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7. Statistical Analysis in R

R was originally created for statistics — it remains one of the most powerful environments for statistical computing in 2026. This section covers the most important statistical techniques used in research, academia, pharma, finance, and data science.

7.1 Descriptive vs Inferential Statistics

Descriptive Statistics → Describe, summarize, and visualize the data you have (the sample).

Common functions in R:

• summary(), mean(), median(), sd(), var(), min(), max(), quantile()

• table(), prop.table() for categorical data

• skimr::skim() for detailed overview

Inferential Statistics → Use sample data to make generalizations / predictions about the population.

Common goals:

• Hypothesis testing (is there a real difference?)

• Confidence intervals (range where true value likely lies)

• Regression (model relationships)

Quick example comparison

R

# Descriptive summary(airquality$Ozone) mean(airquality$Ozone, na.rm = TRUE) sd(airquality$Ozone, na.rm = TRUE) # Inferential (example later) t.test(airquality$Ozone ~ airquality$Month == 5)

7.2 Hypothesis Testing (t-test, ANOVA, Chi-square)

Hypothesis testing helps decide whether observed differences are statistically significant.

One-sample t-test (compare sample mean to known value)

R

t.test(airquality$Ozone, mu = 30, na.action = na.omit) # p-value < 0.05 → reject null (mean ≠ 30)

Two-sample t-test (compare means of two groups)

R

t.test(Ozone ~ Month == 5, data = airquality, na.action = na.omit) # Welch's t-test by default (unequal variances)

Paired t-test (before-after, same subjects)

R

t.test(before, after, paired = TRUE)

ANOVA (compare means across 3+ groups)

R

anova_model <- aov(mpg ~ factor(cyl), data = mtcars) summary(anova_model) # Post-hoc test if significant TukeyHSD(anova_model)

Chi-square test (categorical association)

R

tbl <- table(mtcars$cyl, mtcars$gear) chisq.test(tbl)

Interpretation tip (2026):

• p < 0.05 → statistically significant (evidence against null hypothesis)

• p < 0.01 → very strong evidence

• Always report effect size + confidence interval (p-value alone is incomplete)

7.3 Correlation & Linear Regression

Correlation – measures linear relationship strength & direction

R

# Pearson correlation cor(mtcars$mpg, mtcars$hp) # -0.776 → strong negative # Spearman (rank-based, non-linear) cor(mtcars$mpg, mtcars$hp, method = "spearman") # Correlation matrix cor(mtcars[, c("mpg", "hp", "wt", "qsec")]) corrplot::corrplot(cor(mtcars), method = "color", type = "upper")

Simple Linear Regression

R

model <- lm(mpg ~ wt, data = mtcars) summary(model) # Look at: R-squared, p-value of coefficients, F-statistic # Plot with confidence intervals ggplot(mtcars, aes(x = wt, y = mpg)) + geom_point() + geom_smooth(method = "lm", color = "red") + labs(title = "Linear Regression: MPG vs Weight")

Multiple Linear Regression

R

multi_model <- lm(mpg ~ wt + hp + cyl, data = mtcars) summary(multi_model)

7.4 Logistic Regression & Generalized Linear Models

Logistic Regression – for binary outcome (0/1, yes/no, success/failure)

R

# Titanic survival example titanic <- titanic::titanic_train %>% mutate(Survived = factor(Survived)) log_model <- glm(Survived ~ Pclass + Sex + Age, data = titanic, family = binomial(link = "logit")) summary(log_model) # Odds ratios exp(coef(log_model))

Generalized Linear Models (GLM)

• family = gaussian → linear regression

• family = binomial → logistic

• family = poisson → count data

7.5 Non-parametric Tests & Post-hoc Analysis

Non-parametric – when data violates normality assumption

Wilcoxon rank-sum test (non-parametric t-test)

R

wilcox.test(mpg ~ vs, data = mtcars) # vs = engine type

Kruskal-Wallis (non-parametric ANOVA)

R

kruskal.test(mpg ~ factor(cyl), data = mtcars)

Post-hoc (after significant Kruskal-Wallis)

R

library(dunn.test) dunn.test(mtcars$mpg, mtcars$cyl, method = "bonferroni")

Mini Summary Project – Full Statistical Workflow

R

library(tidyverse) # Load data df <- read_csv("your_data.csv") # 1. Descriptive df %>% group_by(group) %>% summarise(mean = mean(outcome, na.rm = TRUE), sd = sd(outcome, na.rm = TRUE), n = n()) # 2. Visualization ggplot(df, aes(x = group, y = outcome)) + geom_boxplot() + geom_jitter(width = 0.2, alpha = 0.5) # 3. Test anova_result <- aov(outcome ~ group, data = df) summary(anova_result) # 4. Post-hoc if significant TukeyHSD(anova_result)

This completes the full Statistical Analysis in R section — now you can perform professional-grade statistical tests and interpret results correctly!

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