Praktyka wnioskowania statystycznego

Wiesław Szymczak

doi:10.18778/8142-211-6

Słowa kluczowe: wnioskowanie statystyczne, testy statystyczne, teoria Fishera, teoria Neymana-Pearsona, hipoteza zerowa, paradygmat bayesowski

Opublikowane: 5 kwietnia 2019

Kategorie: Psychologia, Otwarty dostęp

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Książka ta nie jest typowym podręcznikiem metod statystycznych, w którym omawia się podstawowe albo zaawansowane metody statystyczne wykorzystywane do opracowywania wyników badań ilościowych w naukach społecznych, medycznych itp. Zwracam w niej uwagę przede wszystkim na problemy wynikające z niespełniania przez materiał empiryczny teoretycznych założeń leżących u podstaw używanych metod, na pewnego typu „uzależnienie” – w sensie skazania się na zaimplementowane tam testy statystyczne – od używanego oprogramowania. Obszerny rozdział poświęcam też krytycznej ocenie zagadnienia wielkości efektu i obserwowalnej mocy testu. Te dwie ostatnie kwestie są o tyle niebezpieczne, że bywają instytucjonalnie wymuszane na autorach artykułów. Publikacja ta będzie więc mniej przydatna dla studentów rozpoczynających naukę statystyki, natomiast powinna być czytana przez badaczy stosujących metody statystyczne do opracowywania wyników swoich badań. Chciałbym mieć nadzieję, że moje rozważania uświadomią im, jak łatwo można zastosować nieprawidłowe rozwiązanie, budując na nim cały gmach interpretacji merytorycznych w oczywisty sposób nieprawdziwych.

Agresti A. (1990): Categorical Data Analysis. John Wiley and Sons, New York.

Ahad N. A., Yin T. S., Othman A. R., Yaacob C. R. (2011): Sensitivity of Normality Tests to Non-normal Data. „Sains Malaysiana”, 40, 6, s. 637–641.

Aitkin M. (2011): Paradigms for Statistical Inference, https://researchers.ms.unimelb.edu.au/~maitkin@unimelb/paradigms2.pdf, https://pdfs.semanticscholar.org/5226/77da13ad4ee11b2e8a9a02b0c1bdf6a77f4f.pdf (dostęp: 29.08.2011).

Allen J., Le H. (2007): An Additive Measure of Overall Effect Size for Logistic Regression Models. „Journal of Educational and Behavioral Statistics”, http://jebs.aera.net (dostęp: 1.12.2008).

Anscombe F. J., Aumann R. J. (1963): A Definition of Subjective Probability. „The Annals of Mathematical Statistics”, 34, 1, s. 199–205.

APA (2010): Publication Manual. Sixth Edition. American Psychological Association, Washington.

Armitage P., Doll R. (1954): The Age Distribution of Cancer and a Multi-stage Theory of Carcinogenesis. „British Journal of Cancer”, 8, 1, s. 1–12.

Armitage P., Doll R. (1961): Stochastic Models for Carcinogenesis. „Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press”, 4, s. 19–38.

Armstrong J. S. (2007): Significance Tests Harm Progress in Forecasting. „International Journal of Forecasting”, 23, 2, s. 321–327.

Awan H. M. (2001): Effect of Departure from Standard Assumptions Used in Analysis of Variance. „Journal of Research (Science)”, 12, 2, s. 180–188.

Babu G. J., Padmanabhan A. R., Puri M. L. (1999): Robust One-Way ANOVA under Possibly Non-Regular Conditions. „Biometrical Journal”, 41, 3, s. 321–339.

Bakeman R. (2005): Recommended Effect Size Statistics for Repeated Measures Designs. „Behavior Research Methods”, 37, 3, s. 379–384.

Bandyopadhyay P. S., Forster M. R. (red.) (2011): Handbook of Philosophy of Science, Vol. 7: Philosophy of Statistics. Elsevier, Amsterdam.

Bernardo J. M. (2011): Modern Bayesian inference: foundations and objective methods. W: Handbook of Philosophy of Science, Vol. 7: Philosophy of Statistics. Red. P. S. Bandyopadhyay, M. R. Forster, s. 263–306. Elsevier, Amsterdam.

Berger J. O. (2003): Could Fisher, Jefreys and Neyman Have Agreed on Testing? „Statistical Sciences”, 18, 1, s. 1–32.

Berger J. O., Berry D. A. (1988): Statistical Analysis and the Illusion of Objectivity. „American Scientist”, 76, s. 159–165.

Blalock H. M. (1975): Statystyka dla socjologów. Państwowe Wydawnictwo Naukowe, Warszawa.

Blume J. D. (2002): Likelihood Methods for Measuring Statistical Evidence. „Statistics in Medicine”, 21, s. 2563–2599.

