Evaluating Rank Histograms Using Decompositions of the Chi-Square Test Statistic

Jolliffe, Ian T.; Primo, Cristina
June 2008
Monthly Weather Review;Jun2008, Vol. 136 Issue 6, p2133
Academic Journal
Rank histograms are often plotted to evaluate the forecasts produced by an ensemble forecasting system—an ideal rank histogram is “flat” or uniform. It has been noted previously that the obvious test of “flatness,” the well-known χ2 goodness-of-fit test, spreads its power thinly and hence is not good at detecting specific alternatives to flatness, such as bias or over- or underdispersion. Members of the Cramér–von Mises family of tests do much better in this respect. An alternative to using the Cramér–von Mises family is to decompose the χ2 test statistic into components that correspond to specific alternatives. This approach is described in the present paper. It is arguably easier to use and more flexible than the Cramér–von Mises family of tests, and does at least as well as it in detecting alternatives corresponding to bias and over- or underdispersion.


Related Articles

  • LIMITED INFORMATION GOODNESS-OF-FIT TESTING IN MULTIDIMENSIONAL CONTINGENCY TABLES. Maydeu-Olivares, Albert; Joe, Harry // Psychometrika;Dec2006, Vol. 71 Issue 4, p713 

    We introduce a family of goodness-of-fit statistics for testing composite null hypotheses in multidimensional contingency tables. These statistics are quadratic forms in marginal residuals up to order r. They are asymptotically chi-square under the null hypothesis when parameters are estimated...

  • ON A GENERAL CLASS OF CHI-SQUARED GOODNESS-OF-FIT STATISTICS. Kvålseth, Tarald O. // Perceptual & Motor Skills;Jun2004 Part 1, Vol. 98 Issue 3, p967 

    A class of chi-squared goodness-of-fit statistics is presented as being based on the so-called divergence of one probability distribution from another. A still more general class of goodness-of-fit statistics is then presented by eliminating some of the restrictions required of divergence-based...

  • Stepwise variable selection in factor analysis. KANO, YUTAKA; HARADA, AKIRA // Psychometrika;Mar2000, Vol. 65 Issue 1, p7 

    It is very important to choose appropriate variables to be analyzed in multivariate analysis when there are many observed variables such as those in a questionnaire. What is actually done in scale construction with factor analysis is nothing but variable selection. In this paper, we take several...

  • Diversity indices to test the goodness of fit to the broken stick distribution. Almorza, David; García, María Hortensia; Salerno, Juan Carlos // International Journal of Computer Science Issues (IJCSI);Sep2014, Vol. 11 Issue 5, p22 

    In this paper, we present the Shannon diversity index, the Shannon exponential index and the Margalef diversity index to test the goodness of fit to the broken stick distribution in several populations. The chi-squared test is the most common test to fit the broken stick distribution, but it has...

  • TWO TI-83 CHI-SQUARE PROGRAMS FOR ELEMENTARY STATISTICS. Thomas, John P. // Mathematics & Computer Education;Winter2000, Vol. 34 Issue 1, p35 

    The article discusses the programs for conducting the Chi-Square test that provide features not available on the TI-83 calculator. The TI-83 calculator has several built-in programs to run various inferential statistics tests, some of which include the one-sample mean z and t-tests. It also has...

  • Testing for censored bivariate distributions with applications to environmental data. Sürücü, Barış // Environmental & Ecological Statistics;Dec2015, Vol. 22 Issue 4, p637 

    Analysis of censored environmental data has been of special interest to many scientists and practitioners for the recent years. Numerous works have been published on modeling bivariate environmental data when variables of interest are below some detection limits. Depending on the problem, one of...

  • A Least Squares Estimation Method for the Linear Learning Model. Wierenga, Berend // Journal of Marketing Research (JMR);Feb1978, Vol. 15 Issue 1, p145 

    The author presents a new method for estimating the parameters of the linear learning model. The procedure, essentially a least squares method, is easy to carry out and avoids certain difficulties of earlier estimation procedures. Applications to three different data sets are reported, as well...

  • Goodness-of-Fit Tests Based on Sample Space Partitions: a Unifying Overview. Thas, O.; Ottoy, J.P. // Journal of Applied Mathematics & Decision Sciences;2002, Vol. 6 Issue 4, p203 

    Provides an overview of the construction of goodness-of-fit tests based on sample space partitions (SSP). Power characteristics of the tests; Example of the one-sample SSP test.

  • AN ASYMMETRIC TEST OF HOMOGENEITY OF PROPORTIONS. Berry, Kenneth J.; Mielke Jr., Paul W. // Psychological Reports;Aug2000, Vol. 87 Issue 1, p259 

    Presents an asymmetrical alternative to the chi square test of homogeneity. Advantages of an asymmetrical test of homogeneity of proportions over a symmetrical test; Use of product multinomial sampling; Description of the Pearson X2 test of homogeneity.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics