Recreating Minitab Normal Probability Plot with R

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In this article, we will explore how to recreate a normal probability plot in R using the probplot function from the MASS package. We will also cover how to add confidence interval bands around the plot and discuss the differences between base graphics and ggplot2.

Understanding Normal Probability Plots

A normal probability plot is a graphical tool used to determine if a dataset follows a normal distribution. The plot displays the data points on a graph with their corresponding quantiles (25th, 50th, and 75th percentiles) marked as horizontal lines. If the data follows a normal distribution, the points should approximately follow a straight line through these quantiles.

Using the probplot Function

The probplot function in R is used to create a normal probability plot. This function takes two arguments: the dataset and the desired number of quantiles.

# Load the MASS package
library(MASS)

# Create a normal probability plot of the dataset x
probplot(x, main = "Normal Probability Plot")

Adding Confidence Interval Bands

To add confidence interval bands around the plot, we can use the ggplot2 package. We will create a new data frame with the quantiles and then add these values to the plot.

# Load the ggplot2 library
library(ggplot2)

# Create a dataframe with the quantiles
quantiles <- data.frame(
  x = c(0.25, 0.5, 0.75),
  y = c(qnorm(0.25), qnorm(0.5), qnorm(0.75))
)

# Create a new data frame with the dataset and quantiles
df <- data.frame(x = x, y = x, q = rep(c(0.25, 0.5, 0.75), each = length(x)))

# Create a ggplot of the dataset with confidence interval bands
ggplot(df, aes(x = x, y = y)) + geom_point() + 
  geom_abline(intercept = int, slope = slope) + 
  geom_line(aes(y = q), color = "red") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5))

Using Base Graphics

To create a normal probability plot using base graphics, we can use the following code:

# Create a new data frame with the dataset and quantiles
df <- data.frame(x = x, y = x, q = rep(c(0.25, 0.5, 0.75), each = length(x)))

# Create a plot of the dataset with confidence interval bands
plot(df$x, df$y)
abline(df$q, lty = "dashed")

Calculating Quantiles and Slope

The quantiles are calculated using the qnorm function in R. The slope is calculated by taking the difference between the 75th percentile and the 25th percentile divided by the difference between the 75th and 25th percentiles.

# Calculate the quantiles
xl <- quantile(x, c(0.25, 0.5, 0.75))
yl <- qnorm(c(0.25, 0.5, 0.75))

# Calculate the slope
slope <- diff(yl)/diff(xl)

# Calculate the intercept
int <- yl[1] - slope * xl[1]

Conclusion

In this article, we have explored how to recreate a normal probability plot in R using the probplot function from the MASS package. We have also covered how to add confidence interval bands around the plot and discussed the differences between base graphics and ggplot2.

The final answer is not applicable here as it’s not a numerical problem but rather an explanation of a concept with code implementation.

Last modified on 2024-05-21