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The numerical strength of the evidence of matching DNA profiles is conveyed by a likelihood ratio. This is the probability under one hypothesis, generally from the Prosecution, divided by the probability of the evidence under an alternative hypothesis, generally from the Defense. The probabilities can be calculated to reflect the effects of population structure or of relatedness between individuals listed under the alternative hypotheses.

Background Misinterpretations of the p-value in null-hypothesis statistical testing are common. We aimed to determine the implications of observed p-values in critical care randomized controlled trials (RCTs). Methods We included three cohorts of published RCTs: Adult-RCTs reporting a mortality outcome, Pediatric-RCTs reporting a mortality outcome, and recent Consecutive-RCTs reporting p-value ≤.10 in six higher-impact journals. We recorded descriptive information from RCTs. Reverse Bayesian implications of obtained p-values were calculated, reported as percentages with inter-quartile ranges. Results Obtained p-value was ≤.005 in 11/216 (5.1%) Adult-RCTs, 2/120 (1.7%) Pediatric-RCTs, and 37/90 (41.1%) Consecutive-RCTs. An obtained p-value .05–.0051 had high False Positive Rates; in Adult-RCTs, minimum (assuming prior probability of the alternative hypothesis was 50%) and realistic (assuming prior probability of the alternative hypothesis was 10%) False Positive Rates were 16.7% [11.2, 21.8] and 64.3% [53.2, 71.4]. An obtained p-value ≤.005 had lower False Positive Rates; in Adult-RCTs the realistic False Positive Rate was 7.7% [7.7, 16.0]. The realistic probability of the alternative hypothesis for obtained p-value .05–.0051 (ie, Positive Predictive Value) was 28.0% [24.1, 34.8], 30.6% [27.7, 48.5], 29.3% [24.3, 41.0], and 32.7% [24.1, 43.5] for Adult-RCTs, Pediatric-RCTs, Consecutive-RCTs primary and secondary outcome, respectively. The maximum Positive Predictive Value for p-value category .05–.0051 was median 77.8%, 79.8%, 78.8%, and 81.4% respectively. To have maximum or realistic Positive Predictive Value >90% or >80%, RCTs needed to have obtained p-value ≤.005. The credibility of p-value .05–.0051 findings were easy to challenge, and the credibility to rule-out an effect with p-value >.05 to .10 was low. The probability that a replication study would obtain p-value ≤.05 did not approach 90% unless the obtained p-value was ≤.005. Conclusions Unless the obtained p-value was ≤.005, the False Positive Rate was high, and the Positive Predictive Value and probability of replication of “statistically significant” findings were low.

This paper proposes two ratio-type statistics to sequentially detect mean and variance change-points in the long-memory time series. The limiting distributions of monitoring statistics under the no change-point null hypothesis, alternative hypothesis as well as change-point misspecified hypothesis are proved. In particular, a sieve bootstrap approximation method is proposed to determine the critical values. Simulations indicate that the new monitoring procedures have better finite sample performance than the available off-line tests when the change-point nears to the beginning time of monitoring, and can discriminate between mean and variance change-point. Finally, the authors illustrate their procedures via two real data sets: A set of annual volume of discharge data of the Nile river, and a set of monthly temperature data of northern hemisphere. The authors find a new variance change-point in the latter data.

We conducted a preregistered multilaboratory project ( k = 36; N = 3,531) to assess the size and robustness of ego-depletion effects using a novel replication method, termed the paradigmatic replication approach. Each laboratory implemented one of two procedures that was intended to manipulate self-control and tested performance on a subsequent measure of self-control. Confirmatory tests found a nonsignificant result ( d = 0.06). Confirmatory Bayesian meta-analyses using an informed-prior hypothesis (δ = 0.30, SD = 0.15) found that the data were 4 times more likely under the null than the alternative hypothesis. Hence, preregistered analyses did not find evidence for a depletion effect. Exploratory analyses on the full sample (i.e., ignoring exclusion criteria) found a statistically significant effect ( d = 0.08); Bayesian analyses showed that the data were about equally likely under the null and informed-prior hypotheses. Exploratory moderator tests suggested that the depletion effect was larger for participants who reported more fatigue but was not moderated by trait self-control, willpower beliefs, or action orientation.

In one-sided testing, Bayesians and frequentists differ on whether or not there is discrepancy between the inference based on the posterior model probability and that based on the p value. We add some arguments to this debate analyzing the discrepancy for moderate and large sample sizes. For small and moderate samples sizes, the discrepancy is measured by the probability of disagreement. Examples of the discrepancy on some basic sampling models indicate the somewhat unexpected result that the probability of disagreement is larger when sampling from models in the alternative hypothesis that are not located at the boundary of the hypotheses. For large sample sizes, we prove that the Bayesian one-sided testing is, under mild conditions, consistent, a property that is not shared by the frequentist procedure. Further, the rate of convergence is $$O(e^{nA})$$ , where A is a constant that depends on the model from which we are sampling. Consistency is also proved for an extension to multiple hypotheses.

The aim of this study is to find out whether or not the use of vlog will enhance the vocabulary of the students. This study used pre-experimental studies consisting of pre-test, treatment, and post-test. The participants in the study were 25 students of the second grade students of Universitas Muhammadiyah Bulukumba. Based on the findings of the study, there is a substantial difference between the mean pre-test score and the mean post-test score, from a very bad classification to a decent classification. In addition, the t-test value of this analysis (16,12) is greater than the t-table value (3,745) with a degree of significance of 0,05. It means that it supports the alternative hypothesis.

This research aims to determine how the implementation and the effect of scientific integration in learning toward the formation of students' morals. The method used in this research was descriptive using a quantitative approach, for data collection was obtained from questionnaires, interviews, and documentation studies. Meanwhile, the data analysis used the percentage technique for descriptive data and linear regression technique for quantitative data. The results obtained in this study explain that the application of scientific integration is included in the very good category with the acquisition of a percentage of 84%. Second, students' moral formation is in the very good category with a percentage gain of 80.5%. Third, the result of a linear regression calculation shows that the alternative hypothesis (Ha) is accepted and hypothesis Null (H0) is rejected. Science integration contributes 20.1% to the moral formation of students.

