scholarly journals T^2 Type Test Statistic and Simultaneous Confidence Intervals for Two Sub-mean Vectors

2019 ◽  
Vol 9 (1) ◽  
pp. 1
Author(s):  
Tamae Kawasaki ◽  
Toshiki Naito ◽  
Takashi Seo
Keyword(s):  
Confidence Intervals ◽  
Degrees Of Freedom ◽  
Normal Approximation ◽  
The Other ◽  
Test Statistic ◽  
Simultaneous Confidence Intervals ◽  
Type Statistic ◽  
Type Test ◽  
F Distribution ◽  
Mean Vectors

In this paper, we consider tests for sub-mean vectors and its simultaneous confidence intervals in two-sample problems. We give the T^2 type test statistic and the simultaneous confidence intervals by using two approximate upper percentiles of T^2 type test statistic. One of the approximate percentiles is obtained by normal approximation for a part of the T^2 type statistic, and the other is an approximation obtained by correcting the degrees of freedom of the F distribution. Finally, we investigate the asymptotic behavior of the approximate upper percentiles of T^2 type statistic by Monte Carlo simulation, and we give an example to illustrate the simultaneous confidence intervals.

scholarly journals New Test Statistics for One and Two Mean Vectors with Two-step Monotone Missing Data

2020 ◽  
Vol 9 (6) ◽  
pp. 56
Author(s):  
Mizuki Onozawa ◽  
Ayaka Yagi ◽  
Takashi Seo
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Asymptotic Behavior ◽  
Missing Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Type Test ◽  
Mean Vectors ◽  
Mean Vector

We consider the tests for a single mean vector and two mean vectors with two-step monotone missing data. In this paper, we propose new test statistics for one sample and two sample designs based on the simplified T^2-type test statistic. Further, we present the approximation to the upper percentiles of these statistics and propose the transformed test statistics. Finally, we investigate the accuracy and asymptotic behavior of the approximation for X^2 distribution by a Monte Carlo simulation.

Was This in Your Statistics Textbook? IV. Frequency Data

1989 ◽  
Vol 25 (1) ◽  
pp. 11-25
Author(s):  
D. J. Finney
Keyword(s):  
Statistical Analysis ◽  
Contingency Tables ◽  
The Other ◽  
Frequency Data ◽  
Significance Tests ◽  
Test Statistic ◽  
Jumping To Conclusions ◽  
Proper Role ◽  
Measure Of Association

SUMMARYObservations that are frequencies rather than measurements often call for special types of statistical analysis. This paper comments on circumstances in which methods for one type of data can sensibly be used for the other. A section on two-way contingency tables emphasizes the proper role of χ2 a test statistic but not a measure of association; it mentions the distinction between one-tail and two-tail significance tests and reminds the reader of dangers. Multiway tables bring new complications, and the problems of interactions when additional classificatory factors are explicit or hidden are discussed at some length. A brief outline attempts to show how probit, logit, and similar techniques are related to the analysis of contingency tables. Finally, three unusual examples are described as illustrations of the care that is needed to avoid jumping to conclusions on how frequency data should be analysed.

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