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Inferential Statistics in R

Inferential statistics is a branch of statistics that allows us to make predictions or inferences about a population based on a sample of data. This tutorial will guide you through the basic concepts of inferential statistics and how to implement them in R. So, let's get started.

Understanding the Basics​

Before we begin, it's important to understand the terminology used in inferential statistics:

  1. Population: This is the entire set of individuals or items you're interested in studying.
  2. Sample: This is a subset of your population. It's usually impractical to study an entire population, so we collect data from a sample and use inferential statistics to make predictions about the population.
  3. Parameter: This is a numerical characteristic of a population. For example, the mean (average) or standard deviation.
  4. Statistic: This is a numerical characteristic of a sample. We use statistics to estimate parameters.

Installing and Loading Necessary Packages​

To perform inferential statistics in R, we'll need to install and load the following packages:

# Install packages
install.packages(c("ggplot2", "dplyr", "infer"))

# Load packages
library(ggplot2)
library(dplyr)
library(infer)

Hypothesis Testing​

Hypothesis testing is a statistical method that helps you make inferences about your population. It involves making an initial claim (null hypothesis), collecting data, and then testing this claim.

Let's do a simple hypothesis test:

# Load the gss_cat dataset from the infer package
data("gss_cat")

# Formulate a null hypothesis
null_hypothesis <- gss_cat %>%
  specify(response = hours, success = "full time") %>%
  hypothesize(null = "point", p = 0.5)

# Perform a hypothesis test
results <- null_hypothesis %>%
  generate(reps = 1000, type = "simulate") %>%
  calculate(stat = "prop")

# Get the p-value
p_value <- get_p_value(results, direction = "both")
p_value

The p-value is a probability that measures the strength of evidence against the null hypothesis. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

Confidence Intervals​

A confidence interval is a range of values, derived from a data sample, that is likely to contain the value of an unknown population parameter. The width of the confidence interval gives us an idea of how uncertain we are about the unknown parameter.

Let's calculate a confidence interval:

# Calculate a 95% confidence interval
confidence_interval <- gss_cat %>%
  specify(response = hours) %>%
  generate(reps = 1000, type = "bootstrap") %>%
  calculate(stat = "mean") %>%
  get_confidence_interval(level = 0.95)

confidence_interval

The output is the lower and upper bounds of the 95% confidence interval for the mean.

Conclusion​

Inferential statistics is a powerful tool for understanding the world around us. By using R, we can easily perform complex statistical analyses and make inferences about populations based on sample data. As with all statistical methods, it's important to use inferential statistics responsibly and understand the limitations and assumptions of your methods.

Remember, practice makes perfect. Keep exploring different datasets and testing your own hypotheses. Happy R-ing!