Friedman's test is a rank-based procedure that can be used to test for differences among t treatment distributions in a randomized complete block design. It is well-known that the test has reasonably good power under locationshift alternatives to the null hypothesis of no difference in the t treatment distributions. However the power of Friedman's test when the alternative hypothesis consists of a non-location difference in treatment distributions can be poor. We develop the properties of an alternative rank-based test that has greater power than Friedman's test in a variety of such circumstances. The test is based on the joint distribution of the possible permutations of the treatment ranks within a block (assuming no ties). We show when our proposed test will have greater power than Friedman's test, and provide results from extensive numerical work comparing the power of the two tests under various configurations for the underlying treatment distributions.

Performance as an ability that a person has includes knowledge and skills. In the world of work, performance is the capacity that exists in a person to fulfill his work responsibilities so as to produce good output. The employee's performance will be said to be successful and optimal if it is in accordance with the company's desired results. The need for information systems to produce optimal employee performance is needed by computers based on Information Technology (computerization), so that it is not only able to optimize employee performance but also facilitate decision making for management because the data and information produced are fast and accurate. To find out the influence of management information system on employee performance, research was made. Thepurpose of this study is to analyze and test the influence of management information system on employee performance. In this study the population is PT Arta Boga Cemerlang Cirebon Branch,Jln. Nyi Gede Cangkring No. 99. To make it easier, save time, effort and cost, the researchers determined the size of the sample based on the Slovin formula. The sample obtained was 55 employees. Data analysis tools used in this study are validity and reliability test, significance test (t test), product moment correlation test (r test), determination coefficient (R2),and linear regression. From this research, it can be concluded that there is a positive and significantinfluence between management information system and employee performance, this can be seen from the results of the study showed a correlation of 0.68 and t calculate = 6,75. From the calculation result t calculate greater than t table which is 6.75 > 2.021; thus Ho hypothesis is rejected and ha alternative hypothesis accepted, i.e. there is a significant influence between management information system on employee performance. The coefficient value of determination of 0.46 or 46%,means that the variation in employee performance change(Y) is influenced by management information system (X) by 46%and the remaining 54%isinfluenced by other factors that are not calculated. Regression test results showed that management information system variables had a positive effect on employee performance with a coefficient of0.96. Performance as an ability that a person has includes knowledge and skills. In the world of work, performance is the capacity that exists in a person to fulfill his work responsibilities so as to produce good output. The employee's performance will be said to be successful and optimal if it is in accordance with the company's desired results. The need for information systems to produce optimal employee performance is needed by computers based on Information Technology (computerization), so that it is not only able to optimize employee performance but also facilitate decision making for management because the data and information produced are fast and accurate. To find out the influence of management information system on employee performance, research was made. Thepurpose of this study is to analyze and test the influence of management information system on employee performance. In this study the population is PT Arta Boga Cemerlang Cirebon Branch,Jln. Nyi Gede Cangkring No. 99. To make it easier, save time, effort and cost, the researchers determined the size of the sample based on the Slovin formula. The sample obtained was 55 employees. Data analysis tools used in this study are validity and reliability test, significance test (t test), product moment correlation test (r test), determination coefficient (R2),and linear regression. From this research, it can be concluded that there is a positive and significantinfluence between management information system and employee performance, this can be seen from the results of the study showed a correlation of 0.68 and t calculate = 6,75. From the calculation result t calculate greater than t table which is 6.75 > 2.021; thus Ho hypothesis is rejected and ha alternative hypothesis accepted, i.e. there is a significant influence between management information system on employee performance. The coefficient value of determination of 0.46 or 46%,means that the variation in employee performance change(Y) is influenced by management information system (X) by 46%and the remaining 54%isinfluenced by other factors that are not calculated. Regression test results showed that management information system variables had a positive effect on employee performance with a coefficient of0.96.

The present study was conducted to explore both the differential and inferential analysis of technology applications and benefits in two country university students. In-depth statistical analysis with parametric and non-parametric tests was performed on primary samples collected from Indian and Hungarian universities. We assumed six null hypotheses and their corresponding alternative hypotheses in line three major objectives of our study. The first two null hypotheses were tested with the Student T-test, and the rest of the four hypotheses were tested with Correspondence Analysis (CA) advance dimension reduction approach. Supporting with results of Cramer’s V (CV) inclusive Fisher’s Exact (FE) and $Chi^{2}$ tests, an in-depth analysis was also performed. The result of the T-test proved that country variable not impacted by Technology Use due to insignificant ${p}$ value ( ${p}$ > 0.05). But, Technology Benefit affected two-country students with significant ${p}$ value ( ${p}$ ${p}$ ${p}$ ${p}$ ${p}$ > 0.05). The paper’s findings are evident in higher technology awareness and association among Hungarian students than Indian students. We also proposed a real-time conceptual design to estimate the differential and inferential analysis using a web application to avoid the conventional method. Our proposed models might be helpful not only for two countries but also for inter-continent institutions to work in a collaborative project to measure; exchange student’s and educators’ perceptions about the technology. Based on the results, we also proposed a futuristic real-time technology impact identification for a university to integrate with extant “E-lection,” a class response system.

Single‐arm one‐ or multi‐stage study designs are commonly used in phase II oncology development when the primary outcome of interest is tumor response, a binary variable. Both two‐ and three‐outcome designs are available. Simon two‐stage design is a well‐known example of two‐outcome designs. The objective of a two‐outcome trial is to reject either the null hypothesis that the objective response rate (ORR) is less than or equal to a pre‐specified low uninteresting rate or to reject the alternative hypothesis that the ORR is greater than or equal to some target rate. Three‐outcome designs proposed by Sargent et al. allow a middle gray decision zone which rejects neither hypothesis in order to reduce the required study size. We propose new two‐ and three‐outcome designs with continual monitoring based on Bayesian posterior probability that meet frequentist specifications such as type I and II error rates. Futility and/or efficacy boundaries are based on confidence functions, which can require higher levels of evidence for early versus late stopping and have clear and intuitive interpretations. We search in a class of such procedures for optimal designs that minimize a given loss function such as average sample size under the null hypothesis. We present several examples and compare our design with other procedures in the literature and show that our design has good operating characteristics.

