Table of Useful R Commands Cheat Sheet, Cheat Sheet of Probability and Statistics

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Table of Useful R commands Command Purpose help() Obtain documentation for a given R command example() View some examples on the use of a command c(), scan() Enter data manually to a vector in R seq() Make arithmetic progression vector rep() Make vector of repeated values data() Load (often into a data.frame) built-in dataset View() View dataset in a spreadsheet-type format str() Display internal structure of an R object read.csv(), read.table() Load into a data.frame an existing data file library(), require() Make available an R add-on package dim() See dimensions (# of rows/cols) of data.frame length() Give length of a vector ls() Lists memory contents rm() Removes an item from memory names() Lists names of variables in a data.frame hist() Command for producing a histogram histogram() Lattice command for producing a histogram stem() Make a stem plot table() List all values of a variable with frequencies xtabs() Cross-tabulation tables using formulas mosaicplot() Make a mosaic plot cut() Groups values of a variable into larger bins mean(), median() Identify “center” of distribution by() apply function to a column split by factors summary() Display 5-number summary and mean var(), sd() Find variance, sd of values in vector sum() Add up all values in a vector quantile() Find the position of a quantile in a dataset barplot() Produces a bar graph barchart() Lattice command for producing bar graphs boxplot() Produces a boxplot bwplot() Lattice command for producing boxplots Command Purpose plot() Produces a scatterplot xyplot() Lattice command for producing a scatterplot lm() Determine the least-squares regression line anova() Analysis of variance (can use on results of lm()) predict() Obtain predicted values from linear model nls() estimate parameters of a nonlinear model residuals() gives (observed - predicted) for a model fit to data sample() take a sample from a vector of data replicate() repeat some process a set number of times cumsum() produce running total of values for input vector ecdf() builds empirical cumulative distribution function dbinom(), etc. tools for binomial distributions dpois(), etc. tools for Poisson distributions pnorm(), etc. tools for normal distributions qt(), etc. tools for student t distributions pchisq(), etc. tools for chi-square distributions binom.test() hypothesis test and confidence interval for 1 proportion prop.test() inference for 1 proportion using normal approx. chisq.test() carries out a chi-square test fisher.test() Fisher test for contingency table t.test() student t test for inference on population mean qqnorm(), qqline() tools for checking normality addmargins() adds marginal sums to an existing table prop.table() compute proportions from a contingency table par() query and edit graphical settings power.t.test() power calculations for 1- and 2-sample t anova() compute analysis of variance table for fitted model R Commands for MATH 143 Examples of usage Examples of usage help() help(mean) example() require(lattice) example(histogram) c(), rep() seq() > x = c(8, 6, 7, 5, 3, 0, 9) > x [1] 8 6 7 5 3 0 9 > names = c("Owen", "Luke", "Anakin", "Leia", "Jacen", "Jaina") > names [1] "Owen" "Luke" "Anakin" "Leia" "Jacen" "Jaina" > heartDeck = c(rep(1, 13), rep(0, 39)) > heartDeck [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 [49] 0 0 0 0 > y = seq(7, 41, 1.5) > y [1] 7.0 8.5 10.0 11.5 13.0 14.5 16.0 17.5 19.0 20.5 22.0 23.5 25.0 26.5 28.0 29.5 31.0 32.5 34.0 [20] 35.5 37.0 38.5 40.0 