 This blog created for educational purposes. Info4mystery archive and support student, teacher, Educationalists, Scholars, and other people for learning by facilitating reflection, questioning by self and others, collaboration and by providing contexts for engaging in higher-order thinking. BestMark Mystery

CHI-SQUARE TEST

### CHI-SQUARE TEST

• INTRODUCTION
Karl Pearson (1880) introduced a test to distinguish whether an observed set of frequencies differs from a specific frequency distribution.
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
“A quantity equal to the summation over all variables of the quotient of the square of the differences between the observed by the expected value of the variable.
(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
Dose not measure the strength of association statistical finding of relationship. This test tells the presence/absence of an associations between the events.
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.