# pchisq Function In R: The Chi-Square Statistic

Today, we will learn how to use the qchisq function to calculate the p-values of a chi-squared statistic in the R programming language. See the syntax and example below to understand it better.

## What is the pchisq Function in R?

In R, the pchisq function is used to compute the probability that a random variable, which follows a chi-squared distribution, will be less than or equal to a given value.

Below is the basic syntax for using the pchisq function in R

### pchisq Function in R: The Syntax

Parameters

• q: The value for which you want to compute the probability.
• df: is the degrees of freedom.
• lower.tail: is a logical value that determines whether to calculate the probability that the random variable is more significant than q (FALSE) or less than q (TRUE) (FALSE).

## How to use the pchisq Function in R?

Now, we will use the pchisq function in R to compute the probability that a chi-squared random variable with 5 degrees of freedom is less than or equal to 4 as follows:

# Calculate the p-value for the Chi-Square statistic
res <- pchisq(q = 4, df = 5)

# View a result
res

Output

[1] 0.450584

If you want to calculate the probability to the right of in the Chi-Square distribution, see the code example below

# Calculate the p-value for the Chi-Square statistic
res <- pchisq(q = 4, df = 5, lower.tail = FALSE)

# View a result
res

Output

[1] 0.549416

The pchisq function can also be used to get the p-values for a vector of test statistics with the q arguments. For instance:

First, we will create a vector as follows

# Create a vector
set.seed(100)
x <- sample(10)

# View a vector
x

Output

[1] 10  7  6  3  1  2  5  9  4  8

Then, we can use the pchisq function to calculate p-values for the vector above. Check out the code example below

# Create a vector
set.seed(100)
x <- sample(10)

# Calculate the p-value for the Chi-Squared statistic
res <- pchisq(x, df = 5)
res

Output

[1] 0.92476475 0.77935969 0.69378108 0.30001416 0.03743423 0.15085496
[7] 0.58411981 0.89093584 0.45058405 0.84376437

The output above can be seen by charting it as shown below.

# Create a vector
set.seed(100)
x <- sample(10)

# Calculate the p-value for the Chi-Squared statistic
res <- pchisq(x, df = 5)

# Plot a chart
plot(res,
type = "l",
main = "The Chi-Squared",
xlab = "The X-Value", ylab = "The P-value"
)

Output

## Summary

In conclusion, this article helps you know how to use the pchisq function in r to calculate Chi-Squared statistics. If you have any questions, do write a comment below.

Have a great day!

Posted in R