Statistical Analysis in R

R was built by statisticians, for statisticians — the language ships with a stats package in base R that covers everything from descriptive summaries to hypothesis tests and linear models without installing a single extra package. Because R is vectorized, functions like mean(), sd(), and t.test() operate directly on whole columns of a data frame, so you rarely need explicit loops to summarize data. This design lets an analyst move from raw data to a defensible statistical conclusion in a handful of lines, which is why R remains the default tool in biostatistics, econometrics, and academic research.

The summary() function on a numeric vector or data frame returns the minimum, first quartile, median, mean, third quartile, and maximum in a single call, giving a fast five-number-plus-mean overview of any variable. Pairing this with sd() for spread, IQR() for the interquartile range, and hist() or density() for visual shape lets you check skewness and detect outliers before running any formal test — a step many beginners skip and later regret when a t-test assumption is silently violated.

R's distribution functions follow a consistent d, p, q, r prefix convention for every named distribution: dnorm() gives the density at a point, pnorm() gives the cumulative probability, qnorm() gives the quantile for a given probability, and rnorm() generates random draws. The same pattern applies to dbinom/pbinom/qbinom/rbinom for the binomial, dpois for Poisson, and dt/pt for the t-distribution used internally by t.test(), so once you learn the convention for one distribution you effectively know it for all of them.

The t.test() function handles one-sample, two-sample, and paired t-tests through its x, y, and paired arguments, returning a t-statistic, degrees of freedom, p-value, and 95% confidence interval in one object. A p-value below your chosen significance level, typically 0.05, suggests the observed difference is unlikely under the null hypothesis of no effect, but R also reports the confidence interval, which is often more informative because it shows the plausible range and direction of the effect rather than a single accept/reject verdict.

When comparing means across three or more groups, aov(response ~ group, data = df) runs an analysis of variance and summary() on the resulting object reports an F-statistic and p-value testing whether any group mean differs; a significant result is typically followed by TukeyHSD() to find which specific pairs differ. For categorical data, chisq.test() takes a contingency table built with table() and tests whether two categorical variables are independent, which is the standard tool for questions like whether purchase rate differs by region.

cor(x, y) computes Pearson's correlation coefficient by default, cor.test() adds a significance test and confidence interval, and switching method = "spearman" gives a rank-based correlation robust to non-linear monotonic relationships. For prediction, lm(y ~ x1 + x2, data = df) fits an ordinary least squares model, and summary(fit) reports each coefficient's estimate, standard error, t-value, and p-value alongside the model's R-squared, which measures the proportion of variance in the outcome explained by the predictors.