An Alternative Multivariate One- and Two-Sample Post Hoc Procedure
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Abstract This paper illustrates the use of a Scheffé-like multivariate post hoc procedure known as the Roy-Bose or simultaneous confidence interval procedure. This method is contrasted with the use of Bonferroni or planned linear combinations for the one- and two-sample cases. The Roy-Bose procedure also is compared to the more frequently employed univariate F tests for post hoc analysis.Keywords:
Post hoc
Post-hoc analysis
Univariate
Bonferroni correction
Sample (material)
Scheffé's method
Multiple comparisons problem
Abstract This paper illustrates the use of a Scheffé-like multivariate post hoc procedure known as the Roy-Bose or simultaneous confidence interval procedure. This method is contrasted with the use of Bonferroni or planned linear combinations for the one- and two-sample cases. The Roy-Bose procedure also is compared to the more frequently employed univariate F tests for post hoc analysis.
Post hoc
Post-hoc analysis
Univariate
Bonferroni correction
Sample (material)
Scheffé's method
Multiple comparisons problem
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Scheffé’s test ( Scheffé, 1953 ), which is commonly used to conduct post hoc contrasts among k group means, is unnecessarily conservative because it guards against an infinite number of potential post hoc contrasts when only a small set would ever be of interest to a researcher. This paper identifies a set of post hoc contrasts based on subsets of the treatment groups and simulates critical values from the appropriate multivariate F-distribution to be used in place of those associated with Scheffé’s test. The proposed method and its critical values provide a uniformly more powerful post hoc procedure.
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Post-hoc analysis
Scheffé's method
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The purpose of this paper is to present basic characteristics and highlight the differences between post hoc tests, as well as to show their application on concrete data of the research conducted. The said tests are applied on data obtained in the research which found evidence of 240 Serbian hotel ratings, given by their 71,700 guests. Each guest rated: cleanliness, comfort, location, facilities, staff, value for money, and free Wi-Fi in the hotel. A difference in ratings in relation to hotel category was observed and explained using several post hoc tests. The use of those tests is made much easier with the development of numerous statistical software packages. Therefore, clearly differentiating each of the tests allows one to select the most appropriate test in the research process, according to the type of data and research objectives. The paper presents the tests used when one-way analysis of variance, which is a method frequently used in statistical processing of experimental data, finds evidence of the existence of statistically significant differences in values of arithmetic mean in groups of data observed. The task of post hoc tests is to determine which group of data leads to the difference observed. Tests thus presented here are: the Fisher LSD, the Tukey HSD, the Bonferroni , the Newman-Keuls, the Dunnett and the Scheffe test.
Scheffé's method
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Post-hoc analysis
Serbian
Bonferroni correction
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Multiple comparisons problem
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Multiple comparisons are repeated tests of a null hypothesis leading to increased Type I error. Methods to adjust for this are the Bonferroni, Scheffé, Tukey procedures applied to pairwise comparison, regression, and ANOVA models. Improvements on Bonferroni (Holm–Hochberg) and Tukey (Newman–Keuls) are presented. The new concept of false discovery rate is introduced. Adjustments for clinical trials include interaction analysis.
Bonferroni correction
Scheffé's method
Multiple comparisons problem
Tukey's range test
False Discovery Rate
Repeated measures design
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Multiple comparison procedures for making linear contrasts and all pairwise multiple comparisons among observed treatment means from designed experiments are introduced. The older and more popular methods of Scheffe, Duncan, Tukey, Student-Newman-Keuls, Fisher, Bonferroni, and Dunnett are described in detail with examples to illustrate their use. Also discussed are some of the new techniques that have gained considerable attention in the literature, such as the methods of Spjoetvoll-Stoline, Games-Howell, Dunn-Sidak, Hotchberg, and Tamhane.
