QUESTION
Explain Chi-Square. Also, discuss it as an independent test.
- Course: Educational Statistics
- Course code 8614
- Level: B.Ed Solved Assignment
ANSWER
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
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.
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