Basic statistical tests - summary measures

Definition

Summary measures (mean, median, mode for central tendency; standard deviation, interquartile range, range for spread) condense a dataset into interpretable single values - measure selection should be matched to the data's distribution shape (mean/SD for normal, median/IQR for skewed) rather than applied by habit or convenience regardless of underlying data characteristics
Reported in essentially every quantitative clinical research paper and routine clinical data summary, making correct interpretation of these measures a foundational skill

Each summary measure captures a different aspect of the dataset (central tendency vs spread), and within each category, different specific measures make different distributional assumptions/have different sensitivity to outliers - understanding these differences (rather than treating all summary measures as interchangeable) is essential to both correctly reporting one's own data and correctly interpreting others' reported results

Reported summary measures should be checked for internal consistency with the described data type (e.g. mean/SD reported for data explicitly described as skewed would be a methodological red flag warranting scrutiny)
See individual notes on mean, standard deviation, interquartile range, and normal distribution for the specific measures within this framework

Correct summary measure selection and reporting supports both accurate data communication in one's own research/clinical reporting and accurate critical appraisal of others' published work
Recognising when a reported summary measure may be a poor fit for the underlying data (e.g. mean reported for clearly skewed data) should prompt more cautious interpretation of the reported values
Central tendency vs spread measure distinction, distribution-appropriate measure pairing (mean/SD vs median/IQR), critical appraisal of summary statistics in published research

Summary measures should always be interpreted as a pair matched to distribution type - mean with standard deviation for normally distributed data, median with interquartile range for skewed data - and seeing a mismatched pairing (e.g. mean reported alongside a clearly skewed dataset) is itself a useful signal for more careful, sceptical reading of the reported statistics

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