Methods for incorporating ordinal information into analysis of variance: Generalizations of one‐tail testsSmith, Philip T.; Macdonald, Ranald R.
doi: 10.1111/j.2044-8317.1983.tb00762.xpmid: N/A
Methods for incorporating ordinal assumptions into the analysis of the means of k treatments (k > 2) are critically reviewed. These methods are examined under three headings: (1) Global: statistics that give an overall assessment of the presence of a trend in the data (e.g. linear and isotonic regression); (2) Multiple comparisons: statistics based on the repetition (explicit or implicit) of comparisons between pairs of treatments; (3) Joint probability: two statistics are computed, one giving an overall assessment of the differences between the means, the other assessing the specifically ordinal information in the data; the joint significance level of these two statistics is then determined. Numerical examples of all the methods are provided.
Testing for differences between means with ordered hypothesesMacdonald, Ranald R.; Smith, Philip T.
doi: 10.1111/j.2044-8317.1983.tb00763.xpmid: N/A
A technique for incorporating an experimenter's predictions of orderings of the treatment means into an analysis of variance testing procedure is presented. The experimenter's predictions are assessed in terms of a statistic based on the ordering of the means (e.g. Kendall's tau). The product of the significances of this statistic and of F is used to obtain the significance level. In comparison with other approaches simulations show this to be the most appropriate technique where the experimenter can predict the order of the treatment means but wishes to have reasonable power even if the predicted ordering is wrong.
A quasi‐statistical model for choosing between alternative configurations derived from ordinally constrained dataLingoes, James C.; Borg, Ingwer
doi: 10.1111/j.2044-8317.1983.tb00764.xpmid: N/A
Present‐day users of MDS techniques are confronted with many choices and options, e.g. whether to use A's procedure or B's,…, whether to select m or m + 1 dimensions, whether to use a metric or ordinally based MDS, would a few more iterations make any difference, is configuration A equivalent to B, has an hypothesis been confirmed or not, …, etc.—in sum, what are the consequences of such choices and on what basis does one select? In this difficult research environment there is little (and sometimes conflicting) guidance. We shall suggest a possible strategy and an objective, quasi‐statistical decision model for such choices, since there are no statistical models completely free from criticism when used in the MDS context.
Non‐linear canonical correlation †Burg, Eeke; Leeuw, Jan
doi: 10.1111/j.2044-8317.1983.tb00765.xpmid: N/A
Non‐linear canonical correlation analysis is a method for canonical correlation analysis with optimal scaling features. The method fits many kinds of discrete data. The different parameters are solved for in an alternating least squares way and the corresponding program is called CANALS. An application of CANALS is discussed and also a study of the stability of the scaling results.
Combining independent estimators in research synthesisHedges, Larry V.
doi: 10.1111/j.2044-8317.1983.tb00768.xpmid: N/A
Extensive research literatures in the social sciences have led some research reviewers to the use of quantitative methods for research synthesis. The methods used most frequently involve estimation of a standardized mean difference (Glass's effect size). Reviewers frequently wish to examine the relationship between study characteristics (experimental conditions) and effect size. This paper presents asymptotic theory for the analysis of linear models for effect sizes. These procedures can be used to obtain efficient estimates of effect size, fit linear models to effect size data and test model specification.
Some non‐parametric tests for analysing ranked data in multi‐group repeated measures designsKatz, Barry M.; McSweeney, Maryellen
doi: 10.1111/j.2044-8317.1983.tb00770.xpmid: N/A
This paper develops two statistical techniques for analysing ranked data. The first technique can be used in designs in which c independent groups of subjects are asked to rank order p objects with respect to a specified criterion. An explicit statement of a statistic which can be used to determine whether differences in ranking patterns exist between the groups is presented together with associated post hoc procedures. The statistic is a generalization of a technique developed by Hollander & Sethuraman (1978). The second technique developed can be used in designs in which subjects in c independent groups are each asked to rank order a set of p items with respect to a certain criterion under q different conditions of ranking. An explicit statement of a statistic which can be used to test the groups by items by conditions three‐way interaction hypothesis is presented together with an analysis strategy for testing the other effects of interest.