Data Visualization in R

Study Notes

Introduction

Data visualization is an essential step in data analysis, allowing us to understand and communicate insights effectively
R provides a range of data visualization tools, including base graphics, lattice, and ggplot2

Types of Plots

Scatter Plots: visualize relationships between two continuous variables
- Example: plot(x, y) or ggplot(data, aes(x, y)) + geom_point()
Bar Charts: compare categorical data across different groups
- Example: barplot(table(x)) or ggplot(data, aes(x, fill = group)) + geom_bar()
Histograms: visualize distribution of a single continuous variable
- Example: hist(x, main = "Histogram of x") or ggplot(data, aes(x)) + geom_histogram()
Boxplots: compare distribution of a continuous variable across different groups
- Example: boxplot(x ~ group) or ggplot(data, aes(x, y)) + geom_boxplot()

Introduction

Hypothesis testing is a statistical technique used to make inferences about a population based on a sample of data
R provides a range of functions for conducting hypothesis tests, including t.test(), wilcox.test(), and prop.test()

Types of Tests

One-Sample T-Test: tests whether the mean of a sample is equal to a known population mean
- Example: t.test(x, mu = 0)
Two-Sample T-Test: tests whether the means of two samples are equal
- Example: t.test(x ~ group)
Wilcoxon Rank-Sum Test: tests whether the distributions of two samples are equal
- Example: wilcox.test(x ~ group)
Proportion Test: tests whether the proportion of successes in a sample is equal to a known population proportion
- Example: prop.test(x, n, p = 0.5)

Interpreting Test Results

P-Value: the probability of observing the test statistic (or a more extreme value) assuming the null hypothesis is true
Alpha Level: the maximum probability of rejecting the null hypothesis when it is actually true (usually set to 0.05)
Reject or Fail to Reject the Null Hypothesis: based on the p-value and alpha level, decide whether to reject the null hypothesis in favor of the alternative hypothesis

Data visualization is a crucial step in data analysis, enabling effective understanding and communication of insights.
R offers various data visualization tools, including base graphics, lattice, and ggplot2.

Scatter Plots: visualize relationships between two continuous variables using plot(x, y) or ggplot(data, aes(x, y)) + geom_point().
Bar Charts: compare categorical data across different groups using barplot(table(x)) or ggplot(data, aes(x, fill = group)) + geom_bar().
Histograms: visualize the distribution of a single continuous variable using hist(x, main = "Histogram of x") or ggplot(data, aes(x)) + geom_histogram().
Boxplots: compare the distribution of a continuous variable across different groups using boxplot(x ~ group) or ggplot(data, aes(x, y)) + geom_boxplot().

Hypothesis testing is a statistical technique used to make inferences about a population based on a sample of data.
R provides various functions for conducting hypothesis tests, including t.test(), wilcox.test(), and prop.test().

One-Sample T-Test: tests whether the mean of a sample is equal to a known population mean using t.test(x, mu = 0).
Two-Sample T-Test: tests whether the means of two samples are equal using t.test(x ~ group).
Wilcoxon Rank-Sum Test: tests whether the distributions of two samples are equal using wilcox.test(x ~ group).
Proportion Test: tests whether the proportion of successes in a sample is equal to a known population proportion using prop.test(x, n, p = 0.5).

P-Value: the probability of observing the test statistic (or a more extreme value) assuming the null hypothesis is true.
Alpha Level: the maximum probability of rejecting the null hypothesis when it is actually true (usually set to 0.05).
Reject or Fail to Reject the Null Hypothesis: based on the p-value and alpha level, decide whether to reject the null hypothesis in favor of the alternative hypothesis.