# Quality Notion

## Exploring new ways of quality and process voyage

## Statistical Tests in Minitab leading to CMMI High Maturity

__In this article, 7 statistical tests are explained which are essential for doing statistical analysis inside a CMMI High Maturity (HM) compliant project or organization.__

**1 Stability test**

**Definition:**

Data stability for the selected parameter is tested using minitab before making performance baselines.

**Steps:**

- Go to Stat->Control Charts-> I-MR (In variables, enter the column containing the parameter)
- From the section for Estimate, choose ‘Average Moving Range” as methods of estimating sigma and ‘2’ as moving range of length
- From section of tests, choose specific tests to perform
- From the section for ‘Options’ enter sigma limit positions as 1 2 3.

**Results: **

After eliminating all the out of turn points, the system attains stability and is ready for baseline.

**2 Capability test**

**Definition:**

Once the selected parameter is baselined, capability of the same to meet the specification limits are tested.

**Steps:**

- Go to Stat->Quality Tools->Capability Sixpack(Normal), Choose single Column, (In variables, enter the column containing the parameter), Enter ‘1’ as subgroup size),Enter Lower spec and upper spec,
- From the section for Estimate choose ‘Average Moving Range” as methods of estimating sigma and ‘2’ as moving range of length,
- From the section for Options, enter ‘6’ as sigma tolerance, choose ‘within subgroup analysis’ and ‘percents’, and Opt ‘display graph’

**Results: **

If the control limits are within specification limits or the C_{p }and C_{pk} values are equal to or greater than one, the data is found to be capable.

**3 Correlation test**

**Definition:**

Correlation test will be conducted between each independent parameter and the dependent parameter (if both are of continuous data type) in the Process Performance Model.

**Steps:**

- Go to Stat->Basis Statistics ->Correlation (Opt display P values)

**Results:**

For each correlation test p-value has to be less than 0.05 (or the decided p value within the organization based on risk analysis)

**4 Regression test**

**Definition:**

Regression test will be conducted including all the independent parameters and the dependent parameter in the Process Performance Model.

**Steps:**

- Go to Stat->regression->regression; (In response and predictors, enter the columns containing the dependent and independent parameters respectively)
- From the section for storage, include Residuals also

**Results: **

- p-value has to be less than 0.05 for each factor as well as for the regression equation obtained. (Or the decided p value within the organization based on risk analysis)
- [R-Sq (adj)] has to be greater than 70 %( or the decided value within the organization based on risk analysis) for ensuring the correlation between the independent parameters and the dependent parameter. Otherwise, the parameter cannot be taken.
- Variance Inflation Factor (VIF) has to be less than 10. If VIF is greater than 10, correlation test (stat->basic statistics->correlation) will be conducted among the different parameters which are influencing Process Performance Model. In cases where correlation is high i.e. correlation greater than 0.5 or -0.5, the factors have dependency. In such cases if degree of correlation is quite high one of the factors will be avoided or relooked for new terms.

**Definition:**

Normality of the data is tested using the Anderson-Darling test.

**Steps:**

- Go to Stat > Basic Statistics > Normality Test> Anderson-Darling test
- In Variables, enter the columns containing the measurement data.

**Results: **

For the data to be normally distributed, null hypothesis cannot be rejected. For this p value has to be greater than 0.05 (or the decided p value within the organization based on risk analysis) and A^{2} value has to be less than .757.

**Definition:**

Test for Two Variances is conducted to analyse whether variances are significantly different in two sets of data.

This null hypothesis is tested against the alternate hypothesis (two samples are having unequal variance)

**Steps:**

- Go to Stat > Basic Statistics > 2 Variances.
- Opt ‘Samples in Different Columns’. In Variables, enter the columns containing the measurement data

**Results:** If the test’s p-value is less than the chosen significance level (normally 0.05), null hypothesis will be rejected.

**Definition:**

Two sample T test is used to check whether means are significantly different in two periods for two groups of data.

The null hypothesis is checked against one of the alternative hypotheses, depending on the situation.

**Steps:**

- Go to Stat > Basic Statistics > 2 Sample T
- Opt ‘Samples in Different Columns’. In Variables, enter the columns containing the measurement data.( First should be the initial data and second should be current data)
- Check or uncheck the box for “Assume equal variances” depending upon the F test results (Two variance Test results)
- In the Options, use the required alternative, whether ‘not equal’, ‘less than’ or ‘greater than’.
- Put test difference as 0 and confidence interval as 95.

**Results:**

If the test’s p-value is less than the chosen significance level (normally 0.05), null hypothesis has to be rejected.

Tags: capability, correlation, F test, normality test, regression, stability, two sample T test, two variance

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