The p value is still misinterpreted as the probability that the null hypothesis is true. Even psychologists who correctly understand that p values do not provide this probability may not realize the degree to which p values differ from the probability that the null hypothesis is true. Importantly, previous research on this topic has not addressed the influence of multiple testing, often a reality in psychological studies, and has not extensively considered the influence of different prior probabilities favoring the null and alternative hypotheses. Simulation studies are presented that emphasize the magnitude by which p values are distinct from the posterior probability that the null hypothesis is true, under an extensive set of conditions including multiple testing. Particular emphasis is placed on p values just under .05, given the prevalence of these p values in the published literature, though p values in other intervals are also assessed. In diverse conditions, results indicate that posterior probabilities favoring the null hypothesis are often far removed from .05, and this pattern quickly gets much worse when multiple testing is conducted. Rather than simply telling researchers that p values do not reflect the probability favoring the null hypothesis, as has been done previously, the results presented here allow psychologists to see the evidence provided by various p values. These results have particularly topical implications for the replication crisis, for how much weight should be placed on a single study, and for how the term statistical significance should be interpreted, particularly in conditions typical in psychological research. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

This article introduces a global hypothesis test intended for studies with multiple endpoints. Our test makes use of a priori predictions about the direction of the result of each endpoint and we weight these predictions using the sample correlation matrix. The global alternative hypothesis concerns a parameter, ϕ , defined as the researcher's ability to correctly predict the direction of each measure, essentially a binomial parameter. This allows for the test to include expected effects that are all positive, all negative or both while still using the cumulative information across those endpoints. A rejection of the null hypothesis ( H0:ϕ≤ϕ0 ) provides evidence that the researcher's underlying theory about the natural process provides a better prediction of the observed results relative to the null hypothesized predictive ability, thus indicating the theory is worthy of further study. We compare our test to O'Brien's ordinary least squares (OLS) test and show that for small samples and situations where the effect is not in the same direction across all endpoints our approach has better power, while if the effect is equidirectional across all endpoints the OLS test can have greater power.

Researchers often misinterpret and misrepresent statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and $P$-values with confidence intervals, Bayes factors, and other devices. Because the core problems appear cognitive rather than statistical, we review simple aids to statistical interpretations. These aids emphasize logical and information concepts over probability, and thus may be more robust to common misinterpretations than are traditional descriptions. We use the Shannon transform of the $P$-value $p$, also known as the binary surprisal or $S$-value $s=-\log_{2}(p)$, to measure the information supplied by the testing procedure, and to help calibrate intuitions against simple physical experiments like coin tossing. We also use tables or graphs of test statistics for alternative hypotheses, and interval estimates for different percentile levels, to thwart fallacies arising from arbitrary dichotomies. Finally, we reinterpret $P$-values and interval estimates in unconditional terms, which describe compatibility of data with the entire set of analysis assumptions. We illustrate these methods with a reanalysis of data from an existing record-based cohort study. In line with other recent recommendations, we advise that teaching materials and research reports discuss $P$-values as measures of compatibility rather than significance, compute $P$-values for alternative hypotheses whenever they are computed for null hypotheses, and interpret interval estimates as showing values of high compatibility with data, rather than regions of confidence. Our recommendations emphasize cognitive devices for displaying the compatibility of the observed data with various hypotheses of interest, rather than focusing on single hypothesis tests or interval estimates. We believe these simple reforms are well worth the minor effort they require., 22 pages; 5 figures; 2 tables; 94 references; Published at BMC Medical Research Methodology

Alternative hypotheses for order restrictions, such as umbrella or inverse umbrella (a.k.a tree) orderings, have been studied extensively in the literature, although less so when the studied response for each individual is the presence or absence of the event of interest. Two families of test statistics for solving the problem of testing against an umbrella or a tree ordering when the responses are binomial proportions are studied in this work and their asymptotic distributions are derived. A simulation study is conducted to compare the empirical power of some members of the derived families of test statistics with competing approaches. The methodology developed here was driven by an applied problem arising in stored products research where despite universal mortality in the case of doses of 1000 ppm of the insecticide phosphine, unexpected survival was noted at higher doses.

This paper investigates the hypothesis test of the parametric component in partial functional linear regression models. Based on a rank score function, the authors develop a rank test using functional principal component analysis, and establish the asymptotic properties of the resulting test under null and local alternative hypotheses. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. The authors also present an illustration through fitting the Berkeley Growth Data and testing the effect of gender on the height of kids.

EFFECT OF THE APPLICATION OF THE DISCOVERY LEARNING MODEL ON LEARNING OUTCOMES IN MATHEMATICS SUBJECTS Effect of the Application of the Discovery Learning Model on Learning Outcomes in Mathematics Subjects in Class IV of Padarincang Elementary School, Cianjur Regency. This study aims to determine the effect of Discovery Learning models on the mathematics learning outcomes of statistical material. The experimental class N-Gain calculation (Discovery Learning group) is 56.99 while the control class N-Gain value (conventional group) is 43.81. So that the N-Gain value in the experimental class is greater than the control class. In the normality test with Lilliefors test both samples were normally distributed because the values of the two samples were smaller than L table . In the Discovery Learning group in L count (0.097) ≤ L table (0.147), in the conventional group obtained L count (0.107) ≤ L table (0.170). Then in the homogeneity test with Fisher's test the value of F count (1.39) ≤ F table (1.81) is obtained. Furthermore, the hypothesis test obtained a value of t count of 3.222 greater than t table of 1.99962, indicating that Ho (null hypothesis) is rejected and H a (alternative hypothesis) is accepted. Based on the results of the above research, it can be concluded that the Discovery Learning model has more influence compared to the conventional learning model towards the improvement of learning outcomes of fourth grade students of Padarincang State Elementary School in Cianjur district even semester 2018/2019 academic year.

