Chi square is a statistical test that examines variation. It compares variation between two different populations and makes a determination of whether the variation is the same. This test helps determine the statistical significance of a relationship between an Attribute X and an Attribute Y in Y = f(X1,X2,..., Xn).
The approach used is to assume the variables (X Data and Y Data) are independent and set up the hypotheses as follows:
The output of the test is a "pvalue" indicates the likelihood of seeing a relationship. A high pvalue means there is no relationship between the X data andY data. A low p value (< .10) indicates there is a relationship. A low p value cannot be purely by random chance. If the pvalue is less than 0.10, then the null hypothesis Ho should be rejected and Ha should be accepted.
As with any statistical test, Chi Square comes with its set of "could be" and "might be" statements.
This Data Analysis Video teaches you the basic tools for understanding, summarizing, and making future predictions with your collected data. Includes MS Excel templates.
The Personnel Department wants to see if there is a link between age and whether an applicant gets hired. Both Age (old and young) and Got Hired (did or didn't) are attribute type data. A Chi^{2} test would be applicable to answer the question:
455 data points were taken and the data distributed amongst the four possible outcomes. The data can then be analyzed in a statistical package, such as Minitab. The software calculates the expected values in each box. ChiSquare compares the observed with the expected frequencies to produce a signaltonoise type ratio using :
Where O is the observed frequency and E is the expected frequency in a box.
The software then looks up the χ2 (the sum of all the discrepancies) value in a statistical table. As a belt using the tool practically, all that is important is the output of the tool, which should be similar to that shown below. The math behind χ2 is not covered here.
This Data Analysis Video teaches you the basic tools for understanding, summarizing, and making future predictions with your collected data. Includes MS Excel templates.
Chi^{2}: Hired, Not Hired
Expected counts are printed below observed counts. Chi Square contributions are printed below expected counts
The first place to look is the pvalue, which in this case p = 0.932. In this instance, the pvalue is not low (not below 0.10). There is no relationship between Age and Hiring Practice is not significant for the sample of data taken.
Chi Square test can be applied in virtually any transactional processes where attribute data usually abounds. For example:
The roadmap to setting up and applying a Chi Square test is as follows:
The first place to look during analysis is to the pvalue. If the pvalue is higher than 0.10 then the conclusion is that the X and Y are not dependent based on the taken sample.
However, if the pvalue is low (less than 0.10) then there is reason to believe that the X and Y are dependent in some way. If everything was based on random chance, the distribution of data points within the table isn't expected
This Data Analysis Video teaches you the basic tools for understanding, summarizing, and making future predictions with your collected data. Includes MS Excel templates.
Consider the data below, which represents loan approval or rejection decisions on different days of the week. The bank clearly would like loan decisions to be independent of the processed work day.
Test analysis results for loan data (output from Minitab v14).
Looking immediately to the pvalue of 0.028 (less than 0.10), it is clear that there is a dependent relationship. Thus, the conclusion is that the null hypothesis should be rejected and the alternate "Data are dependent" should be accepted instead. In English, we conclude there is something fishy going on, because the chances of getting a loan varies by day of the week.
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