What is a Chi-Squared Test?
The Chi-Squared Test is used to determine if an Attribute or Discrete “X” has an association with another Attribute or Discrete “Y.” The example below is a hypothesis (or an educated guess) that there is a relationship in Loan Default Rates between Bank Branches.
The Chi-Squared Test is intended to test how likely it is that an observed Used for determining the confidence interval for means or fo... Learn More... of data is due to chance. The Chi-Squared Test is also called the “goodness of fit” A Sample Statistic, and a Population Parameter A sample for... Learn More... because it measures how well the observed distribution of data Fitted values can also be known as fits. The fitted val... Learn More... with the distribution that is expected if the variables are independent.
The Null and Alternative Hypotheses are:
- Ho = Variable A and Variable B are independent
- There is no It's the change in the average value of the output caused by... Learn More... on Defaulted Loans due to Bank Branches
- An alternative hypothesis (Ha) states that there is a s... Learn More... = Variable A and Variable B are not independent
- There is an It's the change in the average value of the output caused by... Learn More... on Defaulted Loans due to Bank Branches
- A Bank has 200 Loan Approvals
- 100 Approvals from Branch “A”
- 100 Approvals from Branch “B”
- There are:
- 5 Loans defaulted from Branch “A”
- 9 Loans defaulted from Branch “B”
The Question: Is there a “real” difference in the default rates between the branches?
First, collect and summarize the data. This is the observed data.
Entered in Minitab as:
Analyzed as a Cross Tabulation and Chi-Square analysis the results are:
The expected values are calculated as follows:
r = Row total*(Column total / Grand total)
Example: 100*(186/200) = 93
The P value of 0.268 indicates that there is no relationship between branch and loan results. A p-value < 0.05 indicates a relationship may exist.
Next, the r values are investigated and the largest r value will have the most influence on the relationship.
Have you used a Chi-Squared Analysis in a Six Sigma Definition: Six Sigma is a set of techniques and t... Learn More... Project? If so, can you give us a brief example of the analysis?