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R

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Useful Functions

  • .cor(x,y,method="pearson")
    • default method = pearson
      • other methods: “spearman” and “kendall”
  • .aggregate(x~y, data=, FUN=summary)
    • splits data into subsets, computes summary statistics for each, returns result in a convenient form
    • x grouped by y
      • x: var you want to summarise
      • y: grouping var
    • summary gives Min, Q1, Median, Mean, 3Q, Max
    • can also use FUN=sd, FUN=mean, FUN=Skew, etc.

Hypothesis Tests (L7)

# Independent two-sample t-test
t.test(x, y, var.equal=TRUE)     # pooled variance
t.test(x, y, var.equal=FALSE)    # Welch's (unequal variance)
 
# Paired t-test
t.test(before, after, paired=TRUE)
 
# Extract from result
t_out$statistic; t_out$p.value; t_out$conf.int
 
# Wilcoxon Rank-Sum (non-parametric, independent)
wilcox.test(x, y)
 
# Wilcoxon Signed-Rank (non-parametric, paired)
wilcox.test(before, after, paired=TRUE, exact=FALSE)
 
# Normality
shapiro.test(x)
qqnorm(x); qqline(x)

Skewness & Kurtosis (L7, DescTools)

library(DescTools)
aggregate(viscera ~ gender, data=abl, Skew, method=1)
aggregate(viscera ~ gender, data=abl, Kurt, method=1)
# method=1 → method-of-moments estimator (matches lectures)

ANOVA (L8)

# Fit model and get ANOVA table
heifers_lm <- lm(org ~ type, data=heifers)
anova(heifers_lm)      # SS breakdown + F-test
summary(heifers_lm)    # coefficient estimates + t-tests
 
# Factor levels matter — set them explicitly
heifers$type <- factor(heifers$type, levels=c("Control", "Alfacyp", ...))
 
# Residuals
r1 <- residuals(heifers_lm)
hist(r1); qqnorm(r1); qqline(r1)
 
# Tukey HSD (all pairwise, valid post-hoc)
TukeyHSD(aov(heifers_lm), ordered=TRUE)
 
# Kruskal-Wallis (non-parametric ANOVA)
kruskal.test(heifers$org, heifers$type)
 
# t-quantile for CI construction
qt(0.025, df, lower.tail=FALSE)   # returns positive critical value

Linear Regression (L9)

lm_out <- lm(Flow ~ Water, data=concrete)
lm_out <- lm(Flow ~ Water + Slag, data=concrete)         # multiple
lm_out <- lm(registered ~ casual + workingday, data=bike2)  # indicator var
lm_out <- lm(registered ~ casual * workingday, data=bike2)  # interaction
 
summary(lm_out)         # coefficients, R², F-test
anova(lm_out)           # SS decomposition
confint(lm_out)         # 95% CI for all β's
 
# Predictions with CI bands
new_df <- data.frame(Water = seq(160, 240, by=5))
conf_intervals <- predict(lm_out, new_df, interval="conf")
# Returns matrix with columns: fit, lwr, upr
 
# Residual diagnostics
r_s <- rstandard(lm_out)      # standardised residuals
fitted(lm_out)                  # fitted values
influence.measures(lm_out)      # leverage, Cook's distance etc.

Simulation (L10)

set.seed(2137)    # set seed for reproducibility
 
# Random variable generation
rnorm(n, mean=0, sd=1)
runif(n, min=0, max=1)
rgamma(n, shape=2, rate=3)       # or scale=1/rate
rpois(n, lambda=1.3)
rbinom(n, size=2, prob=0.3)
 
# Replicate a function call n times
replicate(2000, generate_one_test())
 
# Apply with type safety (faster than sapply for known output type)
vapply(1:2000, function(x) generate_one_test(), 1L)
 
# Vectorised if-else
ifelse(X >= 11000, 11000, floor(X) + (11000 - floor(X))*(-0.25))

Bootstrap (L10, boot library)

library(boot)
 
stat_fn <- function(d, i) {
  mean(d[i], trim=0.1)    # i = bootstrap indices
}
boot_out <- boot(data, stat_fn, R=1999, stype="i")
boot.ci(boot.out=boot_out, type=c("perc", "bca"))
# perc: percentile interval
# bca: bias-corrected and accelerated (more accurate)

Full reference: R Glossary

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