scholarly journals Correlation Coefficients: Mean Bias and Confidence Interval Distortions

2011 ◽  
Vol 1 (2) ◽  
pp. 52 ◽  
Author(s):  
Richard L. Gorsuch ◽  
Curtis S. Lehmann
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Correlation Coefficients ◽  
Standard Errors ◽  
Design Issues ◽  
Normal Distributions ◽  
Zero Correlation ◽  
Order Of Magnitude ◽  
Restriction Of Range ◽  
Z Transformation

Non-zero correlation coefficients have non-normal distributions, affecting both means and standard deviations. Previous research suggests that z transformation may effectively correct mean bias for N's less than 30. In this study, simulations with small (20 and 30) and large (50 and 100) N's found that mean bias adjustments for larger N's are seldom needed. However, z transformations improved confidence intervals even for N = 100. The improvement was not in the estimated standard errors so much as in the asymmetrical CI's estimates based upon the z transformation. The resulting observed probabilities were generally accurate to within 1 point in the first non-zero digit. These issues are an order of magnitude less important for accuracy than design issues influencing the accuracy of the results, such as reliability, restriction of range, and N. DOI:10.2458/azu_jmmss_v1i2_gorsuch

scholarly journals Correlation Coefficients: Mean Bias and Confidence Interval Distortions

2011 ◽  
Vol 1 (2) ◽  
pp. 52 ◽  
Author(s):  
Richard L. Gorsuch ◽  
Curtis S. Lehmann
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Correlation Coefficients ◽  
Standard Errors ◽  
Design Issues ◽  
Normal Distributions ◽  
Zero Correlation ◽  
Order Of Magnitude ◽  
Restriction Of Range ◽  
Z Transformation

Non-zero correlation coefficients have non-normal distributions, affecting both means and standard deviations. Previous research suggests that z transformation may effectively correct mean bias for N's less than 30. In this study, simulations with small (20 and 30) and large (50 and 100) N's found that mean bias adjustments for larger N's are seldom needed. However, z transformations improved confidence intervals even for N = 100. The improvement was not in the estimated standard errors so much as in the asymmetrical CI's estimates based upon the z transformation. The resulting observed probabilities were generally accurate to within 1 point in the first non-zero digit. These issues are an order of magnitude less important for accuracy than design issues influencing the accuracy of the results, such as reliability, restriction of range, and N. DOI:10.2458/azu_jmmss_v1i2_gorsuch

scholarly journals A Bayesian Approach for Estimation of Coefficients of Variation of Normal Distributions

2021 ◽  
Vol 50 (1) ◽  
pp. 261-278
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Bayesian Approaches ◽  
Normal Distributions ◽  
Generalized Confidence Interval ◽  
Coefficients Of Variation ◽  
The Difference ◽  
Highest Posterior Density

The coefficient of variation is widely used as a measure of data precision. Confidence intervals for a single coefficient of variation when the data follow a normal distribution that is symmetrical and the difference between the coefficients of variation of two normal populations are considered in this paper. First, the confidence intervals for the coefficient of variation of a normal distribution are obtained with adjusted generalized confidence interval (adjusted GCI), computational, Bayesian, and two adjusted Bayesian approaches. These approaches are compared with existing ones comprising two approximately unbiased estimators, the method of variance estimates recovery (MOVER) and generalized confidence interval (GCI). Second, the confidence intervals for the difference between the coefficients of variation of two normal distributions are proposed using the same approaches, the performances of which are then compared with the existing approaches. The highest posterior density interval was used to estimate the Bayesian confidence interval. Monte Carlo simulation was used to assess the performance of the confidence intervals. The results of the simulation studies demonstrate that the Bayesian and two adjusted Bayesian approaches were more accurate and better than the others in terms of coverage probabilities and average lengths in both scenarios. Finally, the performances of all of the approaches for both scenarios are illustrated via an empirical study with two real-data examples.

