Chi Square Test ( X^{2})
Chi Square Test Defined the chi square test is one simplest and most commonly used non parametric tests in statistical work. The Greek letter X_{2} is used to denote this test. The quantity X^{2} describes the magnitude of discrepancy between the observed and expected frequencies. The value of X^{2} is calculated as,
X2 = [ ( O _{i} -E _{i})2/ E _{i}] = ( O-E_{1})^{2}/E1 + ( O_{2}-E_{2})_{2}/E_{2}
+ ( O_{3}-E_{3})^{2}/E_{3} + ( O_{4}-E_{4})^{2}/E_{4}......... ( O-E_{n})^{2}/En
Here O_{1}, O_{2}, O_{3},..........O_{n} are observed frequencies as E_{1}, E_{2}, E_{3}, ......E_{n} are the corresponding expected or theoretical frequencies obtained under some theory or hypothesis.
To determine the value of X2 and to draw conclusion the following steps are required.
a.Calculate the expected frequencies E_{1}, E_{2}, E_{3},......E_{n} corresponding to observed frequencies O_{1}, O_{2}, O_{3}, ..O_{n} under some theory of hypothesis.
b.Compute the deviations ( O-E) for each frequency and then square these deviations to oblation ( O-E)^{2}
( O-E)^{2} / E
c.Divide the square deviation i ,e ( O-E)^{2} by the corresponding expected frequency to obtain
d.Obtain the sum of all values computed in the step (iii) to compute.
X^{2}= ∑ [ (O-E)^{2}/E]
This gives the value of X2 if it s zero it multiples that there is not discrepancy between the observed and expected frequencies. They coincide completely. The greater the value of X2 the greater will be discrepancy between the observed and expected frequencies.
e.Under the nu.. hypothesis theory fits table value. If it is less than the table value the difference between theory and observation is not considered as significant. Such difference is regarded on account of sampling fluctuations and is ignored. On the other hand. If calculated value of X2 exceeds the table value the different between theory and observation is considered significant. In other words the discrepancy between theory and observation cannot be attributed to chance and we reject the null hypothesis and conclude that experiment does not support the theory.