <, "greater" for >, "two.sided" for ≠

Section 11.3: Two-Sample Hypothesis Test for Population Proportions, using z-statistic

• How to perform two-sample hypothesis test for population proportions using z-statistic (using data)
  • prop.test(x = c(x1,x2), n=c(n1,n2), conf.level=C-Level, alternative="two.sided") where x1 and x2 are the number of successes; where n1 and n2 are sample sizes; C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]; alternative is symbol used in alternate hypothesis: "less" for <, "greater" for >, "two.sided" for ≠
• How to find the confidence interval for the difference between two populations proportion using z-statistic (using data)
  • prop.test(x = c(x1,x2), n=c(n1,n2), conf.level=C-Level, alternative="two.sided") where x1 and x2 are the number of successes; where n1 and n2 are sample sizes; C-Level is confidence level as a decimal [i.e., 1 – α/2 or 1 – α]

Section 12.1: Goodness-of-Fit Test

• How to calculate the Χ ²-statistic
  • qchisq(alpha, df)
• Χ ² goodness of fit test
  • chisq.test(c(x1,x2,x3),p=c(p1,p2,p3)) where x1, x2, x3, etc. are data; p1, p2, p3, etc., are the respective probabilities that add to 1

Section 12.2: Tests for Independence and the Homogeneity of Proportions

• Χ ² test of independence
  • Set-up matrix (called data frame) containing counts
    • rowvariable1 = c(c1,1,c1,2,c1,3) where c_1,1,c_1,2,c_1,3, etc. are counts in the first row of matrix;
    • rowvariable2 = c(c2,1,c2,2,c2,3) where c_2,1,c_2,2,c_2,3, etc. are counts in the second row of matrix;
    • rowvariable3 = c(c3,1,c3,2,c3,3) where c_3,1,c_3,2,c_3,3, etc. are counts in the third row of matrix;
    • etc.
  • chisq.test(data.frame(rowvariable1, rowvariable2, rowvariable3))
• Χ ² test for homogeneity
  • Set-up variables containing counts
    • variable.fair = c(c1,1,c1,2,c1,3) where c_1,1,c_1,2,c_1,3, etc. are counts in the first row of matrix;
    • variable.bias = c(c2,1,c2,2,c2,3) where c_2,1,c_2,2,c_2,3, etc. are counts in the second row of matrix;
  • chisq.test(rbind(variable.fair, variable.bias))
  • for expected counts only, use: chisq.test(rbind(variable.fair, variable.bias)) [['exp']]

Section x.x: One-Way Analysis of Variance (ANOVA)

• How to perform hypothesis test on three or more population means using ANOVA
  • Set-up variables containing sample values
    • variable1 = c(c1,1,c1,2,c1,3) where c_1,1,c_1,2,c_1,3, etc. are values in sample 1;
    • variable2 = c(c2,1,c2,2,c2,3) where c_1,1,c_1,2,c_1,3, etc. are values in sample 2;
    • variable3 = c(c3,1,c3,2,c3,3) where c_1,1,c_1,2,c_1,3, etc. are values in sample 3;
    • etc.
  • Store all variables in a new variable
    • samplesvariable = data.frame(variable1, variable2, variable3)
  • Store samples variable as a variable with factors describing values
    • samplesvariable = stack(samplesvariable)
  • oneway.test(values ~ ind, data=samplesvariable, var.equal=TRUE)