The score test statistic computed using the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the likelihood-ratio test and the Wald test. However, several authors have noted that under the alternative hypothesis this no longer holds and in particular the score statistic computed using the observed information can take negative values. We extend the body of work on the score test to a problem of interest in ecology when studying the occurrence of species. This is the comparison of two zero-inflated binomial random variables from two independent samples under imperfect detection. An analysis of eigenvalues associated with the score test in this setting assists in understanding why using the observed information matrix in the score test can be problematic. We demonstrate through a combination of simulations and theoretical analysis that the power of the score test calculated under the observed information decreases as the populations being compared become more dissimilar. In particular, the score test based on the observed information is inconsistent. Finally, we propose a modified rule that rejects the null hypothesis when the score statistic is computed using the observed information is negative or is larger than the usual chi-square cut-off. In simulations in our setting this has power that is comparable to the Wald and likelihood ratio tests and consistency is largely restored. Our new test is easy to use and inference is possible. Supplementary material for this article is available online as per journal instructions.

We consider block bootstrappings for panel mean change test of the squared CUSUM test of Horvath and Huskova (J Time Ser Anal 33:631–648, 2012): the circular block bootstrapping and stationary bootstrapping. First order asymptotic null validity of the test is proved under serial and/or cross-sectional correlation. Consistency of the test under an alternative hypothesis is also proved. A Monte-Carlo experiment reveals that the existing tests of Horvath and Huskova (2012) and others have severe size distortions for serially and/or cross-sectionally correlated panels, and the block bootstrappings remedy this size distortion problem. A real data analysis illustrates the proposed method.

Background: It is never easy to make sample size calculation for two-arm, non-inferiority studies with a primary proportion outcome not only because the different parameterisations involved in the difference, ratio, and odds ratio models lead to different non-inferiority margins and different sample size results, but also because of the different efficiency of the respective sample size formulae. Methods: According to a formal statistical approach, we showed how to express the non-inferiority margins of the three models by keeping the probability (success or failure) of the standard treatment fixed (considered as “known” in the planning phase of a trail), and equal under the null and alternative hypotheses as the statistical basis for sample size calculation. Results: We have obtained the sample size formulae and their respective power formulae for the three considered models both for success and failure probabilities. A sample size table for non-inferiority success studies is reported for illustrative purposes. In addition, we have compared the sample sizes from the three models by means of graphic and theoretical approaches and we have shown their asymptotic relationships. Furthermore, we have obtained the formulae for switching among the three considered models. Finally, we have correct some previously published formulae for sample size calculations. Conclusion: The clearly separate approach to the probabilities of success and failure of the three considered models shown in this paper makes it possible to switch among them consistently and equivalently and to choose the probability formulation for the most parsimonious model.

In the absence of uniformly most powerful (UMP) tests or uniformly most powerful invariant (UMPI) TESTS, King (1987c) suggested the use of Point Optimal (PO) tests, which are most powerful at a chosen point under the alternative hypothesis. This paper surveys the literature and major developments on point optimal testing since 1987 and suggests some areas for future research. Topics include tests for which all nuisance parameters have been eliminated and dealing with nuisance parameters via (i) a weighted average of p values, (ii) approximate point optimal tests, (iii) plugging in estimated parameter values, (iv) using asymptotics and (v) integration. Progress on using point-optimal testing principles for two-sided testing and multi-dimensional alternatives is also reviewed. The paper concludes with thoughts on how best to deal with nuisance parameters under both the null and alternative hypotheses, as well as the development of a new class of point optimal test for multi-dimensional testing.

Multiple imputation (MI) inference handles missing data by imputing the missing values $m$ times, and then combining the results from the $m$ complete-data analyses. However, the existing method for combining likelihood ratio tests (LRTs) has multiple defects: (i) the combined test statistic can be negative, but its null distribution is approximated by an $F$-distribution; (ii) it is not invariant to re-parametrization; (iii) it fails to ensure monotonic power owing to its use of an inconsistent estimator of the fraction of missing information (FMI) under the alternative hypothesis; and (iv) it requires nontrivial access to the LRT statistic as a function of parameters instead of data sets. We show, using both theoretical derivations and empirical investigations, that essentially all of these problems can be straightforwardly addressed if we are willing to perform an additional LRT by stacking the $m$ completed data sets as one big completed data set. This enables users to implement the MI LRT without modifying the complete-data procedure. A particularly intriguing finding is that the FMI can be estimated consistently by an LRT statistic for testing whether the $m$ completed data sets can be regarded effectively as samples coming from a common model. Practical guidelines are provided based on an extensive comparison of existing MI tests. Issues related to nuisance parameters are also discussed., Comment: To appear in Statistica Sinica

Cancer immunotherapy trials have two special features: a delayed treatment effect and a cure rate. Both features violate the proportional hazards model assumption and ignoring either one of the two features in an immunotherapy trial design will result in substantial loss of statistical power. To properly design immunotherapy trials, we proposed a piecewise proportional hazards cure rate model to incorporate both delayed treatment effect and cure rate into the trial design consideration. A sample size formula is derived for a weighted log-rank test under a fixed alternative hypothesis. The accuracy of sample size calculation using the new formula is assessed and compared with the existing methods via simulation studies. A real immunotherapy trial is used to illustrate the study design along with practical consideration of balance between sample size and follow-up time.

