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T-Tests and ANOVA
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T-tests and ANOVA are statistical methods used to compare the means of groups and determine whether the differences between them are statistically significant. These tests are commonly used in data analysis to evaluate hypotheses about group averages.
A t-test is used when comparing the means of one or two groups. It helps determine whether the difference between the group means is significant or occurred by chance.
| Type of T-Test | Purpose | Example |
|---|---|---|
| One-sample t-test | Compares sample mean to a known value | Average height vs expected height |
| Independent t-test | Compares means of two different groups | Test scores of two classes |
| Paired t-test | Compares means of the same group at two times | Before and after treatment |
In R, a t-test can be performed using the t.test() function.
# Independent t-test example
group1 <- c(20, 22, 19, 24, 21)
group2 <- c(30, 28, 32, 29, 31)
t.test(group1, group2)ANOVA, which stands for Analysis of Variance, is used when comparing the means of three or more groups. Instead of performing multiple t-tests, ANOVA evaluates all group means at once to determine whether at least one group mean is significantly different from the others.
| Test | Used For |
|---|---|
| T-test | Comparing means of one or two groups |
| ANOVA | Comparing means of three or more groups |
In R, ANOVA can be performed using the aov() function.
# Sample dataset
scores <- data.frame(
marks = c(78, 85, 88, 92, 76, 81, 95, 89, 84),
group = factor(c("A", "A", "A", "B", "B", "B", "C", "C", "C"))
)
# Perform ANOVA
anova_result <- aov(marks ~ group, data = scores)
summary(anova_result)The ANOVA output provides an F-statistic and a p-value. If the p-value is less than the significance level, it indicates that at least one group mean is significantly different.
T-tests and ANOVA are essential tools in statistical analysis. They help compare group means, test hypotheses, and support data-driven decision-making.
