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      Evaluating statistical difference, equivalence, and indeterminacy using inferential confidence intervals: An integrated alternative method of conducting null hypothesis statistical tests.

      Psychological Methods
      American Psychological Association (APA)

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          Abstract

          Null hypothesis statistical testing (NHST) has been debated extensively but always successfully defended. The technical merits of NHST are not disputed in this article. The widespread misuse of NHST has created a human factors problem that this article intends to ameliorate. This article describes an integrated, alternative inferential confidence interval approach to testing for statistical difference, equivalence, and indeterminacy that is algebraically equivalent to standard NHST procedures and therefore exacts the same evidential standard. The combined numeric and graphic tests of statistical difference, equivalence, and indeterminacy are designed to avoid common interpretive problems associated with NHST procedures. Multiple comparisons, power, sample size, test reliability, effect size, and cause-effect ratio are discussed. A section on the proper interpretation of confidence intervals is followed by a decision rule summary and caveats.

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          Most cited references51

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          Statistical methods in psychology journals: Guidelines and explanations.

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            Using confidence intervals in within-subject designs.

            We argue that to best comprehend many data sets, plotting judiciously selected sample statistics with associated confidence intervals can usefully supplement, or even replace, standard hypothesis-testing procedures. We note that most social science statistics textbooks limit discussion of confidence intervals to their use in between-subject designs. Our central purpose in this article is to describe how to compute an analogous confidence interval that can be used in within-subject designs. This confidence interval rests on the reasoning that because between-subject variance typically plays no role in statistical analyses of within-subject designs, it can legitimately be ignored; hence, an appropriate confidence interval can be based on the standard within-subject error term-that is, on the variability due to the subject × condition interaction. Computation of such a confidence interval is simple and is embodied in Equation 2 on p. 482 of this article. This confidence interval has two useful properties. First, it is based on the same error term as is the corresponding analysis of variance, and hence leads to comparable conclusions. Second, it is related by a known factor (√2) to a confidence interval of the difference between sample means; accordingly, it can be used to infer the faith one can put in some pattern of sample means as a reflection of the underlying pattern of population means. These two properties correspond to analogous properties of the more widely used between-subject confidence interval.
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              Multiple Hypothesis Testing

              J. Shaffer (1995)
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                Author and article information

                Journal
                Psychological Methods
                Psychological Methods
                American Psychological Association (APA)
                1939-1463
                1082-989X
                2001
                2001
                : 6
                : 4
                : 371-386
                Article
                10.1037/1082-989X.6.4.371
                11778678
                55dd458f-8f71-4082-9a09-ece2e89b691c
                © 2001
                History

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