Interval estimation and inference

2019 ◽  
pp. 111-138
Author(s):  
M. D. Edge
Keyword(s):  
Standard Deviation ◽  
Hypothesis Testing ◽  
Confidence Intervals ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Interval Estimation ◽  
Research Literature ◽  
Significance Level ◽  
Specific Hypothesis ◽  
True Value

Interval estimation is the attempt to define intervals that quantify the degree of uncertainty in an estimate. The standard deviation of an estimate is called a standard error. Confidence intervals are designed to cover the true value of an estimand with a specified probability. Hypothesis testing is the attempt to assess the degree of evidence for or against a specific hypothesis. One tool for frequentist hypothesis testing is the p value, or the probability that if the null hypothesis is in fact true, the data would depart as extremely or more extremely from expectations under the null hypothesis than they were observed to do. In Neyman–Pearson hypothesis testing, the null hypothesis is rejected if p is less than a pre-specified value, often chosen to be 0.05. A test’s power function gives the probability that the null hypothesis is rejected given the significance level γ‎, a sample size n, and a specified alternative hypothesis. This chapter discusses some limitations of hypothesis testing as commonly practiced in the research literature.

scholarly journals The Correlation Between Students’ Vocabulary MasteryAnd Their Achievement In Reading Comprehension

2020 ◽  
Vol 13 (1) ◽  
pp. 12-21
Author(s):  
Gina - Larasaty
Keyword(s):  
Reading Comprehension ◽  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Quantitative Method ◽  
Alternative Hypothesis ◽  
Boarding School ◽  
Significance Level ◽  
Coefficient Corrélation ◽  
Correlation Level

This research deals with the correlation between students vocabulary mastery and their achievement in their reading comprehension. The data were taken from 33 students from class X-TKJ of SMK As – Sakienah Boarding School Tugu – Sliyeg. The writer used quantitative method by Pearson Product Moment. From the calculation by using product moment formula, it was found out that the coefficient correlation from this research is 0,8409.. It can be concluded that there is positive and high correlation level between students’ vocabulary mastery and their achievement in reading comprehension. This research used significance level 5%. From the hypothesis testing result, it was found that  r_count is 0,8409 >r _table 0,3494. Based on the fact, it can be concluded that Alternative Hypothesis (Ha) is accepted and the Null Hypothesis (Ho) is rejected. So, there is significance correlation between students’ vocabulary mastery and their achievement reading comprehension.

Hypothesis testing with error correction models

2021 ◽  
pp. 1-9
Author(s):  
Patrick W. Kraft ◽  
Ellen M. Key ◽  
Matthew J. Lebo
Keyword(s):  
Hypothesis Testing ◽  
Error Correction ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Correction Coefficient ◽  
Correction Model ◽  
Long Run ◽  
Independent Variable ◽  
The Right ◽  
General Error

Abstract Grant and Lebo (2016) and Keele et al. (2016) clarify the conditions under which the popular general error correction model (GECM) can be used and interpreted easily: In a bivariate GECM the data must be integrated in order to rely on the error correction coefficient, $\alpha _1^\ast$ , to test cointegration and measure the rate of error correction between a single exogenous x and a dependent variable, y. Here we demonstrate that even if the data are all integrated, the test on $\alpha _1^\ast$ is misunderstood when there is more than a single independent variable. The null hypothesis is that there is no cointegration between y and any x but the correct alternative hypothesis is that y is cointegrated with at least one—but not necessarily more than one—of the x's. A significant $\alpha _1^\ast$ can occur when some I(1) regressors are not cointegrated and the equation is not balanced. Thus, the correct limiting distributions of the right-hand-side long-run coefficients may be unknown. We use simulations to demonstrate the problem and then discuss implications for applied examples.

scholarly journals Asymptotic relative submajorization of multiple-state boxes

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Gergely Bunth ◽  
Péter Vrana
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Standard Form ◽  
Point Of View ◽  
State Discrimination ◽  
Simple Alternative ◽  
Multiple State ◽  
Error Probabilities

AbstractPairs of states, or “boxes” are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde in Phys Rev Res 1(3):033170, 2019. 10.1103/PhysRevResearch.1.033170), where free operations are arbitrary quantum channels that are applied to both states. From this point of view, hypothesis testing is seen as a process by which a standard form of distinguishability is distilled. Motivated by the more general problem of quantum state discrimination, we consider boxes of a fixed finite number of states and study an extension of the relative submajorization preorder to such objects. In this relation, a tuple of positive operators is greater than another if there is a completely positive trace nonincreasing map under which the image of the first tuple satisfies certain semidefinite constraints relative to the other one. This preorder characterizes error probabilities in the case of testing a composite null hypothesis against a simple alternative hypothesis, as well as certain error probabilities in state discrimination. We present a sufficient condition for the existence of catalytic transformations between boxes, and a characterization of an associated asymptotic preorder, both expressed in terms of sandwiched Rényi divergences. This characterization of the asymptotic preorder directly shows that the strong converse exponent for a composite null hypothesis is equal to the maximum of the corresponding exponents for the pairwise simple hypothesis testing tasks.

