**INTRODUCTION**

Statistics defined as the
science which deals with collection presentations analysis and interpretation
of data.

Karl Pearson’s famous
chi-square paper appeared in spring of 1900.

An auspicious beginning
to the wonderful century for the field of statistic.

**What is chi-square test?**

It is a statistical test
to compare observed data with data we would except to obtain according to a
specific hypothesis.

A chi-square test is a
measurement of how expectations compare to results. The data used in
calculating a chi-square statistic must be random, raw mutually exclusive drawn
from independent variables and be drawn from a large enough sample.

**Definition**

(Dictionary.com)

Chi-square is a
statistical test commonly used to compare observed data with data we would
expect to obtain according to a specific hypothesis.

The data used in
calculating a chi-square statistics must be random, raw, mutually, exclusively
drawn from independent variables and be drawn from a large enough sample.

Chi-square statistics
compare the tallies (total score/amount) of categorical response between two or
more independent groups.

Chi-square test can be
used on actual numbers not on percentages, proportions, and means.

A chi-square test could
be defined as a non-parametric test that is used to test hypothesis about
distribution of frequencies across categories of data. it can be used to test
for comparing variance.

**Null Hypothesis**

It is the hypothesis
which assumes that there is no difference between two values.

Data are two types

i-Numerical ii-categorical

Categorical data based on
“biology “or “no”

And numerical data can be
either discrete or continues

**EXAMPLE:**

How many children do you
own? (3or4)

How long hairs are you?
(15.2 inches)

**Formula of chi-square**

Formula x= ∑(O-E)2 /E

O = Observed Value

E = Expected value

X2=∑ (observed frequency
–expected frequency) 2 /expected frequency

∑=is just the Greek
letter sigma which means “sum of”.

(Test which is sum of the
square of observed values minus the expected values divided by the expected
values.)

**IMPORTANCE**

„
Chi-square test is based on frequencies.

„
Chi-square test is for testing hypothesis not for estimation.

„
Chi-square test is very useful test in research work.

„
Chi-square test has no rigid assumptions, no need of parameters.

**APPLICATION OF CHI-SQUARE TEST**

**1 –TEST OF GOODNESS OF FIT OF DISTRIBUTION**

It means the extent to
which data matches the values expected by theory.

Chi-square test enable to
see how well does the assumed theoretical distribution (binomial distribution
fit to observed data)

**2 –TEST OF INDEPENDENCE OF ATTRIBUTUES**

Chi-square test enable to
explain whether or not two attributes are associated. Help

Example.

We may be interested in
knowing whether an iPhone is attracting people or not?

**3 –TEST OF HOMOGENITY**

Chi-square test can also
be used to test whether the occurrence of events follow uniformity or not?

Example

Admission of patient in
government Hospital in all days of week is uniform or not? Can be tested with
the help of chi-square test.

**LIMITATIONS**

Does not indicate the
cause and effect. It only tells the probability of assurance of association by
chance.

**DEGREE OF FREEDOM**

**D.F =(r-1) (c-1)**

The frequencies observed
(O) in each class of one event Row wise and the number in each group of the
other event column wise.

**P-VALUE**

(This means that there is
a 5% chance of finding a difference given degree of freedom)

Chi-square (calculated
value)

Chi-square (tabulated)

**ACCEPTED AND REJECTED OF NULL HYPOTHSIS**

If chi-square (calculated
value) > chi-square (tabulated value)

Than null hypothesis is
rejected.

**STEPS INVOLVED IN THE TEST.**

„
This approach consist of 4 steps.

„
State the hypothesis.

„
Formulate an analysis plan

„
Analyze sample data.

„
Interpret results.

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