The chi-square test is a non-parametric test because it depends only on the set of observed and expected frequencies and degree of freedom. Since the χ2 test is a does not make any assumption about population parameter, it is also called a distribution-free test. χ2the test is a test which describes the magnitudes of difference between observed frequencies and expected (theoretical frequencies under certain assumptions.
In other words, it describes the magnitudes of discrepancy between theory and observations. It is defined as.
$$Where\, O= observed\, frequencies.$$
$$E=expected\, frequencies.$$
Chi-square test distribution typically looks like a normal distribution which is skewed to the right. It is a continuous distribution which assumes only positive value.
Uses of Chi-square test.
Test of association / Independence of attributes.
$$H_0= There \,is \,no \,significance\, association\, between\, two\, factors.$$
$$H_1= There\, is\, the\ ,significance\, association\, between\, two\, factors.$$
Note.
In correlation analysis , the degree of relationship is studied two variable, which can be numerically measured such as age and blood pressure, an amount of rainfall and production of rice etc. But sometimes the variable may not measure such as honesty, beauty, hairstyle, gender, a day of the week or it would be in the form of attributes good/bad , day/night etc. and instead of words variable we use word factors.
Test statistic
$$Where\, O= observed\, frequencies.$$
$$E=expected\, frequencies.$$
$$expected\, frequencies.E\,for\,any\,cell\,is\,determined\,by\,E=\frac{R.T×C.T}{N}$$
$$Where R.T=Row\,total$$
$$C.T=Column\,total$$
Degree of freedom
$$It\,is\,given\,by\,(r-1)(c-1)$$
$$Where\,r=number of rows$$
$$c=number\,of\,columns\,of\,the\,contigency\,table$$
Contingency table.
When two-category variable (factors) are recorded, the data can be summarised by counting the observed number of units that all into each of the various intersection of categories levels. The resulting counts are displayed in an array called a contingency table.
Remark.
A | \(\overline{A}\) | Total | |
B | a | b | a+b |
\(\overline{B}\) | c | d | c+d |
The formula after correlation is.
Reference
Kerlinger, F.N. Foundation of Behavioural Research. New Delhi: Surjeet Publication, 2000.
Kothari, C.R. Research Methodology. India: Vishwa Prakashan, 1990.
Singh, M.L. and J.M Singh. Understanding Research Methodology. 1998.
Singh, Mrigendra Lal. Understanding Research Methodology. Nepal: Natiocentreok centre, 2013.
Chi-square test distribution typically looks like a normal distribution which is skewed to the right. It is a continuous distribution which assumes only positive value.
the degree of relationship is studied two variable, which can be numerically measured such as age and blood pressure, an amount of rainfall and production of rice etc
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