Advertisement

Nonparametric Statistics in Human–Computer Interaction

  • Jacob O. WobbrockEmail author
  • Matthew Kay
Part of the Human–Computer Interaction Series book series (HCIS)

Abstract

Data not suitable for classic parametric statistical analyses arise frequently in human–computer interaction studies. Various nonparametric statistical procedures are appropriate and advantageous when used properly. This chapter organizes and illustrates multiple nonparametric procedures, contrasting them with their parametric counterparts. Guidance is given for when to use nonparametric analyses and how to interpret and report their results.

Keywords

Binomial Test Generalize Estimate Equation Multinomial Logistic Regression Ordinal Logistic Regression Annualize Sale 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Anderson TW, Darling DA (1952) Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Ann Math Stat 23(2):193–212Google Scholar
  2. Anderson TW, Darling DA (1954) A test of goodness of fit. J Am Stat Assoc 49(268):765–769Google Scholar
  3. Brown GW, Mood AM (1948) Homogeneity of several samples. Am Stat 2(3):22Google Scholar
  4. Brown GW, Mood AM (1951) On median tests for linear hypotheses. In: Proceedings of the second Berkeley symposium on mathematical statistics and probability, Berkeley, California. University of California Press, Berkeley, California, pp 159–166Google Scholar
  5. Conover WJ, Iman RL (1981) Rank transformations as a bridge between parametric and nonparametric statistics. Am Stat 35(3):124–129Google Scholar
  6. D’Agostino RB (1986) Tests for the normal distribution. In: D’Agostino RB, Stephens MA (eds) Goodness-of-fit techniques. Marcel Dekker, New York, pp 367–420Google Scholar
  7. Dixon WJ, Mood AM (1946) The statistical sign test. J Am Stat Assoc 41(236):557–566Google Scholar
  8. Fawcett RF, Salter KC (1984) A Monte Carlo study of the F test and three tests based on ranks of treatment effects in randomized block designs. Commun Stat Simul Comput 13(2):213–225Google Scholar
  9. Fisher RA (1921) On the “probable error” of a coefficient of correlation deduced from a small sample. Metron 1(4):3–32Google Scholar
  10. Fisher RA (1922) On the interpretation of \(\chi ^{2}\) from contingency tables, and the calculation of P. J R Stat Soc 85(1):87–94Google Scholar
  11. Fisher RA (1925) Statistical methods for research workers. Oliver and Boyd, EdinburghzbMATHGoogle Scholar
  12. Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J Am Stat Assoc 32(200):675–701Google Scholar
  13. Gilmour AR, Anderson RD, Rae AL (1985) The analysis of binomial data by a generalized linear mixed model. Biometrika \(72\)(3):593–599Google Scholar
  14. Greenhouse SW, Geisser S (1959) On methods in the analysis of profile data. Psychometrika 24(2):95–112Google Scholar
  15. Higgins JJ, Blair RC, Tashtoush S (1990) The aligned rank transform procedure. In: Proceedings of the conference on applied statistics in agriculture. Kansas State University, Manhattan, Kansas, pp 185–195Google Scholar
  16. Higgins JJ, Tashtoush S (1994) An aligned rank transform test for interaction. Nonlinear World 1(2):201–211Google Scholar
  17. Higgins JJ (2004) Introduction to modern nonparametric statistics. Duxbury Press, Pacific GroveGoogle Scholar
  18. Hodges JL, Lehmann EL (1962) Rank methods for combination of independent experiments in the analysis of variance. Ann Math Stat 33(2):482–497Google Scholar
  19. Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6(2):65–70Google Scholar
  20. Kolmogorov A (1933) Sulla determinazione empirica di una legge di distributione. Giornale dell’Istituto Italiano degli Attuari 4:83–91Google Scholar
  21. Kramer CY (1956) Extension of multiple range tests to group means with unequal numbers of replications. Biometrics 12(3):307–310Google Scholar
  22. Kruskal WH, Wallis WA (1952) Use of ranks in one-criterion variance analysis. J Amer Stat Assoc 47(260):583–621Google Scholar
  23. Lehmann EL (2006) Nonparametrics: statistical methods based on ranks. Springer, New YorkzbMATHGoogle Scholar
  24. Levene H (1960) Robust tests for equality of variances. In: Olkin I, Ghurye SG, Hoeffding H, Madow WG, Mann HB (eds) Contributions to probability and statistics. Stanford University Press, Palo Alto, pp 278–292Google Scholar
  25. Liang K-Y, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika 73(1):13–22Google Scholar
