# Parametric and Non-Parametric Tests in R

R is a versatile and powerful programming language commonly used for data analysis and statistical computing. It provides a wide range of tools and packages for conducting various types of statistical tests. Two common types of tests are parametric tests and non-parametric tests. In this article, we will explore these two categories of tests and understand how to perform them in R.

## Parametric Tests

Parametric tests make assumptions about the distribution or shape of the underlying data. These tests are often used when the data follows a normal distribution. Some examples of parametric tests are t-tests, ANOVA, and linear regression.

To perform parametric tests in R, we can use built-in functions from the `stats` package. Let's take a look at two commonly used parametric tests:

### 1. t-test

The t-test is used to compare the means of two independent groups. It assumes that the data in each group follows a normal distribution. In R, we can perform a t-test using the `t.test()` function. Here's an example:

``````# Generate two random samples
group1 <- rnorm(50, mean = 5, sd = 2)
group2 <- rnorm(50, mean = 6, sd = 2)

# Perform independent t-test
result <- t.test(group1, group2)
print(result)``````

### 2. ANOVA

ANOVA (Analysis of Variance) is used to compare the means of multiple groups simultaneously. It assumes that the data in each group follows a normal distribution and has equal variances. In R, we can perform an ANOVA using the `aov()` function. Here's an example:

``````# Generate three random samples
group1 <- rnorm(50, mean = 5, sd = 2)
group2 <- rnorm(50, mean = 6, sd = 2)
group3 <- rnorm(50, mean = 7, sd = 2)

# Perform ANOVA
result <- aov(c(group1, group2, group3) ~ c(rep("G1", 50), rep("G2", 50), rep("G3", 50)))
summary(result)``````

## Non-Parametric Tests

Non-parametric tests are used when the data does not meet the assumptions of parametric tests, such as having a normal distribution. These tests are often based on rankings or other non-parametric measures. Some examples of non-parametric tests include the Mann-Whitney U test, Kruskal-Wallis test, and Wilcoxon signed-rank test.

To perform non-parametric tests in R, we can use functions from the `stats` and `coin` packages. Here's how to conduct two commonly used non-parametric tests:

### 1. Mann-Whitney U test

The Mann-Whitney U test is used to compare the medians of two independent groups. It does not assume any specific distribution of the data. In R, we can perform a Mann-Whitney U test using the `wilcox.test()` function. Here's an example:

``````# Generate two random samples
group1 <- rnorm(50, mean = 5, sd = 2)
group2 <- rnorm(50, mean = 6, sd = 2)

# Perform Mann-Whitney U test
result <- wilcox.test(group1, group2)
print(result)``````

### 2. Kruskal-Wallis test

The Kruskal-Wallis test is used to compare the medians of multiple independent groups. Similar to the Mann-Whitney U test, it does not assume any specific distribution of the data. In R, we can perform a Kruskal-Wallis test using the `kruskal.test()` function. Here's an example:

``````# Generate three random samples
group1 <- rnorm(50, mean = 5, sd = 2)
group2 <- rnorm(50, mean = 6, sd = 2)
group3 <- rnorm(50, mean = 7, sd = 2)

# Perform Kruskal-Wallis test
result <- kruskal.test(list(group1, group2, group3))
print(result)``````

## Conclusion

Parametric and non-parametric tests are valuable tools in statistical analysis. R provides numerous functions and packages to perform these tests accurately and efficiently. By understanding when to use each type of test and implementing them in R, you can make robust statistical inferences and draw meaningful conclusions from your data.