scholarly journals A Critical Evaluation of the FBST ev for Bayesian Hypothesis Testing

2021 ◽  
Author(s):  
Alexander Ly ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Critical Evaluation ◽  
Significance Test ◽  
Bayesian Hypothesis Testing ◽  
Absence Of Evidence ◽  
Evidence Of Absence ◽  
Foregone Conclusion

AbstractThe “Full Bayesian Significance Test e-value”, henceforth FBST ev, has received increasing attention across a range of disciplines including psychology. We show that the FBST ev leads to four problems: (1) the FBST ev cannot quantify evidence in favor of a null hypothesis and therefore also cannot discriminate “evidence of absence” from “absence of evidence”; (2) the FBST ev is susceptible to sampling to a foregone conclusion; (3) the FBST ev violates the principle of predictive irrelevance, such that it is affected by data that are equally likely to occur under the null hypothesis and the alternative hypothesis; (4) the FBST ev suffers from the Jeffreys-Lindley paradox in that it does not include a correction for selection. These problems also plague the frequentist p-value. We conclude that although the FBST ev may be an improvement over the p-value, it does not provide a reasonable measure of evidence against the null hypothesis.

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 PENGARUH MODEL PEMBELAJARAN KOOPERATIF TIPE THINK PAIR SHARE (TPS) TERHADAP HASIL BELAJAR LAGU NUSANTARA SISWA KELAS VIII-I SMP YP PEMBANGUNAN GALANG

2018 ◽  
Vol 7 (1) ◽  
pp. 24
Author(s):  
Sahat Maruli Siahaan
Keyword(s):  
Hypothesis Testing ◽  
Learning Outcomes ◽  
Alternative Hypothesis ◽  
Choice Test ◽  
Control Group ◽  
Significance Level ◽  
Average Value ◽  
Significant Difference ◽  
Class Viii ◽  
Academic Year

This study aimed to determine the effect of student learning outcomes by applying the learningmodel Think Pair Share (TPS) on the archipelago song class VIII-I in SMP YP PembangunanGalang of the Academic Year 2016/2017.This type of research is True experimental design with pretest-Psottest Control GroupDesign. The population in the study were all second semester VIII class consisting of 3 classes.Sampling was done by random sampling. Sample chosen is a class VIII-I as the experimental classlearning model Think Pair Share, amounting to 30 people and VIII-II as a control group withconventional learning models which amounted to 32 people. The instrument used in this studyused multiple-choice test of 25 questions with four possible answers that have validator. Thestatistics are used to test the hypothesis of this study is to test t, As a prerequisite test used to testthe normality and homogeneity.Based on the post-test and analysis of data obtained an average value of 78.26experimental group and the average value of the control group 66. From the results of hypothesistesting, it turns out the alternative hypothesis (Ha) is accepted. Testing the hypothesis in researchusing hypothesis testing t-test two parties and of the calculation of the statistics obtained by value t= 4.60 t the next price compared to the price ttabel with significance level of 5% was obtainedtable = 2.0 then t ≥ t table or - t ≤ - t table is ≥ 2.0 or -4.60 4.60 ≤ -2.0. Then the results of testinghypothesis Ho is rejected and Ha is accepted.Based on data analysis and discussion of the results of hypothesis testing, theconclusion of this study was no significant difference in the use of learning model Think PairShare (TPS) to the learning outcomes obtained by students on track archipelago VIII-I in SMP YPPembangunan Galang of the Academic Year 2016/2017.

Research on the Confidence Interval of Indirect Detection

2011 ◽  
Vol 418-420 ◽  
pp. 532-535
Author(s):  
Hai Bin Chen ◽  
Nan Ge ◽  
Xiao Jun Tong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Concrete Strength ◽  
Interval Estimation ◽  
Point Estimation ◽  
Indirect Detection ◽  
Detection Methods ◽  
Theoretical Formula ◽  
True Value ◽  
Practical Engineering

Abstract. Using the correlation between the measure value and measured value in the indirect detection, the whole presumption method and theoretical formula of the confidence intervals for measured value are put forward. Based on the different detection methods, the confidence interval of high confidence and high accuracy can be given by the proposed method according to random measurement results. Through the Monte Carlo simulation, using the deducing method and the related theory, it may be concluded that the true value is included within the confidence interval which is obtained by this method. The traditional method can only get the point estimation but not give the confidence intervals in the practical engineering. According to the method, the interval estimation of concrete strength can be give. Moreover, this method is used not only in test concrete strength, especially in the evaluation of earthquake, but also in strength detecting for bridges, the pressure vessel, aircraft wing etc.