Bock R. D. (1975): Multivariate Statistical Methods in Behavioral Research. McGraw-Hill Inc., New York.

Bromek T., Pleszczyńska E. (red.) (1988): Teoria i praktyka wnioskowania statystycznego. Państwowe Wydawnictwo Naukowe, Warszawa.

Brown M. B., Forsythe A. B. (1974): Robust Tests for the Equality of Variances. „Journal of the American Statistical Association”, 69, s. 364–367.

Calculating Cancer Risk Due to Occupational Exposure to Genotoxic Carcinogens (1995). Report of the Dutch Expert Committee on Occupational Standards, a Committee of the Health Council of the Netherlands, No. 1995/06WGD, The Hague, 18 October 1995.

Carlin B. P., Louis T. A. (2000): Bayes and Empirical Bayes Methods for Data Analysis. Chapman and Hall/CRC, Boca Raton.

Carver R. P. (1993). The Case against Statistical Significance Testing, Revisited. „Journal of Experimental Education”, 1993, 61, s. 287–292. Cyt. za: A. J. Onwuegbuzie, N. L. Leech (2004): Post Hoc Power: A Concept Whose Time Has Come. „Understanding Statistics”, 3, 4, s. 201–230.

Chinn S. (2000): A Simple Method for Converting an Odds Ratio to Effect Size for Use in Meta-analysis. „Statistics in Medicine”, 19, 22, s. 3127–3131.

Chmura-Kraemer H., Kupfer D. J. (2006): Size of Treatment Effects and Their Importance to Clinical Research and Practice. „Biological Psychiatry”, 56, 11, s. 90–996.

Christensen R. (2005): Testing Fisher, Neyman, Pearson, and Bayes. „The American Statistician”, 59, 2, s. 121–126.

Cohen J. (1988): Statistical Power Analysis for the Behavioral Sciences. Second Edition. Lawrence Erlbaum Associates Inc., Hillsdale.

Cohen J. (1992a): A Power Primer. „Psychological Bulletin”, 112, 1, s. 155–159.

Cohen J. (1992b): Statistical Power Analysis. „Current Directions in Psychological Sciences”, 1, 3, s. 98–101.

Cohen J. (1994): The Earth Is Round (p < .05). „American Psychologist”, 49, 12, s. 997–1003.

Collins J. F., Brown J. P., Dawson S. V., Marty M. A. (1991): Risk Assessment for Benzo[a]pyrene. „Regulatory Toxicology and Pharmacology”, 13, 2, s. 170–184.

Congdon P. (2002): Bayesian Statistical Modelling. John Wiley and Sons, Chichester. Connett J. E., Smith Judith A., McHugh R. B. (1987): Sample Size and Power for Pairmatched Case-control Studies. „Statistics in Medicine”, 6, s. 53–59.

Connor R. J. (1987): Sample Size for Testing Differences in Proportions for the Paired-sample Design. „Biometrics”, 43, s. 207–211.

Conover W. J., Johnson M. E., Johnson M. M. (1981): A Comparative Study of Tests for Homogeneity of Variances, with Applications to the Outer Continental Shelf Bidding Data. „Technometrics”, 23, s. 351–361.

Cumming G. (2014): The New Statistics: Why and How. „Psychological Science ”, 25, 1, s. 7–29.

De Kleijn W. P. E., De Vries J., Petal A. H. M., Wijnen P. A. H. M., Drent M. (2011): Minimal (clinically) important differences for the Fatigue Assessment Scale in sarcoidosis, „Respiratory Medicine”, 105, 1, s. 1388–1395.

Denis D. J. (2003): Alternatives to Null Hypothesis Significance Testing. “Theory and Science”, 4, 1, s. 1–17, http://theoryandscience.icaap.org/content/vol14.1/02_denis.html (dostęp: 6.12.2007).

Dienes Z. (2011): Bayesian Versus Orthodox Statistics: Which Side Are You On? „Perspective on Psychological Science”, 6, 3, s. 274–290.

Donoghue D., Physiotherapy Research and Older People (PROP), Stokes E. K. (2009): How Much Change is True Change? The Minimum Detectable Change of the Berg Balance Scale in Elderly People. „Journal of Rehabilitation Medicine”, 41, s. 343–346.

Dudek B. (2007): Stres związany z pracą: teoretyczne i metodologiczne podstawy badań zależności między zdrowiem a stresem zawodowym. W: Perspektywy psychologii pracy. Red. M. Górnik-Durose, B. Kożusznik, s. 220–246. Wydawnictwo Uniwersytetu Śląskiego, Katowice.

Efron B. (1978): Controversies in the Foundation of Statistics. „American Mathematical Monthly”, 85, 4, s. 231–246.

