Help With Chi-Square Analysis
What is a Chi-Square Analysis/Test?
Researchers utilize statistical tests to analyze data and interpret results correctly. The factors considered to determine the statistical test to apply are the purpose of research, hypothesis, and the type of data.
Scientific studies have parametric and non-parametric tests that researchers use to analyze data significantly and accurately.
A non-parametric trial is an inferential statistical method applied in hypothesis testing and does not assume the variables assessed. In parametric tests, researchers make assumptions about the criteria of a population.
Karl Pearson invented the chi-square in 1904, which is utilized to examine the differences between the observed and the expected distributions. Chi-square (x2) is a non-parametric test that researchers use to make inferences about the relationship between two categorical variables.
Types of Chi-Square Distributions
Chi-square analysis is the statistical method utilized to analyze contingency tables. A contingency table displays the frequency distribution of variables in different rows and columns. A chi-square test is represented by x2, and it is utilized in finding the correlation between variables. Before performing a chi-square test, the following must be fulfilled.
First, a researcher must collect the expected and observed distributions.
Secondly, the items in the sample must be independent.
Thirdly, the groups must contain more than ten elements, and finally, the number of objects must be above 50.
The types of chi-square distributions are the goodness of fit, independence, and homogeneity tests. The goodness of fit test is also called a single sample non-parametric.
The chi-square test of independence is utilized to determine whether two nominal variables have a relationship. Researchers utilize the chi-square test of homogeneity to determine if two or more independent samples vary by distribution.
Purpose of Chi-Square Analysis
Chi-square methods do not depend on the normal distributions, and statisticians utilize the procedures to interpret findings. Chi-square has two purposes which include testing the hypothesis among two or more groups or populations if there are correlations and testing to what length the data distribution observed fits with the expected distribution.
In chi-square analysis, the null hypothesis has no relationship with the population variables.
Steps Followed in a Chi-Square Analysis
Chi-square analysis consists of four steps; specifying the hypothesis, devising an analysis plan, examining sample data, and giving results. Researchers formulate a hypothesis and state if it is null or alternative. Statisticians then devise an analysis plan after stating the hypothesis. The analysis plan initiated must state the significance level, which should have a value between zero and one. Also, the plan must identify the test method.
The chi-square is utilized to determine if there is a relationship between two categorical variables. The third step involves examining the sample data to calculate the degrees of freedom, predictable frequencies, and the p-value.
A researcher tests statistics and determines the degrees of freedom (DF): DF=(r-1) (c-1) where r and c represent the number of levels in each categorical variable.
When presenting results using chi-square, if the p-value is less or equal to the significant level, there is enough evidence to confirm that the observed and expected distribution is not the same.
Summary
To interpret the results of a scientific study correctly, researchers utilize statistical tests. Researchers analyze non-parametric data using a chi-square test to make inferences about the correlation between two categorical variables. Chi-square analysis is a procedure that is utilized to analyze data in contingency tables.
Types of chi-square tests are the goodness of fit, independence, and homogeneity tests. The purpose of chi-square is to test the hypothesis between two or more categories and the extent to which the data observed fits with the expected distribution.
The steps followed when performing a chi-square analysis are hypothesis development, plan analysis, data sampling, and presenting results.