Asymptotic distribution theory for maximum likelihood estimators under fixed alternative hypotheses is reported in the literature even though the power of any realistic test converges to one under fixed alternatives. Under fixed alternatives, authors have established that nuisance parameter estimates are inconsistent when sample size re-estimation (SSR) follows blinded randomization. These results have helped to inhibit the use of SSR. In this paper, we argue for local alternatives to be used instead of fixed alternatives. Motivated by Gould and Shih (1998), we treat unavailable treatment assignments in blinded experiments as missing data and rely on single imputation from marginal distributions to fill in for missing data. With local alternatives, it is sufficient to proceed only with the first step of the EM algorithm mimicking imputation under the null hypothesis. Then, we show that blinded and unblinded estimates of the nuisance parameter [Formula: see text] are consistent, and re-estimated sample sizes converge to their locally asymptotically optimal values. This theoretical finding is confirmed through Monte-Carlo simulation studies. Practical utility is illustrated through a multiple logistic regression example. We conclude that, for hypothesis testing with a predetermined minimally clinically relevant local effect size, both blinded and unblinded SSR procedures lead to similar sample sizes and power.

A challenge arising in cancer immunotherapy trial design is the presence of a delayed treatment effect wherein the proportional hazard assumption no longer holds true. As a result, a traditional survival trial design based on the standard log-rank test, which ignores the delayed treatment effect, will lead to substantial loss of statistical power. Recently, a piecewise weighted log-rank test is proposed to incorporate the delayed treatment effect into consideration of the trial design. However, because the sample size formula was derived under a sequence of local alternative hypotheses, it results in an underestimated sample size when the hazard ratio is relatively small for a balanced trial design and an inaccurate sample size estimation for an unbalanced design. In this article, we derived a new sample size formula under a fixed alternative hypothesis for the delayed treatment effect model. Simulation results show that the new formula provides accurate sample size estimation for both balanced and unbalanced designs.

The additive genetic model as implemented in logistic regression has been widely used in genome-wide association studies (GWASs) for binary outcomes. Unfortunately, for many complex diseases, the underlying genetic models are generally unknown and a mis-specification of the genetic model can result in a substantial loss of power. To address this issue, the MAX3 test (the maximum of three separate test statistics) has been proposed as a robust test that performs plausibly regardless of the underlying genetic model. However, the original implementation of MAX3 utilizes the trend test so it cannot adjust for any covariates such as age and gender. This drawback has significantly limited the application of the MAX3 in GWASs, as covariates account for a considerable amount of variability in these disorders. In this paper, we extended the MAX3 and proposed the CMAX3 (covariate-adjusted MAX3) based on logistic regression. The proposed test yielded a similar robust efficiency as the original MAX3 while easily adjusting for any covariate based on the likelihood framework. The asymptotic formula to calculate the p-value of the proposed test was also developed in this paper. The simulation results showed that the proposed test performed desirably under both the null and alternative hypotheses. For the purpose of illustration, we applied the proposed test to re-analyze a case-control GWAS dataset from the Collaborative Studies on Genetics of Alcoholism (COGA). The R code to implement the proposed test is also introduced in this paper and is available for free download.

Introduction & Objective: Unadjusted analyses, fully adjusted analyses, or adjusted analyses based on tests of significance on covariate imbalance are recommended for covariate adjustment in randomized controlled trials. It has been indicated that the tests of significance on baseline comparability is inappropriate, rather it is important to indicate the strength of relationship with outcomes. Our goal is to understand when the adjustment should be used in randomized controlled trials. Methods: Unadjusted analysis, fully adjusted analysis, and adjusted analysis based on baseline comparability were examined under null and alternative hypothesis by simulation studies. Each data set was simulated 3000 times for a total of 9 scenarios for sample sizes of 20, 40, and 100 each with baseline thresholds of 0.05, 0.1, and 0.2. Each scenario was examined by the change in magnitude of correlation from 0.1 to 0.9. Results: Power of fully adjusted analysis under alternative hypothesis was increased as the correlation increased while adjusted analysis based on the covariate imbalance did not compare favorably to the unadjusted analysis. Type 1 error was decreased in adjusted analysis based on the covariate imbalance under null hypothesis. It was then observed that p-value does not follow a uniform distribution under the null hypothesis. Conclusion: Unadjusted and fully adjusted analyses were valid analyses. Full adjustment could potentially increase the power if adjustment is known. However, adjusted analysis based on the test of significance on covariate imbalance may not be a valid analysis. Tests of significance should not be used for comparing baseline comparability.

Appropriate sample size calculation and power analysis have become major issues in research and publication processes. However, the complexity and difficulty of calculating sample size and power require broad statistical knowledge, there is a shortage of personnel with programming skills, and commercial programs are often too expensive to use in practice. The review article aimed to explain the basic concepts of sample size calculation and power analysis; the process of sample estimation; and how to calculate sample size using G*Power software (latest ver. 3.1.9.7; Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany) with 5 statistical examples. The null and alternative hypothesis, effect size, power, alpha, type I error, and type II error should be described when calculating the sample size or power. G*Power is recommended for sample size and power calculations for various statistical methods (F, t, χ2, Z, and exact tests), because it is easy to use and free. The process of sample estimation consists of establishing research goals and hypotheses, choosing appropriate statistical tests, choosing one of 5 possible power analysis methods, inputting the required variables for analysis, and selecting the “calculate” button. The G*Power software supports sample size and power calculation for various statistical methods (F, t, χ2, z, and exact tests). This software is helpful for researchers to estimate the sample size and to conduct power analysis.

We consider the problem of sparsity testing in the high-dimensional linear regression model. The problem is to test whether the number of non-zero components (aka the sparsity) of the regression parameter $\theta^*$ is less than or equal to $k_0$. We pinpoint the minimax separation distances for this problem, which amounts to quantifying how far a $k_1$-sparse vector $\theta^*$ has to be from the set of $k_0$-sparse vectors so that a test is able to reject the null hypothesis with high probability. Two scenarios are considered. In the independent scenario, the covariates are i.i.d. normally distributed and the noise level is known. In the general scenario, both the covariance matrix of the covariates and the noise level are unknown. Although the minimax separation distances differ in these two scenarios, both of them actually depend on $k_0$ and $k_1$ illustrating that for this composite-composite testing problem both the size of the null and of the alternative hypotheses play a key role., Comment: 50 pages

Based on the test of Wied et al. (2012), we construct a bootstrapping CUSUM test for correlation change. The bootstrap test uses the bootstrap critical value obtained from the distribution of the moving block bootstrap samples. The asymptotic null distribution of the bootstrap test is shown to be the same as that of the original test. Consistency of the bootstrap test is proved under an alternative hypothesis of a correlation change. A Monte Carlo simulation shows that the proposed bootstrap test has a good size performance while the existing tests have serious size distortion for conditionally heteroscedastic samples and for serially correlated samples. The better size of the bootstrap test than the existing tests is achieved at the cost of some power loss in some cases.