Efron B. (1998): R. A. Fisher in the 21st Century. Invited Paper Presented at the 1996 R. A. Fisher Lecture. „Statistical Science”, 13, 2, s. 95–122.

Eisen S. V., Ranganathan G., Seal P., Spiro A. III (2007): Measuring Clinically Meaningful Change Following Mental Health Treatment. „The Journal of Behavioral Health Services and Research”, 34, 3, s. 272–289.

Field A. (2009): Discovering Statistics Using SPSS. Third Edition. Sage Publications, Thousand Oaks.

Fisher R. A. (1922): On the Mathematical Foundations of Theoretical Statistics. „Philosophical Transactions of the Royal Society of London”. Series A, Containing Papers of a Mathematical or Physical Character, 222, s. 309–368.

Fisher R. A. (1935): The Logic of Inductive Inference (with Discussion). „Journal of the Royal Statistical Society”, 98, 1, s. 39–82.

Fisher R. A. (1955): Statistical Methods and Scientific Induction. „Journal of the Royal Statistical Society”. Series B (Methodological), 17, 1, s. 69–78.

Fisher R. A. (1956): Statistical Methods and Scientific Inference. Oliver and Bond, Edinburgh. Cyt. za: G. Gigerenzer (2004): Mindless Statistics. „Journal of Behavioral and Experimental Economics” (formerly „The Journal of Socio-Economics”), 33, 5, s. 587–606.

Fisz M. (1969): Rachunek prawdopodobieństwa i statystyka matematyczna. Państwowe Wydawnictwo Naukowe, Warszawa.

Frans F. A., Nieuwkerk P. T., Met R., Bipat S., Legemate D. A., Reekers J. A., Koelemay M. J. W. (2014): Statistical or Clinical Improvement? Determining the Minimally Important Difference for the Vascular Quality of Life Questionnaire in Patients with Critical Limb Ischemia. „European Journal of Vascular and Endovascular Surgery”, 47, 2, s. 180–186.

Freedman D. (1995/1996): Some Issues in the Foundations of Statistics. „Foundations of Science”, 1, s. 19–39.

Freeman G. H., Halton J. H. (1951): Note on an Exact Treatment of Contingency, Goodness of Fit and Other Problems of Significance. „Biometrika”, 38, s. 141–149.

Games P. A. (1971): Multiple Comparisons of Means. „American Educational Research Journal”, 8, s. 531–565.

Garcia-Perez A. (2008): Approximations for F-Tests Which Are Ratios of Sums of Squares of Independent Variables with a Model Close to Normal. „Test”, 17, 2, s. 350–369.

Garson G. D. (2012): Testing Statistical Assumptions. Statistical Associates Publishing, North Carolina State University, Raleigh.

Gart J. J., Krewski D., Lee P. N., Tarone R. E., Wahrendorf J. (1986): Statistical Methods in Cancer Research, Vol. III: The Design and Analysis of Long-term Animal Experiments. International Agency for Research on Cancer, Lyon.

Gastwirth J. L., Gel Yulia R., Miao W. (2009): The Impact of Levene’s Test of Equality of Variances on Statistical Theory and Practice. „Statistical Science”, 24, 3, s. 343–360.

Gigerenzer G. (2004): Mindless Statistics. „Journal of Behavioral and Experimental Economics” (formerly „The Journal of Socio-Economics”), 33, 5, s. 587–606.

Gigerenzer G., Marewski J. N. (2015): Surrogate Science: The Idol of a Universal Method for Scientific Inference. „Journal of Management”, 41, 2, s. 421–440.

Gigerenzer G., Krauss S., Vitouch O. (2004): The Null Ritual. What You Always Wanted to Know About Significance Testing but Were Afraid to Ask. W: The Sage Handbook of Quantitative Methodology for the Social Sciences. Red. D. Kaplan, s. 391–408. Sage Publications, Thousand Oaks.

Gillett R. (1994): Post Hoc Power Analysis. „Journal of Applied Psychology”, 79, 5, s. 783–785.

Glass G. V., Peckham P. D., Sanders J. R. (1972): Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance. „Review of Educational Research”, 42, 3, s. 237–288.

Gomez J. (2012): Tam gdzie proste są krzywe. Geometrie nieeuklidesowe. RBA Coleccionables, Barcelona.

Gray C. D., Kinnear P. R. (2012): IBM SPSS Statistics 19 Made Simple. Psychology Press, New York. Cyt. za: K. L. Wuensch (2015): Nonparametric Effect Size Estimators. Materiały dydaktyczne. East Carolina University Department of Psychology, core.ecu.edu/psyc/wuenschk/docs30/Nonparametric-EffectSize.pdf (dostęp: 16.06.2015).

Greenland S., Schlesselman J. J., Criqui M. H. (1986): The Fallacy of Employing Standardized Regression Coefficients and Correlations as Measures of Effect. „American Journal of Epidemiology”, 123, 2, s. 203–208.