scholarly journals Confidence Intervals for the Signal-to-Noise Ratio and Difference of Signal-to-Noise Ratios of Log-Normal Distributions

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 164-173 ◽  
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Coverage Probability ◽  
Average Length ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Normal Distributions ◽  
Noise Ratio ◽  
The Difference ◽  
Log Normal

In this article, we propose approaches for constructing confidence intervals for the single signal-to-noise ratio (SNR) of a log-normal distribution and the difference in the SNRs of two log-normal distributions. The performances of all of the approaches were compared, in terms of the coverage probability and average length, using Monte Carlo simulations for varying values of the SNRs and sample sizes. The simulation studies demonstrate that the generalized confidence interval (GCI) approach performed well, in terms of coverage probability and average length. As a result, the GCI approach is recommended for the confidence interval estimation for the SNR and the difference in SNRs of two log-normal distributions.

Statistical Methods for Summarizing Independent Correlational Results

1980 ◽  
Vol 5 (1) ◽  
pp. 83-104 ◽  
Author(s):  
Marios A. G. Viana
Keyword(s):  
Confidence Intervals ◽  
Statistical Methods ◽  
Correlation Coefficients ◽  
Paired Data ◽  
Correlation Parameter ◽  
Bivariate Normal ◽  
Combined Test ◽  
Sample Correlation ◽  
Correlational Data ◽  
Z Transformation

This study discusses the description and application of certain combined tests and estimates based on k independent sets of bivariate normal correlational data. We consider the case in which only the sample correlation coefficients are available and the case in which the original paired data are available. A combined test for the correlation parameter based on Fisher's z-transformation is considered, as well as confidence intervals and a combined estimate for the correlation parameter. A test for the homogeneity assumptions is discussed and a table for the power of the additive test based on Fisher's z-transform is presented. Bayesian single and multiparameter estimation are also considered.

Reliability of an Active-Knee-Extension Test for Determining Hamstring Muscle Flexibility

1992 ◽  
Vol 1 (3) ◽  
pp. 181-187 ◽  
Author(s):  
Teddy W. Worrell ◽  
Michael K. Sullivan ◽  
Joseph J. DeJulia
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Intraclass Correlation ◽  
Muscle Length ◽  
Correlation Coefficients ◽  
Accurate Method ◽  
Knee Extension ◽  
Hamstring Muscle ◽  
Intraclass Correlation Coefficients ◽  
Hamstring Flexibility

This study examined the intratester and intertester reliability of an active-knee-extension test (AKET) for determining hamstring muscle length (flexibility). Three testers performed repeated AKET measurements on 22 subjects. Intraclass correlation coefficients (ICC were used to calculate intratester and intertester reliability. Also, standard error of measurements (SEM) were calculated. The ICC and SEM were .96 and 1.82°, respectively, for Tester 1, .99 and 1.75° for Tester 2, and .99 and 1.80° for Tester 3. Intratester 95% confidence intervals ranged from 60.54 to 69.82°. Intertester ICC and SEM for two testers were .93 and 4.81°, respectively. A 95% intertester confidence interval ranged from 56.35 to 75.21 °; this reveals that intertester AKET values contained more error and suggests that only intratester AKET values should be used when comparing hamstring flexibility values. The AKET may provide a more accurate method for determining hamstring flexibility and quantifying changes that occur as a result of injury and stretching procedures.

scholarly journals Is there a relationship between the overhead press and split jerk maximum performance? Influence of sex

2021 ◽  
pp. 174795412110204
Author(s):  
Marcos A Soriano ◽  
G Gregory Haff ◽  
Paul Comfort ◽  
Francisco J Amaro-Gahete ◽  
Antonio Torres-González ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Body Mass ◽  
Upper Limb ◽  
High Reliability ◽  
Intraclass Correlation ◽  
Correlation Coefficients ◽  
Training Experience ◽  
Maximum Performance ◽  
Repetition Maximum ◽  
Intraclass Correlation Coefficients