Recent studies have demonstrated that Linear mixed model (LMM) successfully correct for population structure and genetic relatedness in genome-wide association studies (GWAS). However, currently available LMM methods usually suffer from computational inefficiency. Here, we propose a novel method, consisting of an LMM using the score test (LMM-Score). Our method takes advantage of score test that does not require estimation of parameters under the alternative hypothesis or the full model. We performed extensive simulation studies to estimate the statistical power of LMM-Score with various assumptions of sample size or marker size under different trait heritabilities. Although the limited power of simulation studies due to small sample size and conservativeness of Bonferroni correction, LMM-Score reduces the computing time greatly and maintained statistical power when compared with routine LMM method. Therefore, we believe that the LMM-Score is a valuable method for identifying the genetic basis of complex traits. We also applied our approach to real beef cattle data and suggested SOX17, RP1, LYN RPS20, snoU54, U1, MOS, PLAG1, CHCHD7, and SDR16C5 on BTA14 as the most promising candidate genes affecting pure meat weight (PMW), foreshank weight (FSW) and silverside weight (SSW) in Chinese Simmental beef cattle.

The global two-sided test for functional means difference got much attention in the literary works. While the global one-sided test for functional means difference has not been studied. However, that could have some applications and implications for longitudinal trials or trials with functional data outcomes. This work introduced superiority and noninferiority hypothesis tests for functional data outcomes, which were viewed as a one-sided problem for functional mean differences. Two global tests statistic have been proposed: a test based on integral and a test based on supremum. The performances of the tests have been evaluated via a simulation example. Both tests got an estimated actual type I error closer to the nominal type I error. The test based on supremum got good estimated power in all considered cases of the alternative hypothesis, while the test based on integral got very poor power performances for some cases of considered alternative hypothesis.

The p-value has dominated research in education and related fields and a statistically non-significant p-value is quite commonly interpreted as ‘confirming’ the null hypothesis (H0) of ‘equivalence’. This is unfortunate, because p-values are not fit for that purpose. This paper discusses three alternatives to the traditional p-value that unfortunately have remained underused but can provide evidence in favor of ‘equivalence’ relative to ‘non-equivalence’: two one-sided tests (TOST) equivalence testing, Bayesian hypothesis testing, and information criteria. TOST equivalence testing and p-values both rely on concepts of statistical significance testing and can both be done with confidence intervals, but treat H0 and the alternative hypothesis (H1) differently. Bayesian hypothesis testing and the Bayesian credible interval aka posterior interval provide Bayesian alternatives to traditional p-values, TOST equivalence testing, and confidence intervals. However, under conditions outlined in this paper, confidence intervals and posterior intervals may yield very similar interval estimates. Moreover, Bayesian hypothesis testing and information criteria provide fairly easy to use alternatives to statistical significance testing when multiple competing models can be compared. Based on these considerations, this paper outlines a pragmatic approach to statistical testing and estimation (PASTE) for research in education and related fields. In a nutshell, PASTE states that all of the alternatives to p-values discussed in this paper are better than p-values, that confidence intervals and posterior intervals may both provide useful interval estimates, and that Bayesian hypothesis testing and information criteria should be used when the comparison of multiple models is concerned. Keywords: Equivalence testing, Information criteria, Bayesian hypothesis testing, Confidence intervals, Posterior intervals

Circular data are data measured in angles or directions, which occur in a wide variety of scientific fields. An often investigated hypothesis is that of circular uniformity, or isotropy. Frequentist methods for assessing the circular uniformity null hypothesis exist, but do not allow the user faced with an insignificant result to distinguish lack of power from support for the null hypothesis. Bayesian hypothesis tests, which solve this issue and several others, are developed here. They are easy to compute and perform well, which is shown in a simulation. Two alternative hypotheses are considered. One is based on the von Mises distribution and performs well against unimodal alternatives. Another is based on a kernel density, which acts as an omnibus test against all other scenarios. Assessing the performance of the tests using different priors, it is shown that they are powerful and allow more elaborate conclusions than classical tests of circular uniformity.

Change-point detection in health care data has recently obtained considerable attention due to the increased availability of complex data in real-time. In many applications, the observed data is an ordinal time series. Two kinds of test statistics are proposed to detect the structural change of cumulative logistic regression model, which is often used in applications for the analysis of ordinal time series. One is the standardized efficient score vector, the other one is the quadratic form of the efficient score vector with a weight function. Under the null hypothesis, we derive the asymptotic distribution of the two test statistics, and prove the consistency under the alternative hypothesis. We also study the consistency of the change-point estimator, and a binary segmentation procedure is suggested for estimating the locations of possible multiple change-points. Simulation results show that the former statistic performs better when the change-point occurs at the centre of the data, but the latter is preferable when the change-point occurs at the beginning or end of the data. Furthermore, the former statistic could find the reason for rejecting the null hypothesis. Finally, we apply the two test statistics to a group of sleep data, the results show that there exists a structural change in the data.

In this chapter, we focus on characteristics of the normal distribution and single-sample significance tests that are used for variables measured at the ratio and interval levels. Specifically, this chapter reviews percentages under the normal curve, application of the 68-95-99.7 rule, and how to conduct a significance test in R for the following: (1) comparing a sample mean to a known population (single-sample z-test for means), (2) comparing a sample mean to an unknown population (single-sample t-test), and (3) comparing a sample proportion to a population proportion (single-sample z-test for proportions). In doing so, the chapter walks through criminal justice-related examples, lays out the null and alternative hypotheses for presented examples, and shows the user how to make a determination about the null hypothesis for the aforementioned tests from R output. Additionally, you will learn how to write your own functions in R.