Greenland S., Maclure M., Schlesselman J. J., Poole C., Morgenstern H. (1991): Standardized Regression Coefficients: A Further Critique and Review of Some Alternatives. „Epidemiology”, 2, 5, s. 387–392.

Greń J. (1968): Modele i zadania statystyki matematycznej. Państwowe Wydawnictwo Naukowe, Warszawa.

Hagen R. L. (1997): In Praise of the Null Hypothesis Statistical Test. „American Psychologist”, 52, 1, s. 15–24.

Häggström O. (2012): Why the Empirical Sciences Need Statistics So Desperately. W: European Congress of Mathematics, Krakow, 2–7 July, 2012. Red. R. Latała, A. Ruciński, P. Strzelecki, J. Świątkowski, D. Wrzosek, P. Zakrzewski, s. 347–360. European Mathematical Society Publishing House, Zurich.

Hartley, H. O. (1950): The Maximum F-rates as a Shortcut Test for Heterogeneity of Variance. „Biometrika”, 37, 308–312.

Hilbe J. M. (2009): Logistic Regression Models. Chapman and Hall/CRC, Boca Raton. Hoenig J. M., Heisey D. M. (2001): The Abuse of Power: The Pervasive Fallacy of Power Calculations for Data Analysis. „The American Statistician”, 55, 1, s. 19–24.

Hosmer D. W., Lemeshow L. (1989): Applied Logistic Regression. John Wiley and Sons, New York.

Hsieh F. Y. (1989): Sample Size Tables for Logistic Regression. „Statistics in Medicine”, 8, s. 795–802.

Hubbard R., Armstrong J. S. (2006): Why We Don’t Really Know What „Statistical Significance” Means: A Major Educational Failure. „Journal of Marketing Education”, 28, 2, s. 114–120.

Hubbard R., Bayarri M. J. (2003): Confusion Over Measures of Evidence (p’s) Versus Errors (α’s) in Classical Statistical Testing. „The American Statistician”, 57, 3, s. 171–182.

Inman H. F. (1994): Karl Pearson and R. A. Fisher on Statistical Tests: A 1935 Exchange From Nature. „The American Statistician”, 48, 1, s. 2–11.

Jacobson N. S., Truax P. (1991): Clinical Significance: A Statistical Approach to Defining Meaningful Change in Psychotherapy Research. „Journal of Consulting and Clinical Psychology”, 59, 1, s. 12–19.

Jeffreys H. (1961): Theory of Probability, 3rd ed. Oxford University Press, Oxford. Cyt. za: J. O. Berger (2003): Could Fisher, Jefreys and Neyman Have Agreed on Testing? „Statistical Sciences”, 18, 1, s. 1–32.

Jones L. V., Tukey J. W. (2000): A Sensible Formulation of the Significance Test. „Psychological Methods”, 5, 4, s. 411–414.

Karni E. (1993): A Definition of Subjective Probabilities with State-dependent Preferences. „Econometrica”, 61, 1, s. 187–198.

Kerby D. S. (2014): The Simple Difference Formula: An Approach to Teaching Nonparametric Correlation. „Innovative Teaching”, 3, 1. Cyt. za: K. L. Wuensch (2015): Nonparametric Eff ct Size Estimators. Materiały dydaktyczne. East Carolina University, Department of Psychology, Greenville.

Keselman H. J., Cribbie R. A., Wilcox R. R. (2002): Pairwise Multiple Comparison Tests When Data Are Nonnormal. „Educational and Psychological Measurement”, 62, 3, s. 420–434.

Khan A., Rayner G. D. (2003): Robustness to Non-Normality of Common Tests for the ManySample Location Problem. „Journal of Applied Mathematics and Decision Sciences”, 7, 4, s. 187–206.

Killeen P. R. (2005): An Alternative to Null-Hypothesis Significance Tests. „Psychological Science”, 16, 5, s. 345–353.

Kirk R. E. (1994): Experimental Design: Procedures for the Behavioral Sciences, 3rd ed. Wadsworth Publishing, Belmont CA.

Kochanski G. (2005): Brute Force as a Statistical Tool, http://kochanski.org/gpk (dostęp: 1.03.2005).

Kołmogorow A. N. (1933): Grundbegriffe der Wahrscheinlichkeitsrechnung. „Ergebnisse der Mathematik und ihrer Grenzgebiete”, 3, s. 1–62. Cyt. za: H. Bauer (1968): Probability Theory and Elements of Measure Theory. Holt, Rinehart and Winston Inc., New York. Krämer W. (2011): The Cult of Statistical Significance. What Economists Should and Should Not Do to Make Their Data Talk. Working Paper Series of the German Data Forum (RatSWD). Working Paper No. 176, April 2011.