data(), dim(), names(), View(), str() > data(iris) > names(iris) [1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" "Species" > dim(iris) [1] 150 5 > str(iris) 'data.frame': 150 obs. of 5 variables: $ Sepal.Length: num 5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ... $ Sepal.Width : num 3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ... $ Petal.Length: num 1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ... $ Petal.Width : num 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ... $ Species : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ... > View(iris) 2 R Commands for MATH 143 Examples of usage sum() > firstTwentyIntegers = 1:20 > sum(firstTwentyIntegers) [1] 210 > die = 1:6 > manyRolls = sample(die, 100, replace=T) > sixFreq = sum(manyRolls == 6) > sixFreq / 100 [1] 0.14 stem() > monarchs = read.csv("http://www.calvin.edu/~scofield/data/comma/monarchReigns.csv") > stem(monarchs$years) The decimal point is 1 digit(s) to the right of the | 0 | 0123566799 1 | 0023333579 2 | 012224455 3 | 355589 4 | 4 5 | 069 6 | 3 table(), table(), mosaicplot(), cut() > pol = read.csv("http://www.calvin.edu/~stob/data/csbv.csv") > table(pol$sex) Female Male 133 88 > table(pol$sex, pol$Political04) Conservative Far Right Liberal Middle-of-the-road Female 67 0 14 48 Male 47 7 6 28 > xtabs(~sex, data=pol) sex Female Male 133 88 > xtabs(~Political04 + Political07, data=pol) Political07 Political04 Conservative Far Left Far Right Liberal Middle-of-the-road Conservative 58 0 2 13 39 Far Right 4 0 3 0 0 Liberal 0 1 1 14 4 Middle-of-the-road 20 0 0 22 32 > mosaicplot(~Political04 + sex, data=pol) 5 R Commands for MATH 143 Examples of usage pol Political04 se x Conservative Far RightLiberal Middle−of−the−road F em al e M al e > monarchs = read.csv("http://www.calvin.edu/~scofield/data/comma/monarchReigns.csv") > table(monarchs$years) 0 1 2 3 5 6 7 9 10 12 13 15 17 19 20 21 22 24 25 33 35 38 39 44 50 56 59 63 1 1 1 1 1 2 1 2 2 1 4 1 1 1 1 1 3 2 2 1 3 1 1 1 1 1 1 1 > xtabs(~years, data=monarchs) years 0 1 2 3 5 6 7 9 10 12 13 15 17 19 20 21 22 24 25 33 35 38 39 44 50 56 59 63 1 1 1 1 1 2 1 2 2 1 4 1 1 1 1 1 3 2 2 1 3 1 1 1 1 1 1 1 > cut(monarchs$years, breaks=seq(0,65,5)) [1] (20,25] (10,15] (30,35] (15,20] (30,35] (5,10] (15,20] (55,60] (30,35] (15,20] (45,50] (20,25] [13] (10,15] (5,10] (35,40] (20,25] <NA> (0,5] (20,25] (35,40] (5,10] (0,5] (40,45] (20,25] [25] (20,25] (20,25] (0,5] (10,15] (5,10] (10,15] (10,15] (30,35] (55,60] (5,10] (5,10] (60,65] [37] (5,10] (20,25] (0,5] (10,15] 13 Levels: (0,5] (5,10] (10,15] (15,20] (20,25] (25,30] (30,35] (35,40] (40,45] (45,50] ... (60,65] > table(cut(monarchs$years, breaks=seq(0,65,5))) (0,5] (5,10] (10,15] (15,20] (20,25] (25,30] (30,35] (35,40] (40,45] (45,50] (50,55] (55,60] 4 7 6 3 8 0 4 2 1 1 0 2 (60,65] 1 > fiveYrLevels = cut(monarchs$years, breaks=seq(0,65,5)) > xtabs(~fiveYrLevels) fiveYrLevels (0,5] (5,10] (10,15] (15,20] (20,25] (25,30] (30,35] (35,40] (40,45] (45,50] (50,55] (55,60] 4 7 6 3 8 0 4 2 1 1 0 2 (60,65] 1 6 R Commands for MATH 143 Examples of usage barplot() pol = read.csv("http://www.calvin.edu/~stob/data/csbv.csv") barplot(table(pol$Political04), main="Political Leanings, Calvin Freshman 2004") barplot(table(pol$Political04), horiz=T) barplot(table(pol$Political04),col=c("red","green","blue","orange")) barplot(table(pol$Political04),col=c("red","green","blue","orange"), names=c("Conservative","Far Right","Liberal","Centrist")) Conservative Liberal Centrist 0 40 80 barplot(xtabs(~sex + Political04, data=pol), legend=c("Female","Male"), beside=T) Conservative Far Right Liberal Middle−of−the−road Female Male 0 10 20 30 40 50 60 7 R Commands for MATH 143 Examples of usage