179. Sample Size Based Indication of Normality in Log-Normally Distributed Samples

1999 ◽  
Author(s):  
N.A. Esmen ◽  
G.A. Day ◽  
T.A. Hall
Keyword(s):  
Sample Size ◽  
Normally Distributed

scholarly journals SEM-Based Methods to Form Confidence Intervals for Indirect Effect: Still Applicable Given Nonnormality, Under Certain Conditions

2020 ◽  
Vol 11 ◽  
Author(s):  
Ivan Jacob Agaloos Pesigan ◽  
Shu Fai Cheung
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Confidence Intervals ◽  
Indirect Effect ◽  
Likelihood Estimation ◽  
Ordinary Least Squares ◽  
Mediation Model ◽  
Coverage Probabilities ◽  
Serial Mediation ◽  
Normally Distributed

A SEM-based approach using likelihood-based confidence interval (LBCI) has been proposed to form confidence intervals for unstandardized and standardized indirect effect in mediation models. However, when used with the maximum likelihood estimation, this approach requires that the variables are multivariate normally distributed. This can affect the LBCIs of unstandardized and standardized effect differently. In the present study, the robustness of this approach when the predictor is not normally distributed but the error terms are conditionally normal, which does not violate the distributional assumption of ordinary least squares (OLS) estimation, is compared to four other approaches: nonparametric bootstrapping, two variants of LBCI, LBCI assuming the predictor is fixed (LBCI-Fixed-X) and LBCI based on ADF estimation (LBCI-ADF), and Monte Carlo. A simulation study was conducted using a simple mediation model and a serial mediation model, manipulating the distribution of the predictor. The Monte Carlo method performed worst among the methods. LBCI and LBCI-Fixed-X had suboptimal performance when the distributions had high kurtosis and the population indirect effects were medium to large. In some conditions, the problem was severe even when the sample size was large. LBCI-ADF and nonparametric bootstrapping had coverage probabilities close to the nominal value in nearly all conditions, although the coverage probabilities were still suboptimal for the serial mediation model when the sample size was small with respect to the model. Implications of these findings in the context of this special case of nonnormal data were discussed.

A comparative review of methods for comparing means using partially paired data

2015 ◽  
Vol 26 (3) ◽  
pp. 1323-1340 ◽  
Author(s):  
Beibei Guo ◽  
Ying Yuan
Keyword(s):  
Missing Data ◽  
Maximum Likelihood ◽  
Sample Size ◽  
T Test ◽  
Type I ◽  
Paired Data ◽  
Modified Maximum Likelihood ◽  
Comparative Review ◽  
Paired T Test ◽  
Normally Distributed

In medical experiments with the objective of testing the equality of two means, data are often partially paired by design or because of missing data. The partially paired data represent a combination of paired and unpaired observations. In this article, we review and compare nine methods for analyzing partially paired data, including the two-sample t-test, paired t-test, corrected z-test, weighted t-test, pooled t-test, optimal pooled t-test, multiple imputation method, mixed model approach, and the test based on a modified maximum likelihood estimate. We compare the performance of these methods through extensive simulation studies that cover a wide range of scenarios with different effect sizes, sample sizes, and correlations between the paired variables, as well as true underlying distributions. The simulation results suggest that when the sample size is moderate, the test based on the modified maximum likelihood estimator is generally superior to the other approaches when the data is normally distributed and the optimal pooled t-test performs the best when the data is not normally distributed, with well-controlled type I error rates and high statistical power; when the sample size is small, the optimal pooled t-test is to be recommended when both variables have missing data and the paired t-test is to be recommended when only one variable has missing data.

scholarly journals The Distributional Behavior of Futures Price Spreads

2000 ◽  
Vol 32 (1) ◽  
pp. 73-87
Author(s):  
Min-Kyoung Kim ◽  
Raymond M. Leuthold
Keyword(s):  
Sample Size ◽  
Temporal Aggregation ◽  
Normal Distributions ◽  
Time Period ◽  
Futures Price ◽  
Larger Sample ◽  
Relative Spread ◽  
Normally Distributed

AbstractThe distributional behavior of futures price spreads is examined for four commodities: corn, live cattle, gold and T-bonds. Remarkably different results are found over commodities, time period, and sample size. Actual spread changes for the smaller sample size of gold and T-bonds and for corn produce more normal distributions for weekly than for daily differencing intervals, while all live cattle spreads for actual changes are normally distributed. However, the larger sample size of both gold and T-bonds and the relative spread changes for corn and live cattle do not become more normally distributed under temporal aggregation of the data.

scholarly journals KETEGARAN UJI-t TERHADAP KETIDAKNORMALAN DATA

2006 ◽  
Vol 7 (1) ◽  
pp. 1-10
Author(s):  
Agus Santoso
Keyword(s):  
Sample Size ◽  
Population Distribution ◽  
T Test ◽  
Computation Techniques ◽  
Two Samples ◽  
The Difference ◽  
Two Populations ◽  
Normally Distributed

t-test used to test means of two populations assumes that  each population is normally distributed. Theoretically, violation of the assumption makes the result of the test  invalid. This research evaluates the robustness of the t-test on various value of sample size using three types of distribution: normal, symmetric non-normal, and not symmetric non-normal. Different computation techniques of t-value which depend on the variance of the two populations were also employed. The simulation showed that t-test used to test mean of two populations is not influenced by non-normality of the population distribution. The exploration of distribution of the difference between two samples means showed that its distribution was normal. Therefore, the robustness against non-normality of the t-test was the consequences of the difference between two sample means that normally is distributed. 

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