Kubot A. (2017): Zastosowanie radialnej fali uderzeniowej i ultradźwięków w leczeniu zespołu łokcia tenisisty. Rozprawa na stopień doktora nauk medycznych, Uniwersytet Medyczny, Łódź.

Kubot A., Grzegorzewski A., Synder M., Szymczak W., Kozłowski P. (2017): Zastosowanie radialnej fali uderzeniowej i ultradźwięków w leczeniu zespołu łokcia tenisisty. „Ortopedia Traumatologia Rehabilitacja”, 19, 5(6), s. 415–426.

Kuhn T. S. (2009): Struktura rewolucji naukowych. Wydawnictwo Aletheia, Warszawa. Tłum. z: The Structure of Scientific Revolutions, 3rd ed. The University of Chicago Press, Chicago–London 1996.

Kyburg H. E., Jr. (1977): Decisions, Conclusions, and Utilities. „Synthese”, 36, s. 87–96.

Lachin J. M. (1986): Evaluation of Sample Size and Power for Analyses of Survival with Allowance for Nonuniform Patient Entry, Losses to Follow-up, Noncompliance, and Stratification. „Biometrics”, 42, s. 507–519.

Lambdin C. (2012): Significance Tests as Sorcery: Science Is Empirical – Significance Tests Are Not. „Theory and Psychology”, 22, 1, s. 67–90.

Lantz B. (2013): The Impact of Sample Non-normality on ANOVA and Alternative Methods. „British Journal of Mathematical and Statistical Psychology”, 66, s. 224–244.

Laplace P. S. (1812): Theorie analytique des probabilites, Courcier, Paris.

Lee H. B., Katz G. S., Restori A. F. (2010): A Monte Carlo Study of Seven Homogeneity of Variance Tests. „Journal of Mathematics and Statistics”, 6, 3, s. 359–366.

Lee M. D., Wagenmakers E.-J. (2005): Bayesian Statistical Inference in Psychology: Comment on Trafimow (2003). „Psychological Review”, 112, 3, s. 662–668.

Lehmann E. L. (1959): Testing Statistical Statistics. John Wiley and Sons, New York. Pol. tłum.: Testowanie hipotez statystycznych. Państwowe Wydawnictwo Naukowe, Warszawa 1968.

Lehmann E. L. (1968): Testowanie hipotez statystycznych. Państwowe Wydawnictwo Naukowe, Warszawa.

Lehmann E. L. (1993): The Fisher, Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two? „Journal of the American Statistical Association”, 88, 424, s. 1242–1249.

Lehmann E. L. (1995): Neyman’s Statistical Philosophy. „Probability and Mathematical Statistics”, 15, s. 29–36.

Lehmann E. L. (2006): Nonparametrics. Statistical Methods Based on Ranks. Springer, New York.

Lemeshow S., Hosmer D. W., Klar J. (1988): Sample Size Requirements for Studies Estimating Odds Ratios or Relative Risks. „Statistics in Medicine”, 7, s. 759–764.

Lenth R. V. (2007): Post Hoc Power: Tables and Commentary. Technical Report No. 378, The University of Iowa, Department of Statistics and Actuarial Sciences, s. 1–13.

Levene H. (1960): Robust Tests of Equality of Variances. W: Contributions to Probability and Statistics. Essays in Honor of Harold Hotelling, Red. I. Olkin, S. G. Ghurye, W. Hoeffding, W. G. Madow, H. B. Mann, s. 278–292. Stanford University Press, Palo Alto.

Leventhal L., Huynh C. L. (1996): Directional Decisions for Two-Tailed Tests: Power, Error Rates and Sample Size. „Psychological Methods”, 1, 3, s. 278–292.

Levine T. R., Hullett C. R. (2002): Eta Squared, Partial Eta Squared, and Misreporting of Effect Size in Communication Research. „Human Communication Research”, 28, 4, s. 612–625.

Levine T. R., Weber R., Hullet C., Park H. S., Lindsey Lisa L. M. (2008): A Critical Assessment of Null Hypothesis Significance Testing in Quantitative Communication Research. “Human Communication Research”, 34, 171–187.

Levy P. S., Lemeshow S. (1991): Sampling of Populations: Methods and Applications. John Wiley and Sons, New York.

Lillestøl J. (2014): Statistical Inference: Paradigms and Controversies in Historic Perspective. NHH Norwegian School of Economics, Bergen, Department of Business and Management Science, https://www.nhh.no/globalassets/departments/business-and-management-science/statistical_inference.pdf (dostęp: 16.06.2015).

Lim T.-S., Loh W.-Y. (1996): A Comparison of Tests of Equality of Variances. „Computational Statistics and Data Analysis”, 22, s. 287–301.

Lindgren B. W. (1962): Statistical Theory. The Macmillan Co., New York.

