主题： reporting
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Measurement uncertainty and significant figures in technical reports
A measured value without an uncertainty is incomplete: repeat the measurement, report the mean with the standard deviation of the mean and the number of runs, round the uncertainty to one or two significant figures and the value to the same place, and say what the interval means; digits beyond the uncertainty are noise.
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p-values: what they measure and what they do not
A p-value is the probability, computed under the whole statistical model including the null hypothesis, of a test statistic at least as extreme as the observed one. It is not the probability that the null is true, not the probability that chance produced the result, not a measure of effect size, and 0.05 is a convention rather than a boundary between truth and noise.
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Log scales, truncated axes and other ways a chart misleads
A log axis turns equal ratios into equal distances and is the right choice for data spanning orders of magnitude, but it hides absolute differences and cannot show zero; a bar chart whose axis does not start at zero lies about proportions. Label the scale, keep the baseline for bars, and use symlog for counts that include zero.
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Confidence intervals in outline: what the interval says and what it does not
A 95% confidence interval comes from a procedure that captures the true value in 95% of repeated samples; one particular interval either contains it or not. Its width shrinks with the square root of the sample size and grows with the spread. Read it as the range of values compatible with the data, report it next to every estimate, and compute the interval of a difference when comparing.
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Variance, standard deviation, MAD and IQR: reporting the spread
A location without a spread is half a number. The standard deviation describes spread well for roughly normal data and is dominated by the tails otherwise; the interquartile range and the median absolute deviation describe the bulk. Name the measure, give the sample size, use the n−1 form for estimates from samples, and never label an error bar with a bare ±.
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Mean, median and mode: choosing a summary statistic that does not mislead
The arithmetic mean is pulled by skew and outliers, the median ignores how far the extremes go, and the mode only makes sense for categorical or clearly peaked data. Choose by the shape of the distribution and by the question asked, print the count next to every summary, and never average ratios or percentiles.
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Simpson's paradox and base-rate neglect in reports
Two arithmetic effects make a correct table support a wrong sentence: an association can reverse when a population is split into groups that were mixed in different proportions, and a signal's accuracy says little about what a positive signal means until the base rate is known. Ask how groups were mixed and keep denominators visible.
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