Descriptive statistics, inference and regression
Describe the distribution before choosing a summary or inferential model. Means and standard deviations can be influenced by extreme observations, while medians and interquartile ranges summarize different aspects of the data. A sample variance uses deviations from the sample mean and normally divides their squared sum by n−1. A standard error describes sampling variability of an estimator rather than the spread of individual observations.
A confidence procedure has a long-run coverage interpretation under its assumptions. A p-value measures how unusual the observed statistic or a more extreme one would be under the specified null model. It is not the probability that the null hypothesis is true. Report effect estimates, uncertainty and substantive importance as well as a threshold decision.
Match the method to the question and design. Paired observations require analysis of the pairing; independent groups require a method appropriate to independent data. A chi-square association test concerns categorical counts. A regression slope describes the fitted change in an outcome per unit of a predictor, with residuals equal to observed minus predicted values. Check assumptions and avoid extrapolation. Explained variation in a fitted model does not by itself establish a causal mechanism.