The chi square
test comprises of comparing the variance of two groups. One group is that being
investigated and the other group is the given group. Closeness in variance
values of the two groups suggests homogeneity and difference suggests
heterogeneity.
To perform a chi
squared test the following conditions should hold good:
v
Quantitative data
v
The data observations should be
made on random basis
v
A sample size of minimum 10
v
More than one group
v
Independent observations
v
Using all the observations
v
Linear constraints
Chi square test
is a non-parametric test without any rigid assumptions regarding the type of
population, only information regarding the degrees of freedom is required to
carry out this test, the degree of freedom is determined by the sample size.
The test consists of forming a hypothesis, the hypothesis is rejected or
accepted on the basis of the closeness of actual chi square value with the
tabular chi square value, if the two values are close, working hypothesis is
accepted, working hypothesis is rejected and its reverse is accepted, if the
chi square values significantly differ.
Chi square test has many uses. It can be used to
infer goodness of fit, such as whether a sample is representative of a
population or not, whether a produced lot confirms with the established quality
standard, whether a medicine is effective as other medicines or not. Information
generated through chi square test enables in making decisions related to sample
size and design, quality conformance and enhancement, in comparing the
difference between expected and observed frequencies. Frequency means the
number of times a particular observation occurs and its comparative study is
used in many fields for example in marketing to study consumer preferences and
tuning the marketing offer as per their preferences. Using frequency method
qualitative data can be assigned quantities (frequencies) and chi square can
hence also be indirectly used on qualitative data as well.