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Sunday, December 3, 2023

Chi-Square | independent test | Educational Statistics | 8614 |

 QUESTION

Explain Chi-Square. Also, discuss it as an independent test.

  • CourseEducational Statistics
  • Course code 8614
  • Level: B.Ed Solved Assignment 

ANSWE

The Chi-Square Distribution

The Chi-Square (or the Chi-Squared - χ2) distribution is a special case of the gamma distribution (the gamma distribution is a family of right skewed, continuous probability distribution. These distributions are useful in real life where something has a natural minimum of 0.). a chi-square distribution with n degree of freedom is equal to a gamma distribution with a = n/2 and b = 0.5 (or β = 2).

Let us consider a random sample taken from a normal distribution. The chi-square distribution is the distribution of the sum of these random samples squared. The degrees of freedom (say k) are equal to the number of samples being summed. For example, if 10 samples are taken from the normal distribution, then the degree of freedom df = 10. Chi-square distributions are always right-skewed. The greater the degree of freedom, the more the chi-square distribution looks like a normal distribution.

Uses of Chi-Square (χ2) Distribution

The chi-square distribution has many uses which include:

i)  Confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation.

ii)  Independence of two criteria of classification of qualitative variables (contingency tables).

iii)  Relationship between categorical variables.

iv)  Sample variance study when the underlying distribution is normal.

v)  Tests of deviations of differences between expected and observed frequencies (one-way table).

vi)  The chi-square test (a goodness of fit test).

What is a Chi-Square Statistic?

A Chi-Square Statistic is one way to a relationship between two categorical (non-numerical) variables. The Chi-Square Statistic a is a single number that tells us how much difference exists between the observed counts and the counts that one expects if there is no relationship in the population.

There are two different types of chi-square tests, both involve categorical data. These are:

a)  A chi-square goodness of fit test, and

b)  A chi-square test of independence.

In the coming lines, these tests will be dealt with in some detail.

 

Chi-Square Independence Test

A chi-square (χ2) test of independence is the second important form of a chi-square test. It is used to explore the relationship between two categorical variables. Each of these variables can have two or more categories.

It determines if there is a significant relationship between two nominal (categorical) variables. The frequency of one nominal variable is compared with different values of the second nominal variable. The data can be displayed in the R*C contingency table, where R is the row and C is the column. For example, the researcher wants to examine the relationship between gender (male and female) and empathy (high vs. low). The researcher will use the chi-square test of independence. If the null hypothesis is accepted there would be no relationship between gender and empathy. If the null hypothesis is rejected then the conclusion will be there is a relationship between gender and empathy (e.g. say females tend to score higher on empathy and males tend to score lower on empathy).

The chi-square test of independence being a non-parametric technique follows less strict assumptions, some general assumptions should be taken care of:

Random Sample –

 The sample should be selected using a simple random sampling method.

Variables –

Both variables under study should be categorical.

Independent Observations –

Each person or case should be counted only once and none should appear in more than one category of group. The data from one subject should not influence the data from another subject.

If the data are displayed in a contingency table, the expected frequency count for each cell of the table is at least 5.

Both the chi-square tests are sometimes confused but they are quite different from each other.

  • The chi-square test for independence compares two sets of data to see if there is a relationship.
  • The chi-square goodness of fit test is to fit one categorical variable to a distribution.


Related Topics

ANOVA and its Logics

Measures of Dispersion

Descriptive and Inferential Statistics

What is data Cleaning? Importance and Benefits of Data Cleaning 

Explain the terms Degree of Freedom,Spread of Score,Sample,Z Score,Confidence Interval 

What is measure of difference? Explain different types of test

Concept of Reliability, Types and methods of Reliability

Level of Measurement

Types of Variable in Stats 

Measures of Central Tedency and Dispersion, 

Role of Normal Distribution, and also note on Skewness and Kurtosis

Methods of Effective Presentation


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