Here's a selection of statistical functions that come with the standard R installation. You'll find many others in R packages. R provides the
shiny package and the
shinydashboard package for developing interactive applications. Here are selected functions from these packages:
Central Tendency and Variability
| 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 |
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 0th, 25th, 50th, 75th, and 100th percentiles (i.e, the quartiles) of the numbers in vector x. (That’s not a misprint: quantile(x) returns the quartiles of x.) |
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. |
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) |
Multiple regression analysis with the numbers in vector y as the dependent variable and the numbers in vectors x and z as the independent variables. Data are in data frame d. |
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)
