In R, you can perform various hypothesis tests, including t-tests, ANOVA, and chi-squared tests, among others. Here are some examples:
## t-tests
# One-sample t-test
x <- c(1, 2, 3, 4, 5)
t.test(x, mu = 3) # Test whether the population mean of x is equal to 3
# Independent two-sample t-test
y <- c(6, 7, 8, 9, 10)
t.test(x, y) # Test whether the means of x and y are equal
# Paired two-sample t-test
z <- c(2, 4, 6, 8, 10)
t.test(x, z, paired = TRUE) # Test whether the means of x and z are equal, but with paired observations
## ANOVA
# One-way ANOVA
data <- data.frame(
group = rep(c("A", "B", "C"), each = 5),
value = rnorm(15, mean = c(1, 2, 3), sd = 1)
)
summary(aov(value
group, data = data)) # Test whether the means of value differ among groups A, B, and C
# Two-way ANOVA
data <- data.frame(
group1 = rep(c("A", "B"), each = 10),
group2 = rep(c("X", "Y"), each = 5, times = 2),
value = rnorm(20, mean = c(1, 2), sd = 1)
)
summary(aov(value
group1 + group2, data = data)) # Test whether the means of value differ among groups defined by the combination of group1 and group2
## Chi-squared test
# Contingency table
data <- data.frame(
group1 = rep(c("A", "B"), each = 5),
group2 = rep(c("X", "Y"), times = 5),
value = c(2, 3, 4, 1, 2, 3, 1, 2, 3, 2)
)
table(data$group1, data$group2) # Create the contingency table
# Chi-squared test
chisq.test(table(data$group1, data$group2)) # Test whether there is a significant association between the groups defined by group1 and group2
In the code above, we first create data objects for each type of test. For t-tests, we use the `t.test()` function, specifying the null hypothesis using the `mu` argument (one-sample test) or comparing two samples using the two-sample t-test. For ANOVA, we use the `aov()` function, specifying the dependent variable and the independent variables asformulas. For the chi-squared test, we use the `table()` function to create a contingency table and then apply the `chisq.test()` function to test for the significance of the association between the groups.
Note that there are many other hypothesis tests available in R, depending on the type of data and research question. You can find more information on these functions in the R documentation or online tutorials and resources.