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(26 Jun 2004,
FrankHarrell
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---+ Miscellaneous Statistics Problems to Avoid ---++ Descriptive Statistics * Mean ± S.D. virtually assumes normality * Mean ± S.E. assumes normality unless N is large; best to use a confidence interval instead of using one S.E. * Median is always representative of a continuous variable, although it is not as precise an estimate of central tendency if the distribution is truly normal * Use percentiles instead of "outside 3 s.d." for lab parameters * Some software makes a test of normality and depending on the result runs a parametric or nonparametric test. The problems with this approach include: * The test of normality may not have adequate power to detect non-normality * Even if the data come from a truly normal distribution, nonparametric tests are almost as efficient as parametric tests (Wilcoxon-Mann-Whitney test is 0.96 as efficient as _t_ -test). * If the data are non-normal, the nonparametric test can be much more powerful than the parametric counterpart. |*Parametric Test*|*Nonparametric Counterpart*| |_t_ -test|Wilcoxon-Mann-Whitney| |Paired _t_ -test|Wilcoxon signed rank| |ANOVA|Kruskal-Wallis test| |Pearson _r_|Spearman rho rank correlation| (_r_ = product-moment linear correlation coefficient) * Geometric means are typically not good for describing central tendency of skewed data. Geometric means are greatly affected by low outliers and may be difficult to interpret. ---++ Interpretation of _P_ -Values * _P_ -values only provide evidence against a hypothesis, never evidence in favor of it. * _P_ =.8 implies there is lack of evidence of an effect, i.e., either: 1 There is little or no effect or 1 There is insufficient information in the sample due to small N or high variability --- "Absence of evidence is not evidence for absence" (Altman and Bland, _BMJ_ 311:485; 1995) * _P_ =.01 implies there is evidence for an effect, but this effect may be clinically insignificant * _P_ =.05 in many cases provides very little evidence against the null hypothesis * Confidence intervals convey much more information than _P_ -values, especially when _P_ is large -- Main.FrankHarrell - 26 Jun 2004
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Topic revision: r1 - 26 Jun 2004,
FrankHarrell
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