Chi-Squared Test

What is chi square test?

Following are the assumptions when the chi square test is taken in use with commonly used approximation:

• Random-sample – It is data’s sampling collected in a random manner from fixed population or distribution.
• Sample-size – Assumptions are done of samples that are having size sufficiently big. If chi square tests are conducted or done on samples having small size, then inference yielded from chi square test will be inaccurate. A researcher may finish the test by committing Type II error, if he uses chi square tests on the small size samples.
• Expected counts of cells - Sufficient expected counts of cells. Few need either five / more than 5, & others may require ten / more than 10. The rule which is used commonly is five / more than 5 in every cell with a table having size of 2 by 2, & five / more than 5 in eighty percent of the cells with tables having large size, but not a single cell with 0 expected-counts.
• Independence – An observation is always pretended as not to be dependent upon each-other. The above statement means that we cannot use chi square test for testing data which are mutually related (such as panel-data, matched-pairs). In such cases we may require to look upon Mc Nermar’s test.

Speaking in general, chi square test has been considered as a test of statistics for examining the differences or dissimilarity with the variables of a category. In the social-world, we can find numerous features of it (such as religion, preferences of politics etc.) which we describe or characterize with the help of variables of a category. For examining hypotheses by using these variables a person should use chi square test.

Pearson's Chi-Square Test

Pearson's chi-square test is taken into use for assessing comparisons of 2 types. The 2 comparison types are tests of independence and goodness of fit. These are mentioned in brief below:

• Tests of independence – Tests of independence makes an assessment that whether the paired-observance on 2 variables, which in contingency table are expressed, are not dependent on each-other, i.e. they are said to be independent. For e.g. a group of people belonging to different areas having different frequencies reports that a particular political-candidate is being supported by them.
• Goodness of fit – Goodness of fit test establishes that whether / whether not a watched frequency distribution has any difference when compared to that of theoretical distribution.

Calculating the statistical chi-square is the 1^st step to be followed in chi square test. For avoiding ambiguity, test-statistic value is referred through Χ² instead of χ² (which can either be uppercase-chi rather than lowercase-chi, or can be uppercase-Roman-X). However, most of the writers use the notation of χ² for test-statistic.