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

2001 ◽  
Vol 6 (4) ◽  
pp. 371-386 ◽  
Author(s):  
Warren W. Tryon
Keyword(s):  
Confidence Intervals ◽  
Null Hypothesis ◽  
Statistical Difference ◽  
Statistical Tests ◽  
Alternative Method

The Merits of Confidence Intervals Relative to Hypothesis Testing

1992 ◽  
Vol 13 (9) ◽  
pp. 553-555 ◽  
Author(s):  
Leon F. Burmeister ◽  
David Bimbaum ◽  
Samuel B. Sheps
Keyword(s):  
Hypothesis Testing ◽  
Confidence Intervals ◽  
Null Hypothesis ◽  
Finite Population ◽  
Extreme Values ◽  
Statistical Tests ◽  
Point Estimate ◽  
Distributed Data ◽  
Average Difference ◽  
Average Value

A variety of statistical tests of a null hypothesis commonly are used in biomedical studies. While these tests are the mainstay for justifying inferences drawn from data, they have important limitations. This report discusses the relative merits of two different approaches to data analysis and display, and recommends the use of confidence intervals rather than classic hypothesis testing.Formulae for a confidence interval surrounding the point estimate of an average value take the form: d= ±zσ/√n, where “d” represents the average difference between central and extreme values, “z” is derived from the density function of a known distribution, and “a/-∨n” represents the magnitude of sampling variability. Transposition of terms yields the familiar formula for hypothesis testing of normally distributed data (without applying the finite population correction factor): z = d/(σ/√n).

scholarly journals Statistical Tests of Symbolic Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 817
Author(s):  
Fernando López ◽  
Mariano Matilla-García ◽  
Jesús Mur ◽  
Manuel Ruiz Marín
Keyword(s):  
Monte Carlo ◽  
Symbolic Dynamics ◽  
Null Hypothesis ◽  
Statistical Tests ◽  
General Applicability ◽  
Monte Carlo Experiments ◽  
The Mean ◽  
Theoretical Application ◽  
New Statistics ◽  
General Method

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

scholarly journals Testing the Validity of a Link Function Assumption in Repeated Type-II Censored General Step-Stress Experiments

Sankhya B ◽  
2021 ◽  
Author(s):  
Stefan Bedbur ◽  
Thomas Seiche
Keyword(s):  
Null Hypothesis ◽  
Statistical Tests ◽  
Operating Conditions ◽  
Link Function ◽  
Asymptotic Results ◽  
Failure Data ◽  
Stress Levels ◽  
Log Linear ◽  
Multiple Samples ◽  
General Step

AbstractIn step-stress experiments, test units are successively exposed to higher usually increasing levels of stress to cause earlier failures and to shorten the duration of the experiment. When parameters are associated with the stress levels, one problem is to estimate the parameter corresponding to normal operating conditions based on failure data obtained under higher stress levels. For this purpose, a link function connecting parameters and stress levels is usually assumed, the validity of which is often at the discretion of the experimenter. In a general step-stress model based on multiple samples of sequential order statistics, we provide exact statistical tests to decide whether the assumption of some link function is adequate. The null hypothesis of a proportional, linear, power or log-linear link function is considered in detail, and associated inferential results are stated. In any case, except for the linear link function, the test statistics derived are shown to have only one distribution under the null hypothesis, which simplifies the computation of (exact) critical values. Asymptotic results are addressed, and a power study is performed for testing on a log-linear link function. Some improvements of the tests in terms of power are discussed.

scholarly journals A Frequentist Alternative to Significance Testing, p-Values, and Confidence Intervals

Econometrics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 26 ◽  
Author(s):  
David Trafimow
Keyword(s):  
Present Article ◽  
Confidence Intervals ◽  
Null Hypothesis ◽  
A Priori ◽  
Significance Testing ◽  
Population Parameters ◽  
Null Hypothesis Significance Testing ◽  
P Values ◽  
Statistical Procedures ◽  
Major Section

There has been much debate about null hypothesis significance testing, p-values without null hypothesis significance testing, and confidence intervals. The first major section of the present article addresses some of the main reasons these procedures are problematic. The conclusion is that none of them are satisfactory. However, there is a new procedure, termed the a priori procedure (APP), that validly aids researchers in obtaining sample statistics that have acceptable probabilities of being close to their corresponding population parameters. The second major section provides a description and review of APP advances. Not only does the APP avoid the problems that plague other inferential statistical procedures, but it is easy to perform too. Although the APP can be performed in conjunction with other procedures, the present recommendation is that it be used alone.

CONCEPTUAL KNOWLEDGE OF CONFIDENCE INTERVALS IN PSYCHOLOGY UNDERGRADUATE AND GRADUATE STUDENTS

2019 ◽  
Vol 18 (1) ◽  
pp. 46-62
Author(s):  
NOELLE M. CROOKS ◽  
ANNA N. BARTEL ◽  
MARTHA W. ALIBALI
Keyword(s):  
Graduate Students ◽  
Confidence Intervals ◽  
Null Hypothesis ◽  
Conceptual Knowledge ◽  
Statistics Education ◽  
Psychology Students ◽  
Sample Mean ◽  
P Values ◽  
Research Journal ◽  
Graduate Psychology Students

In recent years, there have been calls for researchers to report and interpret confidence intervals (CIs) rather than relying solely on p-values. Such reforms, however, may be hindered by a general lack of understanding of CIs and how to interpret them. In this study, we assessed conceptual knowledge of CIs in undergraduate and graduate psychology students. CIs were difficult and prone to misconceptions for both groups. Connecting CIs to estimation and sample mean concepts was associated with greater conceptual knowledge of CIs. Connecting CIs to null hypothesis  significance testing, however, was not associated with conceptual knowledge of CIs. It may therefore be beneficial to focus on estimation and sample mean concepts in instruction about CIs. First published May 2019 at Statistics Education Research Journal Archives

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