Comparison of Some Parametric and Non-Parametric Statistical Methods Chapter One Purpose of the Study

Comparison of Some Parametric and Non-Parametric Statistical Methods

Chapter One

Purpose of the Study

1. To find out if there exists any relationship between indexes of human development reports using both parametric and nonparametric
2. To equally test for independence using both multivariate parametric method and nonparametric method to see if it can produce the same
3. To find out similarities/differences between the two statistical methods based on the result of the analysis used in this
4. To analyze statistically, multivariate data by using parametric and nonparametric tests for independence

CHAPTER TWO

LITERATURE REVIEW

INTRODUCTION

Multivariate analysis deals with the observation of more than one variable where there is some inherent interdependence between variables. There is a wide variety of multivariate techniques. The choice of the most appropriate method depends on the type of data, the problem, and the sort of objectives that are envisaged for analysis. The review in this chapter extends from the existing literature by providing both multivariate parametric and nonparametric tests for independence.

Multinormality Theory

Multivariate analysis lays too much interest on the assumption that all random vectors come from multivariate normal distribution. By definition, the probability density function of a normal variable with mean m and variance s2 is given by

f (x) = (2ps2) exp – ½ (x-m)(s2)-1(x-m)

Then the extension to the p-variate is

f (x) = (2p ) 2 å

– 1

2 exp-

1 (x – m )1 -1 (x – m )

The reasons for its (normal distribution) preference in the multivariate case are among others. (Hollander M and Wolfe DA, 1973)

• The multivariate normal distribution is entirely defined by its first and second
• The multivariate distribution is an easy generalization of its univariate counterpart, and the multivariate analysis runs almost parallel to the corresponding analysis based on univariate
• Linear functions of a multinormal vector are themselves univariate normal.
• In the case of normal variables, zero correlation implies independence and pairwise independence implies total independence.
• Equiprobability contours of the multivariate distribution are simple ellipses, which by a suitable change of coordinates can be made into a circle.
• When the original data is not multinormal, one can often appeal to central limit theorems which prove that certain functions such as the sample mean are normal for large

Parametric versus non-parametric statistics in the analysis of randomized trials with non-normally distributed data.

The following ideas are the contributions and conclusions gotten from Andrew J Vickers, Wolfowitz, (1942) Siegel & Castellan, (1988) & Dr Matthew Ellis (2002). It has generally been argued that parametric statistics should not be applied to data with non-normal distributions. Empirical research has demonstrated that Mann-Whitney (Wilcoxon) generally has greater power than the t-test unless data are sampled from the normal. In the case of randomized trials, we are typically interested in how an endpoint, such as blood pressure or pain, changes following treatment. Such trials should be analyzed using ANCOVA, rather than a t-test. The objectives of this study were:

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CHAPTER THREE

MATERIALS USED FOR THE STUDY

The data set used in this work, listed as Appendix A, consists of eight (8) indicator variables selected from 38 African Countries (HDR 2005).

These indicators are

1. HDI Human Development Index
2. EI Education Index
3. GDP/Index Gross Domestic Product Index
4. LEI Life Expectancy Index
5. HPI-I Human Poverty Index values(%)
6. PNUIWS Population not Using Improved Water Sources
7. AIR Adult Illit
   
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