Lindley D. V. (1961): The Use of Prior Probability Distributions in Statistical Inference and Decisions. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley–Los Angeles.

Lindquist E. F. (1938): A First Course in Statistics. Houghton Mifflin Harcourt, Cambridge.

Cyt za: Huberty C. J. (1993): Historical Origins of Statistical Testing Practices: The Treatment of Fisher Versus Neyman-Pearson Views in Textbooks. „Journal of Experimental Education”, 61, 4, s. 317–333.

Loftus G. R. (1996): Psychology Will Be a Much Better Science When We Change the Way We Analyze Data. „Current Directions in Psychological Science”, 5, 6, s. 161–171.

Machina M. J., Schmeidler D. (1992): A More Robust Definition of Subjective Probability. „Econometrica”, 60, 4, s. 745–780.

Magee L. (1990): R2 Measures Based on Wald and Likelihood Ratio Joint Significance Tests. „The American Statistician”, 44, 3, s. 250–253.

Magiera R. (2007): Modele i metody statystyki matematycznej. Część II: Wnioskowanie statystyczne, wydanie drugie rozszerzone. Oficyna Wydawnicza GiS, Wrocław.

Manthey J. (2010): Elementary Statistics: A History of Controversy. AMATYC 2010 Conference – Bridging Past to Future Mathematics, Boston MA, November 11–14, 2010.

Mara C. A. (2013): Testing for Equivalence of Group Variances. A Dissertation Submitted to the Faculty of Graduate Studies in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy. York University, Toronto.

Maslow A. H. (1966): The Psychology of Science. Harper and Row, New York.

Mehlman M. H. (2017): ANOVA: Analysis of Variance. University of New Haven, http://math.newhaven.edu/mhm/courses/bstat/items.html, http://math.newhaven.edu/mhm/courses/estat/slides/ANOVA.pdf (dostęp: 4.12.2017).

Mehta C. R., Patel N. R. (1983). A Network Algorithm for Performing Fisher’s Exact Test in r × c Contingency Tables. „Journal of the American Statistical Association”, 78, 382, s. 427–434.

Mehta C. R., Patel N. R. (1986): Algorithm 643. FEXACT: A Fortran Subroutine for Fisher’s Exact Test on Unordered r × c Contingency Tables. „ACM Transactions on Mathematical Software”, 12, s. 154–161.

Menard S. (2000): Coefficients of Determination for Multiple Logistic Regression Analysis. „The American Statistician”, 54, 1, s. 17–24.

Miller W. R., Manuel J. K. (2008): How Large Must a Treatment Effect Be Before it Matters to Practitioners? An Estimation Method and Demonstration. „Drug and Alcohol Review”, 27, s. 524–528.

Mises R., von (1936): Wahrscheinlichkeit, Statistik und Wahrheit. Springer Verlag, Wienna. Moolgavkar S. H. (1986): Carcinogenic Modeling: From Molecular Biology to Epidemiology. „The Annual Review of Public Health”, 7, s. 151–169.

Nagelkerke N. J. D. (1991): A Note on a General Definition of the Coefficient of Determination. „Biometrika”, 78, 3, s. 691–692.

Neveu J. (1964): Bases mathématiques du calcul des probabilités. Masson et Cie, Paris.

Neyman J. (1969): Zasady rachunku prawdopodobieństwa i statystyki matematycznej. Państwowe Wydawnictwo Naukowe, Warszawa.

Neyman J. (1977): Frequentist Probability and Frequentist Statistics. „Synthese”, 36, s. 97–131.

Neyman J., Pearson E. S. (1933): On the Problem of the Most Efficient Tests of Statistical Hypotheses. „Philosophical Transactions of the Royal Statistical Society. Section A”, 231, s. 289–337. Cyt. za: E. L. Lehmann (1995): Neyman’s Statistical Philosophy. „Probability and Mathematical Statistics”, 15, s. 29–36.

Nordstokke D. W., Zumbo B. D. (2007): A Cautionary Tale About Levene’s Tests for Equal Variances. „Journal of Educational Research and Policy Studies”, 7, 1, s. 1–14.

O’Keefe D. J. (2007): Post Hoc Power, Observed Power, A Priori Power, Retrospective Power, Prospective Power, Achieved Power: Sorting Out Appropriate Uses of Statistical Power Analyses. „Communication Methods and Measures”, 1, 4, s. 291–299.

Onwuegbuzie A. J., Leech N. L. (2004): Post Hoc Power: A Concept Whose Time Has Come. „Understanding Statistics”, 3, 4, s. 201–230.

Papoulis A. (1972): Prawdopodobieństwo, zmienne losowe i procesy stochastyczne. Tłum. T. Gerstenkorn, Wydawnictwa Naukowo-Techniczne, Warszawa.