dbinom(), pbinom(), qbinom(), rbinom(), binom.test(), prop.test() > dbinom(0, 5, .5) # probability of 0 heads in 5 flips [1] 0.03125 > dbinom(0:5, 5, .5) # full probability dist. for 5 flips [1] 0.03125 0.15625 0.31250 0.31250 0.15625 0.03125 > sum(dbinom(0:2, 5, .5)) # probability of 2 or fewer heads in 5 flips [1] 0.5 > pbinom(2, 5, .5) # same as last line [1] 0.5 > flip5 = replicate(10000, sum(sample(c("H","T"), 5, rep=T)=="H")) > table(flip5) / 10000 # distribution (simulated) of count of heads in 5 flips flip5 0 1 2 3 4 5 0.0310 0.1545 0.3117 0.3166 0.1566 0.0296 > table(rbinom(10000, 5, .5)) / 10000 # shorter version of previous 2 lines 0 1 2 3 4 5 0.0304 0.1587 0.3087 0.3075 0.1634 0.0313 > qbinom(seq(0,1,.2), 50, .2) # approx. 0/.2/.4/.6/.8/1-quantiles in Binom(50,.2) distribution [1] 0 8 9 11 12 50 > binom.test(29, 200, .21) # inference on sample with 29 successes in 200 trials Exact binomial test data: 29 and 200 number of successes = 29, number of trials = 200, p-value = 0.02374 alternative hypothesis: true probability of success is not equal to 0.21 95 percent confidence interval: 0.09930862 0.20156150 sample estimates: probability of success 0.145 > prop.test(29, 200, .21) # inference on same sample, using normal approx. to binomial 1-sample proportions test with continuity correction data: 29 out of 200, null probability 0.21 X-squared = 4.7092, df = 1, p-value = 0.03 alternative hypothesis: true p is not equal to 0.21 95 percent confidence interval: 0.1007793 0.2032735 sample estimates: p 0.145 10 R Commands for MATH 143 Examples of usage pchisq(), qchisq(), chisq.test() > 1 - pchisq(3.1309, 5) # gives P-value associated with X-squared stat 3.1309 when df=5 [1] 0.679813 > pchisq(3.1309, df=5, lower.tail=F) # same as above [1] 0.679813 > qchisq(c(.001,.005,.01,.025,.05,.95,.975,.99,.995,.999), 2) # gives critical values like Table A [1] 0.002001001 0.010025084 0.020100672 0.050635616 0.102586589 5.991464547 7.377758908 [8] 9.210340372 10.596634733 13.815510558 > qchisq(c(.999,.995,.99,.975,.95,.05,.025,.01,.005,.001), 2, lower.tail=F) # same as above [1] 0.002001001 0.010025084 0.020100672 0.050635616 0.102586589 5.991464547 7.377758908 [8] 9.210340372 10.596634733 13.815510558 > observedCounts = c(35, 27, 33, 40, 47, 51) > claimedProbabilities = c(.13, .13, .14, .16, .24, .20) > chisq.test(observedCounts, p=claimedProbabilities) # goodness-of-fit test, assumes df = n-1 Chi-squared test for given probabilities data: observedCounts X-squared = 3.1309, df = 5, p-value = 0.6798 addmargins() > blood = read.csv("http://www.calvin.edu/~scofield/data/comma/blood.csv") > t = table(blood$Rh, blood$type) > addmargins(t) # to add both row/column totals A AB B O Sum Neg 6 1 2 7 16 Pos 34 3 9 38 84 Sum 40 4 11 45 100 > addmargins(t, 1) # to add only column totals A AB B O Neg 6 1 2 7 Pos 34 3 9 38 Sum 40 4 11 45 > addmargins(t, 2) # to add only row totals A AB B O Sum Neg 6 1 2 7 16 Pos 34 3 9 38 84 11 R Commands for MATH 143 Examples of usage prop.table() > smoke = matrix(c(51,43,22,92,28,21,68,22,9),ncol=3,byrow=TRUE) > colnames(smoke) = c("High","Low","Middle") > rownames(smoke) = c("current","former","never") > smoke = as.table(smoke) > smoke High Low Middle current 51 43 22 former 92 28 21 never 68 22 9 > summary(smoke) Number of cases in table: 356 Number of factors: 2 Test for independence of all factors: Chisq = 18.51, df = 4, p-value = 0.0009808 > prop.table(smoke) High Low Middle current 0.14325843 0.12078652 0.06179775 former 0.25842697 0.07865169 0.05898876 never 0.19101124 0.06179775 0.02528090 > prop.table(smoke, 1) High Low Middle current 0.4396552 0.3706897 0.1896552 former 0.6524823 0.1985816 0.1489362 never 