Experimental results are often interpreted through statistical tests, where the alternative hypothesis represents the theory to be evinced; if the experimental results lead to the rejection of the null hypothesis, the theory is supported by empirical evidence. In these cases, the reproducibility of this empirical evidence can be measured by the Reproducibility Probability (RP) of the test, which coincides with the probability of rejecting the null hypothesis. The terminology “Reproducibility” Probability stems from the fact that it is usually computed when an experiment provides a significant result to evaluate the probability that a further identical and independent experiment confirms the statistical significance. In recent literature, some RP estimators have been proposed. They are useful for two reasons: they allow us to evaluate the reliability of the obtained statistical significance and some estimates can be used as a test statistic, owing to the so-called “RP-testing” decision rule (reject the null hypothesis if and only if the RP estimate is greater than 1/2). Unfortunately, the usually adopted RP estimators are affected by a high mean squared error. In this paper, a new class of RP estimators is introduced and examined to improve their estimation precision. Specifically, the performances of the new RP estimators have been compared with those of the existing estimators and a 30% greater reduction in the mean squared error (on average) was observed. Moreover, the new estimator with the best performance allowed the use of the RP-testing decision rule. Hence, this work achieves the double goal of improving Reproducibility Probability estimation and preserving RP-testing.

The vast majority of testing procedures presented in the literature as goodness-of-fit tests fail to accomplish what the term is promising. Actually, a significant result of such a test indicates that the true distribution underlying the data differs substantially from the assumed model, whereas the true objective is usually to establish that the model fits the data sufficiently well. Meeting that objective requires to carry out a testing procedure for a problem in which the statement that the deviations between model and true distribution are small, plays the role of the alternative hypothesis. Testing procedures of this kind, for which the term tests for equivalence has been coined in statistical usage, are available for establishing goodness-of-fit of discrete distributions. We show how this methodology can be extended to settings where interest is in establishing goodness-of-fit of distributions of the continuous type.

Measurement-Based Probabilistic Timing Analysis (MBPTA) produces Probabilistic Worst-Case Execution Times (pWCETs), i.e., WCET estimates associated with known low exceedance probabilities. Despite applicability and goodness-of-fit tests being used within MBPTA, any method based on the sampling of a population is subject to a degree of uncertainty. The acceptance of MBPTA in industrial engineering processes depends on obtaining enough evidence that the produced pWCETs are indeed reliable. In this paper we propose a statistical hypothesis test to check the reliability of pWCET estimates, done at a specified significance level. We assume as null hypothesis that the pWCET estimate is reliable, and as alternative hypothesis that it is optimistic. Both Type I and Type II errors are considered. The reliability test is based on a binomial experiment and it is complementary to applicability and goodness-of-fit tests. We evaluated the test using multiple synthetic and real-hardware execution time samples, and applied it on 20 pWCET estimates generated for each of them. The combined use of the proposed reliability test with applicability and goodness-of-fit tests could detect most of the knowingly unreliable estimates on synthetic samples. Similar behaviour was observed for real-hardware samples, evidencing the test’s usefulness for selecting pWCET estimates with increased confidence.

This paper proposes a test for the null of sphericity in the panel data model. We proposed a novel multivariate sign test for sphericity based on sample splitting and leave out method in the panel data model. The limiting distribution of the proposed test statistic is derived under the null and alternative hypothesis. Simulation studies also demonstrate the advantage of our method.

We develop the distribution of the number of hypotheses found to be statistically significant using the rule from Benjamini and Hochberg (1995) for controlling the false discovery rate (FDR). This distribution has both a small sample form and an asymptotic expression for testing many independent hypotheses simultaneously. We propose a parametric distribution $\,\Psi_I(\cdot)\,$ to approximate the marginal distribution of p-values under a non-uniform alternative hypothesis. This distribution is useful when there are many different alternative hypotheses and these are not individually well understood. We fit $\,\Psi_I\,$ to data from three cancer studies and use it to illustrate the distribution of the number of notable hypotheses observed in these examples. We model dependence of sampled p-values using a copula model and a latent variable approach. These methods can be combined to illustrate a power analysis in planning a large study on the basis of a smaller pilot study. We show the number of statistically significant p-values behaves approximately as a mixture of a normal and the Borel-Tanner distribution., Comment: 29 pages; 6 figures; 3 tables

Several methods for comparing k populations have been proposed in the literature. These methods assess the same null hypothesis of equal distributions but differ in the alternative hypothesis they consider. We focus on two important alternative hypotheses: monotone and umbrella ordering. Two new families of test statistics are proposed, including two known tests, as well as two new powerful tests under monotone ordering. Furthermore, these families are adapted for testing umbrella ordering. We compare some members of the families with respect to power and Type I errors under different simulation scenarios. Finally, the methods are illustrated in several applications to real data.

This investigation deal with quasi experimental in the form non-randomize control group design or non-equivalent by purposing at finding out teaching reading through three stay one stray. The investigation used total sampling technique in determining the sample of the research. The data was taken by using test in the form of multiples choice and it analyzed by using descriptive statistic and inferential analysis. Based on the data analysis was gotten that the result of analysis shown that t-test was higher than t-table. It can be inferred that alternative hypothesis accepted and null hypothesis rejected. Therefore, it concluded that there was significant effect teaching reading through three stay one stray

The purpose of this study is to determine how much influence professional competence, credibility and emotional intelligent toward pilot performance, either partially or simultaneously. The research design used in the preparation of this research is quantitative, aimed to determine the effect of independent variables on the dependent. The study applied descriptive and deductive of multivariate regression method it’s include 91 respondents as the samples. The samples were selected through simple random sampling. The statistical tool were used is SPSS Software as the means to examine the data. Hypothesis testing based on determinate coefficient (R2) of 76,2% can be summed up the effect of the variable independent to variable Y where the influence are positive either partially or simultaneously. The results of this research can be stated that the multiple correlation is significant. Thus the null hypothesis (H0) that states there are no effect between professional competence, credibility and emotional intelligent toward pilot performance are rejected, while the alternative hypothesis (Ha) are accepted

