AKA | Chi-Square Analysis |
Classification | Decision Making (DM) |
Hypothesis testing is a decision-making procedure that requires a random sample to be taken from a defined population and, through statistical testing, the difference or relationship of the hypothesized population mean and the actual sample mean is determined. Since the null hypothesis (H0) assumes no statistical significant difference or relationship, a test result is measured against critical value (level of significance) to decide if the null hypothesis is a reasonable statement and should not be rejected, or if the observed difference or relationship is statistically significant and therefore should be rejected.
To reject or not reject a stated null hypothesis (H0)
To perform inferential statistics—that is, to make inferences to a defined population on the basis of test results from a sample of that population.
To use a systematic process or decision rule to make a decision.
→ | Select and define problem or opportunity |
→ | Identify and analyze causes or potential change |
Develop and plan possible solutions or change | |
→ | Implement and evaluate solution or change |
→ | Measure and report solution or change results |
Recognize and reward team efforts |
1 | Research/statistics |
Creativity/innovation | |
2 | Engineering |
Project management | |
Manufacturing | |
Marketing/sales | |
Administration/documentation | |
Servicing/support | |
4 | Customer/quality metrics |
3 | Change management |
before
Data collection strategy
Demographic Analysis
Sampling Methods
Surveying
Descriptive Statistics
after
Response Data Encoding Form
Two-Dimensional Survey Grid
Response Matrix Analysis
Information Needs Analysis
SWOT analysis
Note | Sufficient supporting information is presented here to provide a good overview of the hypotheisis-testing procedure using the chi-square test to illustrate the sequential steps involved to arrive at a decision. It is suggested, however, that the reader refer to a text on statistics for additional information and examples. |
Recommended procedure for testing a null hypothesis
(Note: A chi-square (χ2) test is used for this example):
Data Source: Customer satisfaction visits by executives
Business unit visited: □ X □ Y
Corrective action required: □ Yes □ N
Research and Null Hypotheses (H1 − H0)
H1: There is a statistically significant relationship in the number of action items required to be done as a result of customer visits by executives to business units X and Y.
H0: There is no statistically significant relationship in the number of action items require to be done as a result of customer visits by executives to business units(X) and (Y) measured at .05 level of significance using a χ test of independence.
Test used: Chi-square (χ2) test of indepennce
Level of significance used: .05
Degress of freedom: 1 df = (c − 1) (r − 1)
Test result: χ2 = 3.63
Critical value: 3.841 (See Chi-Square Distribution Table)
Decision: Accept H0! (If the test result is lower than the critical value, the H0 is accepted. The test result is in the acceptance region under the curve.)
Chi-square analysis: A contingency matrix table constructed to cross classify at least two characteristics and to test whether they are related. These tables can be configured to have 2 2, 2 3, 2 4, 2 5, 3 5, 4 5 or 5 5 cells.
STEP 1 Data has been collected a result of customer satisfaction visits by executives. As a result of these visits, the following data were tabulated:
STEP 2 Since the data shown are nominal (qualitative) data, a chi-square test is used to perform a hypothesis testing procedure (see notes and key points).
STEP 3 Steps 1 through 8 of the hypothesis testing procedure are completed. The calculations are found in the example shown.
STEP 4 The decison rule reflected that the null hypothesis (H0) has been accepted. There is no statistical significant relationship in business units with corrective action items required.