  26. Mann HB, Whitney DR (1947) On a test of whether one of two random variables is stochastically larger than the other. Ann Math Stat 18(1):50–60Google Scholar
  27. Mansouri H (1999a) Aligned rank transform tests in linear models. J Stat Plann Inference 79(1):141–155Google Scholar
  28. Mansouri H (1999b) Multifactor analysis of variance based on the aligned rank transform technique. Comput Stat Data Anal 29(2):177–189Google Scholar
  29. Mansouri H, Paige RL, Surles JG (2004) Aligned rank transform techniques for analysis of variance and multiple comparisons. Commun Stat Theory Methods 33(9):2217–2232Google Scholar
  30. Massey FJ (1951) The Kolmogorov-Smirnov test for goodness of fit. J Am Stat Assoc 46(253):68–78Google Scholar
  31. Mauchly JW (1940) Significance test for sphericity of a normal n-variate distribution. Ann Math Stat 11(2):204–209Google Scholar
  32. McCullagh P (1980) Regression models for ordinal data. J R Stat Soc Ser B 42(2):109–142Google Scholar
  33. Mehta CR, Patel NR (1983) A network algorithm for performing Fisher’s exact test in r \(\times \) c contingency tables. J Am Stat Assoc 78(382):427–434Google Scholar
  34. Nelder JA, Wedderburn RWM (1972) Generalized linear models. J R Stat Soc Ser A \(135\)(3):370–384Google Scholar
  35. Pearson K (1900) On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philos Mag Ser 5 50(302):157–175Google Scholar
  36. Razali NM, Wah YB (2011) Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests. J Stat Model Anal \(2\)(1):21–33Google Scholar
  37. Richter SJ (1999) Nearly exact tests in factorial experiments using the aligned rank transform. J Appl Stat \(26\)(2):203–217Google Scholar
  38. Salter KC, Fawcett RF (1985) A robust and powerful rank test of treatment effects in balanced incomplete block designs. Commun Stat Simul Comput \(14\)(4):807–828Google Scholar
  39. Salter KC, Fawcett RF (1993) The ART test of interaction: a robust and powerful rank test of interaction in factorial models. Commun Stat Simul Comput \(22\)(1):137–153Google Scholar
  40. Sawilowsky SS (1990) Nonparametric tests of interaction in experimental design. Rev Educ Res \(60\)(1):91–126Google Scholar
  41. Shapiro SS, Wilk MB (1965) An analysis of variance test for normality (complete samples). Biometrika \(52\)(3, 4):591–611Google Scholar
  42. Smirnov H (1939) Sur les écarts de la courbe de distribution empirique. Recueil Mathématique (Matematiceskii Sbornik) 6:3–26Google Scholar
  43. Sokal RR, Rohlf FJ (1981) Biometry: the principles and practice of statistics in biological research. W. H. Freeman, OxfordzbMATHGoogle Scholar
  44. Stewart WM (1941) A note on the power of the sign test. Ann Math Stat \(12\)(2):236–239Google Scholar
  45. Stiratelli R, Laird N, Ware JH (1984) Random-effects models for serial observations with binary response. Biometrics 40(4):961–971Google Scholar
  46. Student (1908) The probable error of a mean. Biometrika \(6\)(1):1–25Google Scholar
  47. Tukey JW (1949) Comparing individual means in the analysis of variance. Biometrics 5(2):99–114Google Scholar
  48. Tukey JW (1953) The problem of multiple comparisons. Princeton University, PrincetonGoogle Scholar
  49. von Bortkiewicz L (1898) Das Gesetz der kleinen Zahlen (The law of small numbers). Druck und Verlag von B.G. Teubner, LeipzigGoogle Scholar
  50. Wald A (1943) Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans Amer Math Soc \(54\)(3):426–482Google Scholar
  51. Welch BL (1951) On the comparison of several mean values: an alternative approach. Biometrika \(38\)(3/4):330–336Google Scholar
  52. White H (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48(4):817–838Google Scholar
  53. Wilcoxon F (1945) Individual comparisons by ranking methods. Biomet Bull 1(6):80–83Google Scholar
  54. Wobbrock JO, Findlater L, Gergle D, Higgins JJ (2011) The Aligned Rank Transform for nonparametric factorial analyses using only ANOVA procedures. In: Proceedings of the ACM conference on human factors in computing systems (CHI ’11), Vancouver, British Columbia, 7–12 May 2011. ACM Press, New York, pp 143–146Google Scholar
  55. Zeger SL, Liang K-Y, Albert PS (1988) Models for longitudinal data: a generalized estimating equation approach. Biometrics 44(4):1049–1060Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.The Information SchoolUniversity of WashingtonSeattleUSA
  2. 2.Department of Computer Science and EngineeringUniversity of WashingtonSeattleUSA

Personalised recommendations