In biomedical applications, it is often of interest to test the alternative hypothesis that the means of three or more groups follow a strictly monotonic trend such as µ1> µ2> µ3 against the null hypothesis that the group means are either equal or unequal but are not monotonic. This is useful, for example, for detecting biomarkers whose level in healthy, low-risk cancer and aggressive cancer subjects increases or decreases throughout the three groups. Various trend tests are available for testing monotonic alternatives. However, existing methods are designed for a highly restrictive null hypothesis where all group means are equal, which represents a special case of the null space in our problem. We demonstrate that these methods fail to control type I error when the group means may be unequal under the null. To test this broader null hypothesis, develop a greedy testing method which has an intuitive interpretation related to two-sample t tests. We show both theoretically and through simulations that the proposed method effectively controls type 1 error throughout the entire null space and achieves higher power than a naive implementation of multiple t-tests. We illustrate the greedy trend test method in real data to study microbial associations with parasite-related pathology in zebrafish.

Human subjects differentially weight different stimuli in averaging tasks, which has been interpreted as reflecting encoding bias. We examine the alternative hypothesis that stimuli are encoded with noise, then optimally decoded. Under a model of efficient coding, the amount of noise should vary across stimuli, and depend on statistics of the stimuli. We investigate these predictions through a task in which participants are asked to compare the averages of two series of numbers, each sampled from a prior distribution that varies across blocks of trials. Subjects encode numbers with a bias and a noise that both depend on the number. Infrequently occurring numbers are encoded with more noise. We show how an efficient-coding, Bayesian-decoding model accounts for these patterns, and best captures subjects’ behaviour. Finally, our results suggest that Wei and Stocker’s “law of human perception”, which relates the bias and variability of sensory estimates, also applies to number cognition.

I thank the Editor and the two referees for their helpful comments that improved the quality of the manuscript., Background: The comparison of the performance of two binary diagnostic tests is an important topic in Clinical Medicine. The most frequent type of sample design to compare two binary diagnostic tests is the paired design. This design consists of applying the two binary diagnostic tests to all of the individuals in a random sample, where the disease status of each individual is known through the application of a gold standard. This article presents an R program to compare parameters of two binary tests subject to a paired design. Results: The “compbdt” program estimates the sensitivity and the specificity, the likelihood ratios and the predictive values of each diagnostic test applying the confidence intervals with the best asymptotic performance. The program compares the sensitivities and specificities of the two diagnostic tests simultaneously, as well as the likelihood ratios and the predictive values, applying the global hypothesis tests with the best performance in terms of type I error and power. When the global hypothesis test is significant, the causes of the significance are investigated solving the individual hypothesis tests and applying the multiple comparison method of Holm. The most optimal confidence intervals are also calculated for the difference or ratio between the respective parameters. Based on the data observed in the sample, the program also estimates the probability of making a type II error if the null hypothesis is not rejected, or estimates the power if the if the alternative hypothesis is accepted. The “compbdt” program provides all the necessary results so that the researcher can easily interpret them. The estimation of the probability of making a type II error allows the researcher to decide about the reliability of the null hypothesis when this hypothesis is not rejected. The “compbdt” program has been applied to a real example on the diagnosis of coronary artery disease. Conclusions: The “compbdt” program is one which is easy to use and allows the researcher to compare the most important parameters of two binary tests subject to a paired design. The “compbdt” program is available as supplementary material., This research was supported by the Spanish Ministry of Economy, Grant Number MTM2016–76938-P.

An important inferential task in functional linear models is to test the dependence between the response and the functional predictor. The traditional testing theory was constructed based on the functional principle component analysis which requires estimating the covariance operator of the functional predictor. Due to the intrinsic high-dimensionality of functional data, the sample is often not large enough to allow accurate estimation of the covariance operator and hence causes the follow-up test underpowered. To avoid the expensive estimation of the covariance operator, we propose a nonparametric method called Functional Linear models with U-statistics TEsting (FLUTE) to test the dependence assumption. We show that the FLUTE test is more powerful than the current benchmark method (Kokoszka P,2008; Patilea V,2016) in the small or moderate sample case. We further prove the asymptotic normality of our test statistic under both the null hypothesis and a local alternative hypothesis. The merit of our method is demonstrated by both simulation studies and real examples.

Self and Mauritsen (1988) developed a sample size determination procedure for score tests in generalized linear models under contiguous alternatives. Its performance may deteriorate when the effect size is large. We propose a modification of the Self-Mauritsen method by taking into account of the variance of the score statistic under both the null and alternative hypotheses, and extend the method to noninferiority trials. The modified approach is employed to calculate the sample size for the logistic regression and negative binomial regression in superiority and noninferiority trials. We further explain why the formulae recently derived by Zhu and Lakkis tend to underestimate the required sample size for the negative binomial regression. Numerical examples are used to demonstrate the accuracy of the proposed method., Comment: 26 pages, 1 figure. Statistics in Biopharmaceutical Research 2020

The principle of predictive irrelevance states that when two competing models predict a data set equally well, that data set cannot be used to discriminate the models and – for that specific purpose – the data set is evidentially irrelevant. To highlight the ramifications of the principle, we first show how a single binomial observation can be irrelevant in the sense that it carries no evidential value for discriminating the null hypothesis θ = 1∕2 from a broad class of alternative hypotheses that allow θ to be between 0 and 1. In contrast, the Bayesian credible interval suggests that a single binomial observation does provide some evidence against the null hypothesis. We then generalize this paradoxical result to infinitely long data sequences that are predictively irrelevant throughout. Examples feature a test of a binomial rate and a test of a normal mean. These maximally uninformative data (MUD) sequences yield credible intervals and confidence intervals that are certain to exclude the point of test as the sequence lengthens. The resolution of this paradox requires the insight that interval estimation methods – and, consequently, p-values – may not be used for model comparison involving a point null hypothesis.