Six Sigma Tool Navigator: The Master Guide for Teams

2017-07-07 02:10:07

AKA

Chi-Square Analysis

Classification

Decision Making (DM)

Tool description

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.

Typical application

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.

Problem-solving phase

→	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

Typically used by

1	Research/statistics
	Creativity/innovation
2	Engineering
	Project management
	Manufacturing
	Marketing/sales
	Administration/documentation
	Servicing/support
4	Customer/quality metrics
3	Change management

links to other tools

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

Notes and key points

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-by-step procedure

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.