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Statistical and Practical Significance. Advanced Statistics Petr Soukup. Outline. Reminder of statistical significance Limits of statistical significance Misuses of statistical significance Alternatives to statistical significance Practical significance Effect sizes.
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Statistical and Practical Significance Advanced Statistics Petr Soukup
Outline • Reminder of statistical significance • Limits of statistical significance • Misuses of statistical significance • Alternatives to statistical significance • Practical significance • Effect sizes
Hypotheses and tests • Tested hypothesis in experiments (Fisher, 1925) • Null and alternative hypothesis (NHST) (Neyman&Pearson, 1937) • Common tests - t-tests, analysis of variance, analysis of covariance, correlation analysis etc.
Definition of statistical significance Definition: Conditionalprobability, that our sample can be drawn from population in which null hypothesis is valid (α). Statistical significance is P(D/H0) and not P(H0/D)
Assumptions for classical NHST • Big big probability samples from infinite or very big finite populations Three assumptions: • Big (infinite) population (at least 100times bigger than the sample) • Probability sampling (all units same probability of selection) • Big sample (> 30-50 units)
LIMITS OF NHST • 1.data from censuses • 2. data from non-probability samples • 3. data from small samples • 4. data based on sample that are big proportion of the basic population • 5. big data samples from merged (internationally or by time) files
Beyond the limits of NHST in CSR* N=32 articles, Czech sociological review 2000-2006 (selected 29 issues), own research *CSR-Czech sociological review
Objections against NHST (Misuses of NHST) a) Insufficient statement about population, b) null hypotheses are unreal (nill null), c) mechanical usage of classical 5% statistical significance (asterisks, stepwise methods, best models etc.), d) statistical significant doesn’t mean important, e) publishing only statistical significant results (file drawer problem).
Misuses of NHST in CSR* N=32 articles, Czech sociological review 2000-2006 (selected 29 issues), own research *CSR-Czech sociological review
Some alternatives to statistical significance a) Confidence Intervals (Problems for r, formulas, regression etc.) b) Test power (quite good in sociology), c) Estimate of minimum sample size & What if strategy, d) Comparison of models via information criterias (AIC, BIC) e) Bayesian approach
Practical significance - terminology • Practical significance b) Substantive significance c) Logical significance d) Scientific significance sometimes also: e) result importance or f) result meaningfulness
How to measure Practical sig.? History - Absolute and relative approach Example: Income differencies Absolute and relative difference
How to measure Practical sig.? Effect sizes – measures of practical significance Some well known: Cohen d Hayes ω But also R2, r, C, Fisher η2 are effect sizes Problem: Sometimes published but not interpreted
Special significances • Economic significance • Clinical significance • Etc.
CONCLUSION? Statistical significance is: LIMITED MISUSED BUT NOT BAD Substantive significance is: NOT OFTEN USED BUT NECESSARY