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R stats cheatsheet

Summary statistics and general math

  • mean(x): calculate the mean of a vector x
    • mean(c(1,2,3,4,5))
    • mean(c(1,2,3,4,NA), na.rm = T): make sure to use na.rm = T if your sample has NA values
  • sd(x): calculate the standard deviation of a vector x
    • sd(c(1,2,3,4,5))
  • summary(x): calculate six number summary statistics of a vector x (min, q1, median, mean, q3, max)
    • summary(c(1,2,3,4,5))
  • table(x): counts the number of unique values of x
    • table(ice_cream$ice_cream) returns the number of students that like each of the three flavors of ice cream
  • sum(x): calculate sum of vector x
    • sum(c(1,2,3,4,5))
  • prod(x): calculate product of vector x
    • prod(c(4,5,2))
  • sqrt(x): calculate the sqare root of a value
    • sqrt(100)

Sampling from a distribution

  • seq(from, to, by): Generate a sequence of values
    • seq(1, 10, 1)
    • seq(10, 1000, 20)
  • rep(x, times = 1): generates a vector of x repeating times times
    • rep(1, 10)
  • set.seed(x): sets seed for random number generator. If you provide the same seed number before your analysis you will get the same 'random' sample each time.
    • set.seed(1753)
  • sample(x, size, replace = FALSE, prob = NULL): takes a sample of size from vector x with our without replacement
    • sample(seq(1,10,1), 3)
    • sample(seq(1,10,1), 3, replace = T)
    • Can use prob as a vector of probabilities for each element of x: sample(c("H", "T"), 10, replace = T, prob = c(0.6, 0.4))

Distributions

A note on distribution functions

  • "r" functions (i.e. rbinom()) generate a vector of random variables following said distribution type
    • rbinom(10, size = 1, prob = 0.5) would simulate 10 coin flips with 1 being heads and 0 being tails
  • "d" functions (i.e. dbinom()) returns the value of the probability density function of said distribution
    • dbinom(5, 10, 0.37) returns a single value: the probability of getting exactly 5 out of 10 successes when the probability of each success is 0.37
  • "p" functions (i.e. pbinom()) returns the value of the cumulative density function of said distribution
    • pbinom(5, 10, 0.37) returns a single value: the probability of getting five OR LESS successes when the probability of each success is 0.37. This could be thought of as the area under the curve and is commonly used to answer questions with a normal distribution
  • "q" functions (i.e. qbinom()) returns the value of the quantile (or z score) that gives you the given area under the curve. You can think of "q" and "p" functions as being inverses
    • qbinom(0.879, 10, 0.37) returns the value (5) where the area under the curve is 0.879. Note, the answer to pbinom(5,10,0.37) is 0.879.

Note: many of these functions have an optional argument lower.tail = TRUE/FALSE meant to calculate the area under the curve to the left (TRUE) or right (FALSE) of your value

More explanation and examples can be found here

Binomial distributions

*binom

  • rbinom(n, size, prob) - generate random variable
  • dbinom(x, size, prob) - calculate the probability of seeing a specific value
  • pbinom(q, size, prob) - calculate the cumulative probability of seeing at most a specific value (inverse of qbinom())
  • qbinom(p, size, prob) - calculate the specific value given a probability of at most that value (inverse of pbinom())

Normal distributions

*norm

  • rnorm(n, mean = 0, sd = 1) - generate random variable
  • dnorm(x, mean = 0, sd = 1) (rarely used)
  • pnorm(q, mean = 0, sd = 1) - calculate the probability (p-value) of a given quantile (z score) (inverse of qnorm())
  • qnorm(p, mean = 0, sd = 1) - calculate the quantile (z score) of a given probability (p-value) (inverse of pnorm())

Q-Q plots

# generate random normal data
data <- rnorm(100)
# plot Q-Q plot and line
qqnorm(data)
qqline(data)

Student's t distribution

*t

  • rt(n, df) - generate random variable
  • dt(x, df) (rarely used)
  • pt(q, df) - calculate the probability (p-value) of a given quantile (or t statistic) (inverse of qt())
  • qt(p, df) - calculate the quantile (t statistic) of a given probability (p-value) (inverse of pt())