Parra-Frutos I. (2009): The Behaviour of the Modified Levene’s Test When Data Are Not Normally Distributed. „Computational Statistics”, 24, s. 671–693.

Pawłowski Z. (1976): Statystyka matematyczna. Państwowe Wydawnictwo Naukowe, Warszawa.

Portier C. J., Kopp-Schneider A., Sherman C. D. (1993): Using Cell Replication Data in Mathematical Modeling in Carcinogenesis. „Environ Health Perspect” 101 (Suppl. 5), s. 79–86.

Rao C. R. (1965): Linear Statistical Inference and Its Applications. John Wiley and Sons, New York. Pol. tłum.: Modele liniowe statystyki matematycznej. Państwowe Wydawnictwo Naukowe, Warszawa, 1982.

Rao C. R. (1994): Statystyka i prawda. Wydawnictwo Naukowe PWN, Warszawa.

Rasch D. (2012): Hypothesis Testing and the Error of the Third Kind. „Psychological Test and Assessment Modeling”, 54, 1, s. 90–99.

Razali N. M., Wah Y. B. (2011): Power Comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling Tests. „Journal of Statistical Modeling and Analytics”, 2, 1, s. 21–33.

Richardson J. T. E. (1996): Measures of Effect Size. „Behavior Research Methods, Instruments and Computers”, 28, 1, s. 12–22.

Richardson J. T. E. (2011): Eta Squared and Partial Eta Squared as Measures of Effect Size in Educational Research. „Educational Research Review”, 6, s. 135–147.

Roberts S., Pashler H. (2000): How Persuasive Is a Good Fit? A Comment on Theory Testing. „Psychological Review”, 107, 2, s. 358–367.

Robinson D. H., Wainer H. (2001): On the Past and Future of Null Hypothesis Significance Testing. Research Report RR-01-24, Educational Testing Service, Princeton.

Rodgers J. L. (2010): The Epistemology of Mathematical and Statistical Modeling. A Quiet Methodological Revolution. „American Psychologist”, 65, 1, s. 1–12.

Rosenthal R. (1991): Meta-analytic Procedures for Social Research, 2nd ed. Sage Publications, Newbury Park CA. Cyt. za: A. Field (2009): Discovering Statistics Using SPSS, 3rd ed. Sage Publications, Newbury Park.

Rosnow R. L., Rosenthal R. (2005): Beginning Behavioural Research: A Conceptual Primer, 5th ed. Pearson/Prentice Hall, Englewood Cliffs. Cyt. za: A. Field (2009): Discovering Statistics Using SPSS, 3rd ed. Sage Publications, Thousand Oaks.

Royall R. (2000a): On the Probability of Observing Misleading Statistical Evidence (with Comments). „Journal of the American Statistical Association”, 95, 451, s. 760–780.

Royall R. (2000b): Statistical Evidence. A Likelihood Paradigm. Chapman and Hall/CRC, Boca Raton.

Royston P. (1982): An Extension of Shapiro and Wilks’s W Test for Normality to Large Samples. „Applied Statistics”, 31, s. 115–124.

Royston P. (1983): A Simple Method for Evaluating the Shapiro-Francia W Test of Nonnormality. „Statistician”, 32, s. 297–300.

Satten G. A., Kupper L. L. (1990): Sample Size Requirements for Interval Estimation on the Odds Ratio. „American Journal of Epidemiology”, 131, 1, s. 177–184.

Savage L. J. (1954): The Foundations of Statistics. John Wiley and Sons, New York.

Savage L. J. (1958): Recent Tendencies in the Foundations of Statistics. Invited address to Section VI of the International Congress of Mathematicians, Edinburgh, 14–21 August 1958.

Schoenfeld D. A. (1983): Sample-Size Formula for the Proportional-Hazards Regression Model. „Biometrics”, 39, s. 499–503.

Sedlmeier P., Gigerenzer G. (1989): Do Studies of Statistical Power Have an Effect on the Power of Studies. „Psychological Bulletin”, 105, 2, s. 309–316.

Shapiro S. S., Francia R. S. (1972): An Approximate Analysis of Variance Test for Normality. „Journal of the American Statistical Association”, 67, s. 215–216.

Shapiro S. S., Wilk M. B. (1965): An Analysis of Variance Test for Normality (Complete Samples). „Biometrika”, 52, s. 591–611.

Silvey S. D. (1978): Wnioskowanie statystyczne. Państwowe Wydawnictwo Naukowe, Warszawa.

Sink C. A., Mvududu N. H. (2010): Statistical Power, Sampling, and Effect Sizes: Three Keys to Research Relevancy. „Counseling Outcome Research and Evaluation”, 1, 2, s. 1–18.

