CHI SQUARE ASSIGNMENT

Collecting and Using Business Data



Collecting and Using Business Data

Introduction

The Chi square test ((2) can be used even with measured data on a nominal scale. The null hypothesis of the chi-square postulates a fully specified probability distribution as the mathematical model of the population that generated the sample. To make this contrast data is available in a frequency table. For each value or range of values indicates the absolute frequency is observed or empirical (Oi). Then, assuming the null hypothesis is true, are calculated for each value or range of values that the absolute frequency or expected frequency expected. The test statistic is based on the differences between Oi and Ei is defined as:

This statistic has a chi-square distribution with k-1 degrees of freedom if n is large enough, i.e. if all expected frequencies are greater than 5. In practice, it tolerates a maximum of 20% of frequencies below 5. If there is perfect agreement between the observed and expected frequencies statistic takes a value of 0, on the contrary, if there is a large discrepancy between these frequencies the statistic takes a large value and, therefore, reject the null hypothesis. Thus, the critical region is located in the upper end of the Chi-square distribution with k-1 degrees of freedom.

The purpose of this paper is to test hypothesis based on chi square calculation, to see whether there is a systematic relationship between the specified variables. The independent variable is the quality or characteristic that the researcher hypothesizes helps to predict or explain some other characteristic or behavior (the dependent variable). Researchers control the independent variable (in this example, by sampling males and females) and elicit and measure the dependent variable to test their hypothesis that there is some relationship between the two variables.

Though one can apply the chi-square test to a single variable and judge whether the frequencies for each category are equal (or as expected), a chi-square is applied most commonly to frequency results reported in bivariate tables, and interpreting bivariate tables is crucial to interpreting the results of a chi-square test. Bivariate tabular analysis (sometimes called cross break analysis) is used to understand the relationship (if any) between two variables.

Discussion

When the aim is to compare two or more groups of subjects with respect to a categorical variable, the results are often presented as two-way tables that are called contingency tables. It is the representation of the joint distribution of two variables designed to investigate the relationship between them. Contingency table is the most versatile tool for studying the statistical relations, since it can be represented by variables with any level of measurement. The easiest way to illustrate these contexts is a cross table (contingency table). For the description of the systematic relationships exist several measures of association, the most famous is the chi-square test. The chi-square test checks whether a trait in two or more samples is identically distributed. The corresponding null hypothesis is: H0: The proportion of each characteristic value is ...