Implement Z-scores to Percentiles in R
To convert Z-scores to percentiles in R ‘pnorm()’ function is use, which calculates quantiles from a normal distribution.
The formula is
percentile=pnorm(Z_Score)*100
Convert Z-scores to percentiles first need to calculate the Z-scores for your data points and then convert these Z-scores to percentiles.
Single Z-score Conversion
# Define a single Z-score
z_score <- 1.75
# Convert the Z-score to percentile
percentile <- pnorm(z_score) * 100
# Display the result
cat("Z-score:", z_score, "=> Percentile:", percentile, "\n")
Output:
Z-score: 1.75 => Percentile: 95.99408
In this scenario, we have a Z-score of 1.75, and we convert it to its corresponding percentile using the pnorm() function. The output shows the Z-score alongside its percentile.
Multiple Z-scores Conversion
# Define a vector of Z-scores
z_scores <- c(-2.0, -1.0, 0.0, 1.0, 2.0)
# Convert each Z-score to percentile
percentiles <- pnorm(z_scores) * 100
# Display the results
for (i in 1:length(z_scores)) {
cat("Z-score:", z_scores[i], "=> Percentile:", percentiles[i], "\n")
}
Output:
Z-score: -2 => Percentile: 2.275013
Z-score: -1 => Percentile: 15.86553
Z-score: 0 => Percentile: 50
Z-score: 1 => Percentile: 84.13447
Z-score: 2 => Percentile: 97.72499
In this scenario, we have a vector of Z-scores ranging from -2.0 to 2.0. We use a loop to convert each Z-score to its corresponding percentile and then display the outputs.
Negative Z-score Conversion
# Define a negative Z-score
z_score <- -1.25
# Convert the Z-score to percentile
percentile <- pnorm(z_score) * 100
# Display the result
cat("Z-score:", z_score, "=> Percentile:", percentile, "\n")
Output:
Z-score: -1.25 => Percentile: 10.56498
In this scenario, we have a negative Z-score (-1.25), and we convert it to its percentile using the pnorm() function. The output percentile indicates the relative position of the data point within the distribution.
How to Convert Between Z-Scores and Percentiles in R
In statistical analysis, converting between Z-scores and percentiles helps researchers understand data distribution clearly. R, a powerful programming language, simplifies this conversion process, making it accessible to analysts. This guide offers a simple walkthrough of how to perform these conversions in R Programming Language enabling users to interpret data effectively and make informed decisions.
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