Module 2: Descriptive and Inferential Statistics

Measures of Variability

Range: You can calculate the range (the difference between the maximum and minimum values) of your data using the range() function. It returns a vector containing the minimum and maximum values.

range_result <- range(data_vector)

Variance and Standard Deviation: The var() function computes the variance, while the sd() function calculates the standard deviation. Both are used to assess the spread of data.

variance_result <- var(data_vector)

sd_result <- sd(data_vector)

Skewness and Kurtosis: You can use the moments package to calculate skewness and kurtosis. First, you need to install and load the package:

install.packages("moments")

library(moments)

Then, you can use skewness() for skewness and kurtosis() for kurtosis:

skewness_result <- skewness(data_vector)

kurtosis_result <- kurtosis(data_vector)

Graphical Displays

Histogram: To create a histogram, you can use the hist() function. It visualizes the distribution of your data by dividing it into bins. For example:

hist(data_vector, main = "Histogram of Data", xlab = "Values", ylab = "Frequency")

Boxplot: The boxplot() function is used to create boxplots, which provide information about the distribution's central tendency and spread, as well as any potential outliers.

boxplot(data_vector, main = "Boxplot of Data", ylab = "Values")

By following these steps and utilizing R's built-in functions and packages, you can effectively calculate and visualize descriptive statistics for your dataset. This provides a solid foundation for understanding your data's characteristics and preparing it for further analysis.

Inferential Statistics in R: Unlocking the Secrets of Data Inference

Inferential statistics elevate your analytical abilities to the next level by enabling data-driven decisions and hypothesis testing. Here's what you can expect in this section:

Hypothesis Testing: Learn the foundations of hypothesis testing in R. You'll understand the logic behind hypothesis testing, the significance level (alpha), and the p-value. We will explore common hypothesis tests, including the t-test and chi-square test, and walk through the step-by-step process of conducting these tests.
Confidence Intervals: Discover the power of confidence intervals in quantifying the uncertainty surrounding point estimates. You will not only learn how to calculate confidence intervals for means and proportions but also how to interpret them in a real-world context.
p-Values Unveiled: Unravel the mysteries of p-values, a vital component in hypothesis testing. We will discuss their meaning, interpretation, and the role they play in determining the statistical significance of results.

Inferential statistics in R is a crucial part of data analysis, enabling data-driven decision-making and hypothesis testing. Here's a step-by-step guide on how to perform hypothesis testing, calculate confidence intervals, and understand the significance of p-values in R:

» 1. Hypothesis Testing

Logic of Hypothesis Testing: The first step in hypothesis testing is to understand the logic behind it. You start with a null hypothesis (H0), which represents a default assumption, and an alternative hypothesis (Ha), which represents what you want to test. For example, H0: μ = 100 (population mean is 100) vs. Ha: μ ≠ 100 (population mean is not 100).

Choosing the Significance Level (Alpha): The significance level, denoted as alpha (α), is the probability of making a Type I error (incorrectly rejecting a true null hypothesis). Common values for alpha are 0.05 or 0.01. You can set alpha using alpha <- 0.05.

Performing Hypothesis Tests: R provides various functions for hypothesis testing, such as t.test() for t-tests and chisq.test() for chi-square tests. For a two-sample t-test, you can use:

t_test_result <- t.test(x, y, alternative = "two.sided")

» 2. Confidence Intervals

Calculating Confidence Intervals: Confidence intervals help quantify the uncertainty around point estimates. You can calculate a confidence interval for the mean using the t.test() function. For a 95% confidence interval:

ci_result <- t.test(data_vector, conf.level = 0.95)$conf.int

Interpreting Confidence Intervals: A 95% confidence interval for a mean, say (8.5, 9.5), means that if you were to sample from the population many times and calculate intervals, approximately 95% of those intervals would contain the true population mean.

» 3. P-Values Unveiled

Understanding P-Values: P-values are essential in hypothesis testing. They quantify the strength of evidence against the null hypothesis. Smaller p-values indicate stronger evidence against the null. In R, p-values are typically calculated and returned by hypothesis testing functions.

Interpreting P-Values: If your p-value is less than alpha (α), you reject the null hypothesis. For example, if p < 0.05 (with α = 0.05), you have evidence to reject H0. If p > α, you fail to reject H0. Keep in mind that p-values do not prove a null hypothesis; they provide evidence for or against it.

By following these steps and using R's built-in functions for hypothesis testing, confidence intervals, and p-value calculations, you can unlock the secrets of inferential statistics. This allows you to make data-driven decisions, draw meaningful conclusions, and test hypotheses based on your data analysis in R.