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The discussion on the use and misuse of p-values in 2016 by the American Statistician Association was a timely assertion that statistical concept should be properly used in science. Some researchers, especially the economists, who adopt significance testing and p-values to report their results, may felt confused by the statement, leading to misinterpretations of the statement. In this study, we aim to re-examine the accuracy of the p-value and introduce an alternative way for testing the hypothesis. We conduct a simulation study to investigate the reliability of the p-value. Apart from investigating the performance of p-value, we also introduce some existing approaches, Minimum Bayes Factors and Belief functions, for replacing p-value. Results from the simulation study confirm unreliable p-value in some cases and that our proposed approaches seem to be useful as the substituted tool in the statistical inference. Moreover, our results show that the plausibility approach is more accurate for making decisions about the null hypothesis than the traditionally used p-values when the null hypothesis is true. However, the MBFs of Edwards et al. [Bayesian statistical inference for psychological research. Psychol. Rev. 70(3) (1963), pp. 193–242]; Vovk [A logic of probability, with application to the foundations of statistics. J. Royal Statistical Soc. Series B (Methodological) 55 (1993), pp. 317–351] and Sellke et al. [Calibration of p values for testing precise null hypotheses. Am. Stat. 55(1) (2001), pp. 62–71] provide more reliable results compared to all other methods when the null hypothesis is false. [ABSTRACT FROM AUTHOR]

Although choosing between several alternatives is the basic and most common process of decision-making, it has been well established that when having to decide, people are prone to various biases and seldom elect an alternative rationally. One of the most common and well-researched biases is the 'choice-bias' and many researches demonstrated its effect on decision-makers (both high-level and daily decisions) of the previous generations. This research examined the hypothesis that since the psychological development of 'generation Y' differs significantly from the researched generations, youth today are more resistant to this specific bias. A lifetime of constant exposure to the overabundance of suggestions and opportunities may have influenced decision-making capabilities. A study conducted on two separate groups of students (256 participants) revealed that no choice bias was observed, unlike similar studies conducted with previous generation populations. [ABSTRACT FROM AUTHOR]

Quantifying the uncertainty in hydrological forecasting is valuable for water resources management and decision-making processes. The hydrological uncertainty processor (HUP) can quantify hydrological uncertainty and produce probabilistic forecasts under the hypothesis that there is no input uncertainty. This study proposes a HUP based on a copula function, in which the prior density and likelihood function are explicitly expressed, and the posterior density and distribution obtained using Monte Carlo sampling. The copula-based HUP was applied to the Three Gorges Reservoir, and compared with the meta-Gaussian HUP. The Nash-Sutcliffe efficiency and relative error were used as evaluation criteria for deterministic forecasts, while predictive QQ plot, reliability, resolution and continuous rank probability score (CRPS) were used for probabilistic forecasts. The results show that the proposed copula-based HUP is comparable to the meta-Gaussian HUP in terms of the posterior median forecasts, and that its probabilistic forecasts have slightly higher reliability and lower resolution compared to the meta-Gaussian HUP. Based on the CRPS, both HUPs were found superior to deterministic forecasts, highlighting the effectiveness of probabilistic forecasts, with the copula-based HUP marginally better than the meta-Gaussian HUP. [ABSTRACT FROM PUBLISHER]

It is common practice to treat coverage probability as the only requirement for interval estimation. This allows the use of one-sided confidence intervals. These achieve their coverage probabilities by including parameter values with relative likelihood approaching 0. This violates the law of likelihood, a post-data concept of statistical evidence introduced by Ronald Fisher in 1921. Coverage probability and the law of likelihood are both necessary for interval estimation, but neither is sufficient. When combined, they minimize the possibility of users with the same data, model, and confidence level getting different answers. [ABSTRACT FROM AUTHOR]

