Tool 92: Hypothesis Testing (Chi-Square)


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

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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

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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):

  1. Data Source: Customer satisfaction visits by executives

    • Business unit visited: X Y

    • Corrective action required: Yes N

  2. 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.

  3. Test used: Chi-square (χ2) test of indepennce

  4. Level of significance used: .05

  5. Degress of freedom: 1 df = (c 1) (r 1)

  6. Test result: χ2 = 3.63

  7. Critical value: 3.841 (See Chi-Square Distribution Table)

  8. 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.

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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.

Example of tool application

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Six Sigma Tool Navigator(c) The Master Guide for Teams
Six Sigma Tool Navigator: The Master Guide for Teams
ISBN: 1563272954
EAN: 2147483647
Year: 2005
Pages: 326

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