Spiegelhalter D. J., Abrams K. R., Myles J. P. (2004): Bayesian Approaches to Clinical Trials and Health-Care Evaluation. John Wiley and Sons, Chichester.

Starek A., Szabla J., Szymczak W., Zapór L. (2006): Comparison of Acute Haematotoxicity of 2-mthoxyethanol, 2-ethoxyethanol and 2-butoxyethanol in Male Rats. „Acta Toxicologica”, 14, 1–2, s. 63–71.

Sterne J. A. C. (2002): Teaching Hypothesis Tests – Time for Significant Change? „Statistics in Medicine”, 21, 7, s. 985–994.

Szymczak W. (1999): Ryzyko choroby nowotworowej a narażenie na substancje chemiczne. Instytut Medycyny Pracy, Łódź.

Szymczak W. (2018): Podstawy statystyki dla psychologów, wydanie trzecie rozszerzone. Wydawnictwo Difin, Warszawa.

Tabachnick B. G., Fidell L. S. (2007): Using Multivariate Statistics, 5th ed. Pearson Education Inc., Boston.

Thalheimer W., Cook S. (2002): How to Calculate Effect Sizes from Published Research Articles: A Simplified Methodology, http://work-learning.com/effect_sizes.htm (dostęp: 28.08.2012).

Thompson Bill. (2007): The Nature of Statistical Evidence. Springer, New York.

Thompson Bruce. (1994): The Concept of Statistical Significance Testing. „Practical Assessment, Research and Evaluation”, 4, 5, s. 1–3.

Trafi ow D. (2003): Hypothesis Testing and Theory Evaluation at the Boundaries: Surprising Insights from Bayes’ Theorem. „Psychological Review”, 110, 3, s. 526–535.

US EPA (1984) (U.S. Environmental Protection Agency): Health Eff cts Assessment for Benzo[a]pyrene. EPA 540/1-86-022. Environmental Criteria and Assessment Office, Cincinnati.

US EPA (1988) (U.S. Environmental Protection Agency): Recommendations for and Documentation of Biological Values for Use in Risk Assessment. EPA 600/6-87-008. Office of Health and Environmental Assessment, Cincinnati.

Valentine J. C., Cooper H. (2003): Effect Size Substantive Interpretation Guidelines: Issues in the Interpretation of Effect Sizes. What Works Clearinghouse, Washington.

Volker M. A. (2006): Reporting Effect Size Estimates in School Psychology Research. „Psychology in the Schools”, 43, 6, s. 653–672.

Vorapongsathorn T., Taejaroenkul S., Viwatwongkasem C. (2004): A Comparison of Type I Error and Power of Bartlett’s Test, Levene’s Test and Cochran’s Test under Violation of Assumptions. „Songklanakarin Journal of Science and Technology”, 26, 4, s. 537–547.

Wasserman L. (2006): All of Nonparametric Statistics. Springer, New York.

Welch B. L. (1951): On the Comparison of Several Mean Values: An Alternative Approach, „Biometrika”, 38, s. 330–336.

Whittemore A. S. (1981): Sample Size for Logistic Regression with Small Response Probability. „Journal of the American Statistical Association”, 76, 373, s. 27–32.

Wilcox R. R. (2002): Understanding the Practical Advantages of Modern ANOVA Methods. „Journal of Clinical Child and Adolescent Psychology”, 31, 3, s. 399–412.

Williams R. H., Zimmerman D. W. (1989): Statistical Power Analysis and Reliability of Measurement. „Journal of General Psychology”, 116, 4, s. 359–369.

Winer (1971): Statistical Principles in Experimental Design, 2nd ed. McGraw-Hill, Tokyo.

Winer B. J., Brown D. R., Michels K. M. (1991): Statistical Principles in Experimental Design, 3rd ed. McGraw-Hill, Boston.

Woolson R. F. (1987): Statistical Methods for the Analysis of Biomedical Data. John Wiley and Sons, New York.

Wuensch K. L. (2015): Nonparametric Effect Size Estimators. Materiały dydaktyczne. East Carolina University Department of Psychology, http://core.ecu.edu/psyc/wuenschk/docs30/Nonparametric-EffectSize.pdf (dostęp: 16.06.2015).

Young G. A., Smith R. L. (2005): Essentials of Statistical Inference. Cambridge University Press, Cambridge.

Ziliak S. T., McCloskey D. N. (2009): The Cult of Statistical Significance. Presented at the Joint Statistical Meetings, August 3rd, Washington.

Zimmerman D. W. (2004): A Note on Preliminary Tests of Equality of Variances. „British Journal of Mathematical and Statistical Psychology”, 57, s. 173–181.

Zubrzycki S. (1970): Wykłady z rachunku prawdopodobieństwa i statystyki matematycznej. Państwowe Wydawnictwo Naukowe, Warszawa.

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