Understanding the Basics of Statistical Tests and Data Visualization

In this article, we will delve into the world of statistical tests and data visualization using R. We’ll explore how to calculate and display results from various statistical tests such as mean, min, max, median, P-value, and Anderson-Darling test on a plot.

Loading Necessary Libraries

To begin with, we need to load the necessary libraries in R. These include dplyr for data manipulation and ggplot2 for creating visualizations.

library(dplyr)
library(ggplot2)

Generating Normally Distributed Data

Next, we generate a normally distributed dataset using set.seed() and rnorm(). The set.seed() function ensures reproducibility of results, while rnorm() generates random numbers according to the specified distribution.

set.seed(11235813)
x <- rnorm(2000, mean = 70.0, sd = 11.5)

Calculating Statistical Parameters

We then calculate the minimum, maximum, mean, median, and standard deviation of our dataset using min(), max(), mean(), median(), and sd() respectively.

xpars <- sapply(c("min", "max", "mean", "median", "sd"), do.call, list(x = x)) %>%
  round(., 2) %>% 
  paste(names(.), ., sep = " = ") %>% 
  paste(., collapse = "\n")

Creating the Dataset and Plot

Finally, we create a dataset containing our data and plot it using ggplot2.

data.frame(x = x) %>%
  ggplot(aes(x = x)) +
  geom_histogram(aes(y = ..density..), binwidth = 2, 
                 colour = "black", fill = "blue", alpha = .2) +
  geom_density(aes(y = ..density..), colour = "red", lty = 2) +
  annotate(
    "text",  
    x     = .9 * max(x), 
    y     = .9 * max(density(x)$y), 
    label = xpars, 
    hjust = 0
  ) +
  ggtitle("Normal에 대한 요약보고서") +
  theme_classic()

Understanding the Different Statistical Tests

Mean

The mean is a measure of central tendency that represents the average value of a dataset.

mean(x)

Min and Max

Min and max are used to find the smallest and largest values in a dataset, respectively.

min(x) ; max(x)

Median

The median is another measure of central tendency that represents the middle value in an ordered dataset.

median(x)

Standard Deviation (SD)

Standard deviation measures the amount of variation or dispersion from the mean value in a dataset.

sd(x)

P-value

A p-value is a statistical term used to describe the probability of observing a result as extreme or more extreme than the one observed, assuming that the null hypothesis is true. It’s often used in hypothesis testing.

p.value <- 2 * (1 - pnorm(abs(x - mean(x))))

Anderson-Darling Test

The Anderson-Darling test is a non-parametric goodness-of-fit test that compares the empirical distribution function of a sample to several hypothesized distributions.

ad.test(x, "pnorm", silent = TRUE)

Final Thoughts

In this article, we have covered how to calculate and display results from various statistical tests such as mean, min, max, median, P-value, and Anderson-Darling test on a plot using R. We also explored the basics of data visualization using ggplot2 and created an example dataset and plot.

By understanding these concepts, you’ll be better equipped to analyze and visualize your data effectively.

Example Use Cases

• Analyzing a large dataset: When working with big datasets, it’s essential to understand how to efficiently calculate statistical parameters like mean, min, max, median, P-value, and Anderson-Darling test results.
• Visualizing data trends: By visualizing these results on a plot, you can easily identify patterns and trends in your data.
• Comparing distributions: The Anderson-Darling test is useful for comparing the empirical distribution function of a sample to several hypothesized distributions.

By using R to calculate and display statistical parameters on a plot, you’ll be able to gain valuable insights into your data.

Last modified on 2023-09-17