scholarly journals Utility Theory as a Method to Minimise the Risk in Deformation Analysis Decisions

2014 ◽  
Vol 8 (4) ◽  
Author(s):  
Yin Zhang ◽  
Ingo Neumann
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Utility Theory ◽  
Alternative Hypothesis ◽  
Main Idea ◽  
Deformation Monitoring ◽  
Deformation Analysis ◽  
Utility Values ◽  
Alternative Hypotheses ◽  
The Given

AbstractDeformation monitoring usually focuses on the detection of whether the monitored objects satisfy the given properties (e.g. being stable or not), and makes further decisions to minimise the risks, for example, the consequences and costs in case of collapse of artificial objects and/or natural hazards. With this intention, a methodology relying on hypothesis testing and utility theory is reviewed in this paper. The main idea of utility theory is to judge each possible outcome with a utility value. The presented methodology makes it possible to minimise the risk of an individual monitoring project by considering the costs and consequences of overall possible situations within the decision process. It is not the danger that the monitored object may collapse that can be reduced. The risk (based on the utility values multiplied by the danger) can be described more appropriately and therefore more valuable decisions can be made. Especially, the opportunity for the measurement process to minimise the risk is an important key issue. In this paper, application of the methodology to two of the classical cases in hypothesis testing will be discussed in detail: 1) both probability density functions (pdfs) of tested objects under null and alternative hypotheses are known; 2) only the pdf under the null hypothesis is known and the alternative hypothesis is treated as the pure negation of the null hypothesis. Afterwards, a practical example in deformation monitoring is introduced and analysed. Additionally, the way in which the magnitudes of utility values (consequences of a decision) influence the decision will be considered and discussed at the end.

scholarly journals A CORRELATION BETWEEN SKIMMING SKILL AND READING COMPREHENSION ACHIVEMENT OF THE STUDENTS OF HIGH SCHOOL IN BEKASI

2018 ◽  
Vol 2 (01) ◽  
pp. 9-18
Author(s):  
Sarsono Sarsono
Keyword(s):  
High School ◽  
Reading Comprehension ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
T Test ◽  
Degree Of Freedom ◽  
Significance Level ◽  
Positive Correlation ◽  
Normality Test ◽  
Coefficient Corrélation

The research is aimed at proving or determining correlation between skimming skill and reading comprehension achivement of the students of high school. The collection of data was carried out by questionnaire, the data was analyzed statistically by Person Product Moment Correlation of coefficient correlation preceded by Lillifors normality test as prerequisite analysis ( Lo < L-table ). The research found that ; 1) Based on Person Product Moment Correlation, reveals r = 0,969, while the r-table for degree of freedom(df) = (N-2) = 40 and the significance level 5% (0,05) is 0,304. Therefore the Null Hypothesis (Ho) which expresses that there is no significant Correlation Between Skimming Skill and Reading Comprehension achievement is rejected, and the alternative Hypothesis (Ha), which expresses that there is significant Correlation Between Skimming Skill and Reading Comprehension Achievement can be accepted. 1) There is a significant correlation with t-test (t-count) is 98,80 and degree of freedom (df) n-2 = 40, at level 5 % (0,05) sig ( two tail test), t-table is 2,326 t-count > t –table ( 98,80 > 2,326, so Ho is rejected and Ha is accepted. It means that the correlation has positive correlation. 2) The degree of correlation based on the table of coefficient correlation (r) is 0.969. the interval coefficient relation is between 0,80 and 1,00, so the correlation is very strong.

scholarly journals Hypothesis Testing, p Values, Confidence Intervals, Measures of Effect Size, and Bayesian Methods in Light of Modern Robust Techniques

2016 ◽  
Vol 77 (4) ◽  
pp. 673-689 ◽  
Author(s):  
Rand R. Wilcox ◽  
Sarfaraz Serang
Keyword(s):  
Hypothesis Testing ◽  
Confidence Intervals ◽  
Bayesian Methods ◽  
Effect Size ◽  
Null Hypothesis ◽  
P Values ◽  
Null Hypothesis Testing ◽  
Robust Techniques ◽  
Alternative Techniques ◽  
Robust Statistical Methods

The article provides perspectives on p values, null hypothesis testing, and alternative techniques in light of modern robust statistical methods. Null hypothesis testing and p values can provide useful information provided they are interpreted in a sound manner, which includes taking into account insights and advances that have occurred during the past 50 years. There are, of course, limitations to what null hypothesis testing and p values reveal about data. But modern advances make it clear that there are serious limitations and concerns associated with conventional confidence intervals, standard Bayesian methods, and commonly used measures of effect size. Many of these concerns can be addressed using modern robust methods.

Sign in / Sign up

Export Citation Format

Share Document