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R provides a wide array of functions to help you with statistical analysis with R—from simple statistics to complex analyses. Several statistical functions are built into R and R packages. R statistical functions fall into several categories including central tendency and variability, relative standing, t-tests, analysis of variance and regression analysis.

Base R Statistical Functions for Central Tendency and Variability

Here’s a selection of statistical functions having to do with central tendency and variability that come with the standard R installation. You’ll find many others in R packages.

Each of these statistical functions consists of a function name immediately followed by parentheses, such as mean(), and var(). Inside the parentheses are the arguments. In this context, “argument” doesn’t mean “disagreement,” “confrontation,” or anything like that. It’s just the math term for whatever a function operates on.

Function	What it Calculates
`mean(x)`	Mean of the numbers in vector x.
`median(x)`	Median of the numbers in vector x
`var(x)`	Estimated variance of the population from which the numbers in vector x are sampled
`sd(x)`	Estimated standard deviation of the population from which the numbers in vector x are sampled
`scale(x)`	Standard scores (z-scores) for the numbers in vector x

Base R Statistical Functions for Relative Standing

Here’s a selection of R statistical functions having to do with relative standing.

Function What it Calculates

sort(x) The numbers in vector x in increasing order

sort(x)[n] The nth smallest number in vector x

rank(x) Ranks of the numbers (in increasing order) in vector x

rank(-x) Ranks of the numbers (in decreasing order) in vector x

rank(x, ties.method= “average”) Ranks of the numbers (in increasing order) in vector x, with tied numbers given the average of the ranks that the ties would have attained

rank(x, ties.method= “min”)

Ranks of the numbers (in increasing order) in vector x, with tied numbers given the minimum of the ranks that the ties would have attained

rank(x, ties.method = “max”) Ranks of the numbers (in increasing order) in vector x, with tied numbers given the maximum of the ranks that the ties would have attained

quantile(x) The 0^th, 25^th, 50^th, 75^th, and 100^th percentiles (i.e, the quartiles) of the numbers in vector x. (That’s not a misprint: quantile(x) returns the quartiles of x.)

T-Test Functions for Statistical Analysis with R

Here’s a selection of R statistical functions having to do with t-tests.

Function	What it Calculates
`t.test(x,mu=n, alternative = “two.sided”)`	Two-tailed t-test that the mean of the numbers in vector x is different from n.
`t.test(x,mu=n, alternative = “greater”)`	One-tailed t-test that the mean of the numbers in vector x is greater than n.
`t.test(x,mu=n, alternative = “less”)`	One-tailed t-test that the mean of the numbers in vector x is less than n.
`t.test(x,y,mu=0, var.equal = TRUE, alternative = “two.sided”)`	Two-tailed t-test that the mean of the numbers in vector x is different from the mean of the numbers in vector y. The variances in the two vectors are assumed to be equal.
`t.test(x,y,mu=0, alternative = “two.sided”, paired = TRUE)`	Two-tailed t-test that the mean of the numbers in vector x is different from the mean of the numbers in vector y. The vectors represent matched samples.

ANOVA and Regression Analysis Functions for Statistical Analysis with R

Here’s a selection of R statistical functions having to do with Analysis of Variance (ANOVA) and correlation and regression.

When you carry out an ANOVA or a regression analysis, store the analysis in a list. For example,

a <- lm(y~x, data = d)

Then, to see the tabled results, use the summary() function:

summary(a)

**Analysis of Variance (ANOVA)**
Function	What it Calculates
`aov(y~x, data = d)`	Single-factor ANOVA, with the numbers in vector y as the dependent variable and the elements of vector x as the levels of the independent variable. The data are in data frame d.
`aov(y~x + Error(w/x), data = d)`	Repeated Measures ANOVA, with the numbers in vector y as the dependent variable and the elements in vector x as the levels of an independent variable. Error(w/x) indicates that each element in vector w experiences all the levels of x (i.e., x is a repeated measure). The data are in data frame d.
`aov(y~x*z, data = d)`	Two-factor ANOVA, with the numbers in vector y as the dependent variable and the elements of vectors x and z as the levels of the two independent variables. The data are in data frame d.
`aov(y~x*z + Error(w/z), data = d)`	Mixed ANOVA, with the numbers in vector z as the dependent variable and the elements of vectors x and y as the levels of the two independent variables. Error(w/z) indicates that each element in vector w experiences all the levels of z (i.e., z is a repeated measure). The data are in data frame d.

**Correlation and Regression**
Function	What it Calculates
`cor(x,y)`	Correlation coefficient between the numbers in vector x and the numbers in vector y
`cor.test(x,y)`	Correlation coefficient between the numbers in vector x and the numbers in vector y, along with a t-test of the significance of the correlation coefficient.
`lm(y~x, data = d)`	Linear regression analysis with the numbers in vector y as the dependent variable and the numbers in vector x as the independent variable. Data are in data frame d.
`coefficients(a)`	Slope and intercept of linear regression model a.
`confint(a)`	Confidence intervals of the slope and intercept of linear regression model a
`lm(y~x+z, data = d)`

Statistical Packages For Mac