Quantitative Data Analysis

Quantitative Data Analysis

Introduction

Data can be analyzed quantitatively and q1ualitatively but the ways are different. Quantitative analysis can be done by different statistical techniques and methods. There are various methods which can be used for the analysis of quantitative data (Abeyasekera, 2005, pp. 1- 2). The below discussion covers the interaction and interpretation of general linear model, goodness of fit for logistic regression and in the end there is a discussion about the ways by which a person can improve the statistical power in the data analysis. In statistics the concept of interaction refers to the relationship between the variables and the impact of one variable onto other. The concept of interactions strongly refers to regression analyses.

This concept is very important for the inference of any statistical model. The second part of the discussion covers the concept of logistic regression. Briefly the logistic regression is used to find the value of dependent variable. It can be binomial or multinomial. As the prefix “bi” refers that in binomial logistic regression there is possibility of only two results. In contrast multinomial logistic regression refers the variety of results.

The last part of the discussion is about a very important concept in any statistical analysis i.e. statistical power. It refers to the significance level of the model as well as individual variable. There are various reasons of low statistical power but the most common is small sample size. Researches mostly increase sample size in order to increase statistical power. The below discussion explains the number of ways for increasing statistical power rather than increasing sample size.

Discussion

The general linear model refers to a statistical linear model in which dependent variable(Y) acts as a matrix of multivariate measurements and X can be represented as design matrix while ß acts a parameter which is needed to estimate and in last there is also an error term( µ).

Y= Xß +µ

Concept of Interaction in a General Linear Model and Its Interpretation

In various empirical studies there are many generalized linear models with specific limited dependent variables modes. The incorporation of various interactions terms have been using in the applications of linear models for many years. But the attention is not enough on the role of the terms which are used for interaction in social science literature. In addition only few writers have pointed out the complexity arise from the nature of specifications in their studies.

The main problem is that the interpretation of interactions in generalized models is more difficult as compared to basic linear model (Gill, J., 2001). The interaction effects are introduced in general linear models by the use of link function. If the interaction effects are not properly analyze then the models may be invalid and wrong. Let consider the treatment of interactions in linear model as a product term

Y = ß0 + ß 1X1 + ß 2X2 + ß3X1X2 (1)

In the above equation 1 the ß3 is the coefficient estimate corresponding to the product while ß3X1X2 is called first order ...