Proceedings of 14th International Conference on Computer and Infonnation Technology (ICCIT 2011) 22-24 December, 2011, Dhaka, Bangladesh
A Simulation Study on Some Parametric Confidence Intervals for the Difference of Means of Two Skewed Populations t + Shipra Banik and B.M. Golam Kibria tSchool of Engineering and Computer Science, Independent University, Bangladesh, Dhaka, Bangladesh. tDepartment of Mathematics and Statistics, Florida International University, Miami, USA.
[email protected],
[email protected] likelihood interval and possibly its bootstrap version. The
Abstract Skewed data are common in the Biosciences and in life testing
objective of this paper is to consider several parametric
modeling. In this paper, we evaluate several existing techniques and
confidence intervals for the difference of means of two
propose some new techniques for estimating the differences of means
skewed distributions. Since a theoretical comparison is not
of two skewed populations. A simulation study has been made to
compare the performance of the selected intervals and a real life example has been considered to illustrate the applications of the techniques. We believe the findings of this paper will be helpful for different health researchers those are interested to choose the proper
possible, a simulation study will be conducted to compare the performance of confidence intervals. The plan of the paper is as follows: The considered interval estimators are described in section II. A simulation study along with discussion of the
techniques for estimating the differences of means for two skewed
results is presented in section Ill. A real life data has been
populations.
analyzed in section IV. Finally, some concluding remarks are given in section V.
Keywords: Biometric variable, Coverage probability, Monte Carlo simulation, Polymorphism, Positively skewed, Primary hypertension patients, Statistical inference. I. INTRODUCTION
II. STATISTICAL METHODOLOGY
Let Xlo Xz, ... , Xn and Ylo yZ, ... , Yn be two independent random samples from two populations with means ill and il2 respectively. We want to construct confidence interval for the
others are often interested in comparing the difference of some
mean difference of ill-il2' Let x and y are the sample means and s and s are the sample variances respectively.
measures between two groups (for example, drug effects
A. Ordinary Method
Bio-informatricians, Bio-statisticians, health professionals and
between normal group and treatment group). Recently, health professionals
[1]
studied
total
cholesterol
measurements
(mg/dl) for 133 primary hypertensive (PH) patients and 4 I
/
/
For small samples, the commonly used t-based confidence
interval for il1-il2 is
normotensive (NT) patients. In this paper our plan is to revise the above problem using recent statistical methodologies. Here our focus of analysis is on the difference of means of above two populations using the major branch in Statistics, namely statistical
inference.
This
inference
may
be
finding
a
confidence interval or testing a hypothesis to find the value of population means. Confidence interval is an interval estimate that will capture the true parameter value in the samples.
For a typical testing
repeated
hypothesis, a p-value is
necessary to find whether one should accept or reject the null hypothesis. A convenient way to perform significance test is to compute a confidence interval for the parameter and accept the alternative hypothesis if the assumed parameter lie outside the confidence interval. Using the major branch in Statistics, our target is to test whether PH patients have, on average, higher total cholesterol levels than NT patients?
We have
taken data from [1]. Summary statistics of the total cholesterol measurements (mg/dl) for 133 PH patients and 41 NT patients
UCL
=
(x
-
S2 S2 y) + tn 1 +n,_2 '2