Hypergeometric distribution

*hyper

  • rhyper(nn, m, n, k) - generate random variable (not often used)
  • dhyper(x, m, n, k) - calculate the probability of seeing a specific value
  • phyper(q, m, n, k) - calculate the cumulative probability (p-value) of a given value (inverse of qhyper())
  • qhyper(p, m, n, k) - calculate the value/quantile of a given probability (p-value) (inverse of phyper()) (not often used)

Chi-square distribution

*chisq

  • rchisq(n, df) - generate random variable (not often used)
  • dchisq(x, df) - calculate the probability of seeing a specific value
  • pchisq(q, df) - calculate the cumulative probability (p-value) of a given value (inverse of qchisq())
  • qchisq(p, df) - calculate the value/quantile of a given probability (p-value) (inverse of pchisq()) (not often used)

F distribution

*f

  • rf(n, df1, df2) - generate random variable (not often used)
  • df(x, df1, df2) - calculate the probability of seeing a specific value (not often used)
  • pf(q, df1, df2) - calculate the cumulative probability (p-value) of a given value (inverse of qf())
  • qf(p, df1, df2) - calculate the value/quantile of a given probability (p-value) (inverse of pf())

Hypothesis testing

Parametric

  • t.test(x, mu) - One sample t-test
  • t.test(x, y) - Two (independent) sample t-test
  • t.test(x, y, paired = T) - Paired (dependent) sample t-test
  • lm(y ~ x) - linear model of y given x
  • anova(lm(y ~ x)) - analysis of variance of y given x where x is categorical with several values
  • TukeyHSD(model) - Pairwise t-tests with adjusted p-values for multiple testing. Requires aov() as input.

Non-parametric

  • wilcox.test(x) - One sample Mann-Whitney (or Wilcoxon Rank Sum) test
  • wilcox.test(x, y) - Two (independent) sample Mann-Whitney (or Wilcoxon Rank Sum) test
  • wilcox.test(x, y, paired = T) - Paired (dependent) sample test (aka Wilcoxon signed-rank)
  • fisher.test(x, alternative = "greater") - Fisher's exact test. Use alternative = greater to test one-sided for enrichment. Can also use a non-directional alternative. x is a 2x2 contingency table
  • chisq.test(x, correct = F) - Chi-Square test for contingency tables and goodness-of-fit tests on count data. Default is correct = T which applies a continuity correction. To get the same answers as in doing it by hand, you need to use correct = F
  • mcnemar.test(x, correct = F) - Chi-square test for paired data (didn't really talk about in class, just a note in case it is useful in your research)
  • kruskal.test(y ~ x) - Non-parametric alternative for anova. Uses rank-sum method.

Note: most hypothesis tests have the optional argument alternative = c("two.sided", "less", "greater") for one-sided or two-sided tests

Choosing a test

Misc.

  • quantile(x, probs) - calculate the quantile of a sequence or distribution at a given probability (probs)) (*Note: quantile(rnorm(100), probs = 0.95) returns the 95% percentile of the random distribution).
  • shapiro.test(x) - test of non-normality. (P > 0.1 = normal distribution)
  • power.t.test(n, delta, sd, sig.level, power) - perform power test (provide 4/5 parameters and get the 5th)
  • p.adjust(p, method) - adjust p-values for multiple testing. Several differnt methods available including fdr and bonferroni
  • cor(x, y, method = c("pearson", "spearman", "kendall")) - calculate correlation between two variables. Defaults to pearson (parametric) but can choose spearman or kendall as non-parametric options
  • cor.test(x, y, method = c("pearson", "spearman", "kendall")) - test if the linear corrleation between two variables is different from zero. Defaults to pearson (parametric) but can choose spearman or kendall as non-parametric options
  • cov(x, y) - calculates covariance between two variables
  • summary(model) - returns summary statistics for a model (i.e. linear model lm())

Plotting

  • ggplot2 cheatsheet
  • Base R plotting cheatsheet
  • qqnorm(data) - Q-Q plot. Can also add qqline(data) to add the line to test for normality
  • plot(model, 0) - plot a linear model
  • plot(model, 1) - plot residuals from a model
  • ggplot2::qplot(x, y) - easy ggplot plots
  • interaction.plot(y, x1, x2) - plot interaction between two variables (x1 and x2) for two-way anova

Outside links: