Chi square test
Good morning sir, good morning all me and with my
team members Aurobindo, Kriti, Deepa, are going to
present the topic Chi square test.
1 WHAT IS CHI-SQUARE TEST?
A chi-square (χ2) statistic is a test that measures how a model
compares to actual observed data. The data used in calculating
a chi-square statistics must be random, raw, mutually
exclusive, drawn from independent variables, and drawn from a
large enough sample. For example, the results of tossing a fair
coin meet these criteria.
2
Reasons why Chi Square is suitable for descriptive statistics:
1. If the sample size is large, it will always prove significant,
hence not reliable for large sample size.
2. A large sample size requires probability sampling (random),
hence Chi Square is not suitable for determining if sample is
well represented in the population (parametric). This is why Chi
Square behave well as a non-parametric technique.
Chi square is a non parametric stastics and it is two types
Test of goodness of fit
Test of homogenity
3 CHARACTERISTICS OF A CHI SQUARE TEST
• This test (as a non-parametric test) is based on
frequencies and not on the parameters like mean and
standard deviation.
• The test is used for testing the hypothesis and is not
useful for estimation.
•
This test can also be applied to a complex contingency
table with several classes and as such is a very useful test
in research work.
•
This test is an important non-parametric test as no rigid
assumptions are necessary in regard to the type of
population, no need of parameter values and relatively
less mathematical details are involved.
4 Formula
5 TEST OF GOODNESS OF FIT
• Chi-Square goodness of fit test is a non-parametric test
that is used to find out how the observed value of a given
phenomena is significantly different from the expected
value.
•
In Chi-Square goodness of fit test, the term goodness of
fit is used to compare the observed sample distribution
with the expected probability distribution.
• Chi-Square goodness of fit test determines how well
theoretical distribution (such as normal, binomial, or
Poisson) fits the empirical distribution.
•
In Chi-Square goodness of fit test, sample data is divided
into intervals. Then the numbers of points that fall into the
interval are compared, with the expected numbers of
points in each interval.
Over to Kriti
17
• Chi square test for independence of two attributes.
Suppose N observations are considered and classified
according two characteristics say A and B. We may be
interested to test whether the two characteristics are
independent. In such a case, we can use Chi square test for
independence of two attributes.
When to Use the Chi-Square Test on Survey Results
• The Chi-Square test is most useful when analyzing cross
tabulations of survey response data.
• Because cross tabulations reveal the frequency and percentage of
responses to questions by various segments or categories of
respondents like (gender, profession, education level, etc.) the
Chi-Square test informs researchers about whether or not there is
a statistically significant difference between how the various
segments or categories answered a given question.
Important things to note when considering using the
Chi-Square test
• First, Chi-Square only tests whether two individual
variables are independent in a binary, “yes” or “no” format.
Chi-Square testing does not provide any insight into the
degree of difference between the respondent categories,
meaning that researchers are not able to tell which
statistic (result of the Chi-Square test) is greater or less
than the other.
• Second, Chi-Square requires researchers to use
numerical values, also known as frequency counts,
instead of using percentages or ratios. This can limit the
flexibility that researchers have in terms of the processes
that they use.
Conclusion
As conclusion we can say that the chi-square test is an
important test amongst the several tests of significance
developed by statisticians. Being a non-parametric test, its
calculations are easier than other tests. It tests for effect of one
variable over the other, hence it is very helpful to understand
the effectiveness of products.
It is very useful for all researchers to  Test goodness of fit.
 Test the significance of association between two
attributes.
 Test the homogeneity or the significance of population
variance.
Thank you
Kajal
Is it possible to perform chi-squared test on continuous data?
No it is not possible to perform chi-squared test on continuous data.
because The Chi-Square Test of Independence can only compare
categorical variables.
It cannot make comparisons between continuous variables or
between categorical and continuous variables. If your categorical
variables represent "pre-test" and "post-test" observations, then also
the chi-square test of independence is not appropriate. This is
because the assumption of the independence of observations is
violated.
Ananya
What is the difference between chi square and Fisher's exact test?
The difference between chi-squared test applies an approximation
assuming the sample is large, and the Fisher's exact test runs
an exact procedure especially for small-sized samples.