0.6868687 0.2222222 0.0909091 > barplot(smoke,legend=T,beside=T,main='Smoking Status by SES') High Low Middle current former never Smoking Status by SES 0 20 40 60 80 12 R Commands for MATH 143 Examples of usage qt(), pt(), rt(), dt() > qt(c(.95, .975, .995), df=9) # critical values for 90, 95, 99% CIs for means [1] 1.833113 2.262157 3.249836 > pt(-2.1, 11) # gives Prob[T < -2.1] when df = 11 [1] 0.02980016 > tSamp = rt(50, 11) # takes random sample of size 50 from t-dist with 11 dfs > # code for comparing several t distributions to standard normal distribution > xs = seq(-5,5,.01) > plot(xs, dnorm(xs), type="l", lwd=2, col="black", ylab="pdf values", + main="Some t dists alongside standard normal curve") > lines(xs, dt(xs, 1), lwd=2, col="blue") > lines(xs, dt(xs, 4), lwd=2, col="red") > lines(xs, dt(xs, 10), lwd=2, col="green") > legend("topright",col=c("black","blue","red","green"), + legend=c("std. normal","t, df=1","t, df=4","t, df=10"), lty=1) −4 −2 0 2 4 0. 0 0. 2 0. 4 Some t dists alongside standard normal curve xs pd f v al ue s std. normal t, df=1 t, df=4 t, df=10 by() > data(warpbreaks) > by(warpbreaks$breaks, warpbreaks$tension, mean) warpbreaks$tension: L [1] 36.38889 --------------------------------------------------------------------------- warpbreaks$tension: M [1] 26.38889 --------------------------------------------------------------------------- warpbreaks$tension: H [1] 21.66667 15 R Commands for MATH 143 Examples of usage t.test() > data(sleep) > t.test(extra ~ group, data=sleep) # 2-sample t with group id column Welch Two Sample t-test data: extra by group t = -1.8608, df = 17.776, p-value = 0.0794 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -3.3654832 0.2054832 sample estimates: mean in group 1 mean in group 2 0.75 2.33 > sleepGrp1 = sleep$extra[sleep$group==1] > sleepGrp2 = sleep$extra[sleep$group==2] > t.test(sleepGrp1, sleepGrp2, conf.level=.99) # 2-sample t, data in separate vectors Welch Two Sample t-test data: sleepGrp1 and sleepGrp2 t = -1.8608, df = 17.776, p-value = 0.0794 alternative hypothesis: true difference in means is not equal to 0 99 percent confidence interval: -4.027633 0.867633 sample estimates: mean of x mean of y 0.75 2.33 qqnorm(), qqline() > qqnorm(precip, ylab = "Precipitation [in/yr] for 70 US cities", pch=19, cex=.6) > qqline(precip) # Is this line helpful? Is it the one you would eyeball? ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ●● ● ● ●● ● ●●● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● −2 −1 0 1 2 10 30 50 Normal Q−Q Plot Theoretical QuantilesP re ci pi ta tio n [in /y r] fo r 70 U S c iti es 16 R Commands for MATH 143 Examples of usage power.t.test() > power.t.test(n=20, delta=.1, sd=.4, sig.level=.05) # tells how much power at these settings Two-sample t test power calculation n = 20 delta = 0.1 sd = 0.4 sig.level = 0.05 power = 0.1171781 alternative = two.sided NOTE: n is number in *each* group > power.t.test(delta=.1, sd=.4, sig.level=.05, power=.8) # tells sample size needed for desired power Two-sample t test power calculation n = 252.1281 delta = 0.1 sd = 0.4 sig.level = 0.05 power = 0.8 alternative = two.sided NOTE: n is number in *each* group anova() require(lattice) require(abd) data(JetLagKnees) xyplot(shift ~ treatment, JetLagKnees, type=c('p','a'), col="navy", pch=19, cex=.5) anova( lm( shift ~ treatment, JetLagKnees ) ) Analysis of Variance Table Response: shift Df Sum Sq Mean Sq F value Pr(>F) treatment 2 7.2245 3.6122 7.2894 0.004472 ** Residuals 19 9.4153 0.4955 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 treatment sh ift −2 −1 0 control eyes knee ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● 17