Bonferroni correction
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Multiple comparisons problem
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Abstract Multiple comparison procedures are important tools used in the analysis and interpretation of linear combinations of means from several populations. These procedures are used for two different types of comparisons: 1) the comparisons of all possible pairs of means and 2) testing a set of “g” comparisons. The Scheffé procedure is one of several techniques available for multiple comparisons but is generally regarded as too conservative for most practical analyses. Some authors have suggested ad hoc adjustments to the significance level to overcome the conservative nature of the Scheffé method. A heuristic approach is proposed to achieve the same objective which is quite satisfactory for commonly encountered numbers of comparisons Simulations clearly indicate that the modification of the Scheffé test is always superior to the unmodi-fied Scheffé and has acceptable experimentwise error rates and more power than the Bonferroni test for the investigation of a moderate number of comparisons. Keywords: Linear contrastsPairwise comparisonsBonferroni procedureScheffé procedure
Scheffé's method
Bonferroni correction
Multiple comparisons problem
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Ury & Wiggins (1971) have used the Bonferroni inequality to obtain shorter confidence intervals for multiple comparisons among means, for most situations of interest, than those proposed by Marascuilo (1966). Their attempt to extend this technique to contrasts chosen post hoc has been shown to be not generally valid by Rodger (1973). A valid extension is given here.
Bonferroni correction
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Post hoc
Multiple comparisons problem
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For a number of common multiple comparison procedures controlling Type I error at .05 refers to what Ryan called the experimentwise error rate. This expression represents the chance of making at least one Type I error within a given experiment. This approach ignores, however, the potential detriments of multiple errors within a single experiment, that is, it fails to acknowledge what Ryan referred to as the error rate per experiment. The current study uses a computer simulation to evaluate the differences between experimentwise error rates and error rates per experiment for a variety of multiple comparison procedures. For pairwise comparisons, Newman-Keuls's and Tukey's tests are examined, as is Dunnett's test for comparisons with a control group and Scheffe's test for all possible post hoc comparisons. For planned contrasts, a standard Bonferroni and Shaffer's sequentially rejective Bonferroni are simulated using both a nonorthogonal and an orthogonal set.
Bonferroni correction
Scheffé's method
Multiple comparisons problem
Word error rate
Post hoc
False Discovery Rate
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The online support of IBM SPSS proposes that users alter the syntax when performing post-hoc analyses for interaction effects of ANOVA tests. Other authors also suggest altering the syntax when performing GEE analyses. This being done, the number of possible comparisons (k value) is also altered, therefore influencing the results from statistical tests that k is a component of the formula, such as repeated measures-ANOVA and Bonferroni post-hoc of ANOVA and GEE. This alteration also exacerbates type I error, producing erroneous results and conferring potential misinterpretations of data. Reasoning from this, the purpose of this paper is to report the misuse and improper handling of syntax for ANOVAs and GEE post-hoc analyses in SPSS and to illustrate its consequences on statistical results and data interpretation.
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Post-hoc analysis
Bonferroni correction
Gee
Repeated measures design
Statistical Analysis
Analysis of covariance
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In this paper we have conducted comparison of four post-hoc tests (LSD, Bonferroni, Scheffe, Tukey), whom have we used on four data sets. Every one of four biometrics sets contained three groups and every group had equal number of observations. Data sets differed in size (n 30) and in the coefficient of variation ( CV 20%). We have used one-way analysis of variance, calculated by GLM procedure, to perform statistical analysis. Results were further analysed by computer program Statistica v.8.0. (StatSoft, Inc., 2007). Based on results of analysis we have observed that most liberal of all test was LSD test (lowest statistically significant differences between all observations in all data sets). More conservative tests (Bonferroni, Scheffe and Tukey) had higher values of statistically significant differences between all groups of observations (A-B, A-C and B-C). Also, usage of conservative tests in post-hoc can show no statistical significance between observations, what won't be the case if more liberal tests, like LSD test, are used.
Scheffé's method
Bonferroni correction
Post-hoc analysis
Post hoc
Tukey's range test
Statistical Analysis
Multiple comparisons problem
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