The ranked-set sampling literature includes both inference procedures that rely on the assumption of perfect rankings and inference procedures that are robust to violations of this assumption. Procedures that assume perfect rankings tend to be more efficient when rankings are in fact perfect, but they may be invalid when perfect rankings fail. As a result, users of ranked-set sampling must decide between efficiency and robustness, and there is at present little to guide their decision. In this article we introduce three rank-based goodness-of-fit tests that may be consulted in making these decisions. Our strategy in producing these tests is to think of the judgment order statistic classes as separate samples, compute the ranks of the units from each sample within the combined sample, and use these ranks to test whether the judgment rankings are perfect. Consideration of both power and ease of use leads us to recommend use of a test that rejects when the concordance between the vector of mean ranks and its null expectation is small. Tables of critical values and appropriate asymptotic theory for applying this test are provided, and we illustrate the use of the tests by applying them to a biological dataset. [ABSTRACT FROM AUTHOR]

In recent work we introduced a general, a weak, and a strong partitioning principles for the construction of multiple decision procedures as multiple testing or selection procedures. Partitioning principles can be viewed as natural extensions of the closure principle and sometimes yield more powerful decision procedures. In this article we consider the problem of establishing equivalence with the best with respect to k treatment means, where equivalence is defined in terms of a threshold value δ > 0. We reformulate the original selection problem as a multiple testing problem and develop various step-down and step-up procedures by applying the closure principle and partitioning principles. The new step-down procedure is shown to provide a uniform improvement over procedures currently in use. Moreover, we propose some projection methods that yield confidence intervals being compatible with stepwise tests and selection procedures. [ABSTRACT FROM AUTHOR]

It is generally recognized that when deciding on a significance level for a test, its power must also be taken into account. Determination of the optimal significance level, however, is not a straightforward task. It is pointed out here that by use of critical significance level and power we can achieve the usual objective of making a reject-or-accept decision without explicitly determining the optimal significance level. [ABSTRACT FROM AUTHOR]

Explores the use of statistical tests for decision-making in regional geographical construction in the United States. Chi square; Variance analysis; Relationship between regional constructs and the areal dispersion of selected traits within regional frames.

Cronholm and Revusky [4] have proposed a rank test based on independent subexperiments for the comparison of a treatment effect with a control when the treatment is destructive but the control produces at most a transient effect. This article provides a thorough study of its performance under two sampling situations. With the aid of a computer, the exact small sample power of the test is evaluated for some important alternatives. A modification of the test is proposed for the situation where numerical measurements are available rather than merely the ranks within each stage. The modification is found to substantially improve the power. Both tests are shown to be unbiased. Finally, the Pitman asymptotic efficiencies are obtained and comparisons are made with the appropriate Wilcoxon tests. [ABSTRACT FROM AUTHOR]

A double sample test for a hypothesis concerning the mean mu of a normal random variable with unknown variance sigma[sup 2] is presented in this note. This test is an alternative to the usual single sample t test and is made by taking samples at two stages. After the first sample has been observed the hypothesis is rejected, accepted or a second sample is taken. This double sample test is a modification of a double sample test suggested by D. Owen. However, for the test being suggested here if the second sample is taken the information from the first sample is used in making the final decision. A table is included which is a tabulation of the rejection and acceptance points for various sample sizes and alpha = .05 and alpha = .01. Additional tables are included which give some power values and expected sample sizes for the new test and Owen's test. These power values are compared with power values of various single sample t tests. Conclusions about desirable sample sizes are presented for both the new test and Owen's test. [ABSTRACT FROM AUTHOR]

In an earlier paper [5] the authors compared the power of the BLUS test with the probability of a correct decision of the Durbin-Watson bounds test. A method to compute the distribution of the Von Neumann ratio under the null hypothesis and under the alternative hypothesis was given. In the present paper the latter method is used to tabulate the BLUS-test statistic and to compute the exact significance points of the Durbin-Watson test for several examples. Powers of both tests are computed and compared. It appears that, for the cases considered, the power of the exact Durbin-Watson test exceeds that of the BLUS procedure, while the latter is greater than the probability of a correct decision in the Durbin-Watson bounds test. [ABSTRACT FROM AUTHOR]

The problem of iterated tests of hypotheses has been treated from the standpoint of multiple decision theory. Under the assumption that there is a UMP test (not necessarily similar) for each component hypothesis, a procedure has been developed which ensures an upper bound for various probabilities of misclassification and which maximizes the probabilities of correct classification in some class. [ABSTRACT FROM AUTHOR]