The aims of this study were to (I) determine the differences and relationship between the overhead press and split jerk performance in athletes involved in weightlifting training, and (II) explore the magnitude of these differences in one-repetition maximum (1RM) performances between sexes. Sixty-one men (age: 30.4 ± 6.7 years; height: 1.8 ± 0.5 m; body mass 82.5 ± 8.5 kg; weightlifting training experience: 3.7 ± 3.5 yrs) and 21 women (age: 29.5 ± 5.2 yrs; height: 1.7 ± 0.5 m; body mass: 62.6 ± 5.7 kg; weightlifting training experience: 3.0 ± 1.5 yrs) participated. The 1RM performance of the overhead press and split jerk were assessed for all participants, with the overhead press assessed on two occasions to determine between-session reliability. The intraclass correlation coefficients (ICC) and 95% confidence intervals showed a high reliability for the overhead press ICC = 0.98 (0.97 – 0.99). A very strong correlation and significant differences were found between the overhead press and split jerk 1RM performances for all participants (r = 0.90 [0.93 – 0.85], 60.2 ± 18.3 kg, 95.7 ± 29.3 kg, p ≤ 0.001). Men demonstrated stronger correlations between the overhead press and split jerk 1RM performances (r = 0.83 [0.73-0.90], p ≤ 0.001) compared with women (r = 0.56 [0.17-0.80], p = 0.008). These results provide evidence that 1RM performance of the overhead press and split jerk performance are highly related, highlighting the importance of upper-limb strength in the split jerk maximum performance.

Empirical Nonparametric Bootstrap Strategies in Quantitative Trait Loci Mapping: Conditioning on the Genetic Model

Genetics ◽  
1998 ◽  
Vol 148 (1) ◽  
pp. 525-535
Author(s):  
Claude M Lebreton ◽  
Peter M Visscher
Keyword(s):  
Quantitative Trait Loci ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Quantitative Trait ◽  
Genetic Factors ◽  
Genetic Model ◽  
Original Data ◽  
Nonparametric Bootstrap ◽  
Test Protocol ◽  
Trait Loci

AbstractSeveral nonparametric bootstrap methods are tested to obtain better confidence intervals for the quantitative trait loci (QTL) positions, i.e., with minimal width and unbiased coverage probability. Two selective resampling schemes are proposed as a means of conditioning the bootstrap on the number of genetic factors in our model inferred from the original data. The selection is based on criteria related to the estimated number of genetic factors, and only the retained bootstrapped samples will contribute a value to the empirically estimated distribution of the QTL position estimate. These schemes are compared with a nonselective scheme across a range of simple configurations of one QTL on a one-chromosome genome. In particular, the effect of the chromosome length and the relative position of the QTL are examined for a given experimental power, which determines the confidence interval size. With the test protocol used, it appears that the selective resampling schemes are either unbiased or least biased when the QTL is situated near the middle of the chromosome. When the QTL is closer to one end, the likelihood curve of its position along the chromosome becomes truncated, and the nonselective scheme then performs better inasmuch as the percentage of estimated confidence intervals that actually contain the real QTL's position is closer to expectation. The nonselective method, however, produces larger confidence intervals. Hence, we advocate use of the selective methods, regardless of the QTL position along the chromosome (to reduce confidence interval sizes), but we leave the problem open as to how the method should be altered to take into account the bias of the original estimate of the QTL's position.

Uncertainty in protein–ligand binding constants: asymmetric confidence intervals versus standard errors

2021 ◽  
Author(s):  
Vaida Paketurytė ◽  
Vytautas Petrauskas ◽  
Asta Zubrienė ◽  
Olga Abian ◽  
Margarida Bastos ◽  
...  
Keyword(s):  
Ligand Binding ◽  
Confidence Intervals ◽  
Binding Constants ◽  
Standard Errors
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