- Open
**Customer Data.xlsx**(to access, click**SigmaXL > Help > Open Help Data Set Folder**or**Start > Programs > SigmaXL > Sample Data**). Click**Sheet 1**Tab. - Click
**SigmaXL > Statistical Tools > Descriptive Statistics**. - Check
**Use Entire Data Table**, click**Next**. - Select
*Overall Satisfaction*, click**Numeric Data Variable (Y) >>**, select*Customer Type*, click**Group Category (X1) >>**, as shown: - Click
**OK**. - Descriptive Statistics are given for Customer Satisfaction grouped by Customer Type:
- Click
**Recall SigmaXL Dialog**menu or press**F3**to recall last dialog. Change the format selected to**Column Format**as shown:

- Click
**OK**. Descriptive Statistics are given for Customer Satisfaction broken out by Customer Type in Column Format:

Which Customer Type has the highest mean satisfaction score? Clearly Type 2. However, we have to be careful concluding that there is a significant difference in satisfaction solely by looking at the Means. In the Analyze Phase, we will run tests of hypothesis to validate that Type 2 Customers are, in fact, significantly more satisfied.

- Click
**Recall SigmaXL Dialog**menu or press**F3**to recall last dialog. Click**Options**. Check**Select All**and change Percentile Confidence Intervals to**Percentile**to display all Percentile values in the report.

**Tip**: Select only those options that are of interest in order to minimize the size of the report. Here we are selecting all options for demonstration purposes. Note that when any option is checked,**Row Format**is automatically selected,**Column Format**and**Group Category (X2)**are greyed out. These display options are limited due to the amount of information displayed in the extended report.

- Click
**OK**. Extended Descriptive Statistics are given for Customer Satisfaction grouped by Customer Type:

- The
**Additional Descriptive Statistics**are:

5% Trimmed Mean. The highest 5% and lowest 5% are excluded and mean calculated with the rest of the data. This gives a robust alternative to the Median as a measure of centraltendency in the presence of outliers.

Standard Error of Mean (StDev/√𝑁)

Variance (StDev2)

Coefficient of Variation (100 * StDev/Mean)

Short Term StDev (MR-bar/d2)

- The
**Additional Normality Tests**are:

- Shapiro-Wilk (n <= 5000) and Kolmogorov-Smirnov-Lilliefors (KSL, n > 5000)
- This is a popular alternative to Anderson Darling.
- Doornik-Hansen (DH)
- Univariate omnibus test based on Skewness and Kurtosis. (Note, the
bivariate DH

test is used in Correlation Matrix to test bivariate normality). - Best for data with ties, i.e. chunky data. Anderson-Darling,
Shapiro-Wilk and KSL

are severely affected by ties in the data and will trigger a low P-Value even if the

data are normal. - See Appendix Doornik-Hansen (DH) Normality Test for further details
and

references.

- The
**Percentile Report**gives 27 values from 0.135 to 99.865.

- The
**Percentile Ranges**are:

- 75 - 25 (50%, Interquartile Range IQR)
- 90 - 10 (80%, Interdecile Range IDR)
- 95 - 5 (90%, Span)
- 97.5 - 2.5 (95%, +/- 1.96 Sigma Equivalent)
- 99 - 1 (98%)
- 99.5 - 0.5 (99%)
- 99.865 - 0.135 (99.73%, +/- 3 Sigma Equivalent)

- The Percentile Confidence Intervals give 27 values from 0.135 to 99.865.
- The Quartile Confidence Intervals give 3 values: 25, 50 and 75.
- The Percentile Tolerance Intervals are 50%, 80%, 90%, 95%, 98%, 99%, and 99.73%.
- Confidence Intervals and Tolerance Intervals can be exact or
interpolated. If exact, the actual exact confidence level will be a value greater than or equal to
specified, due to percentile values being discrete in nature. The actual exact level will
also be reported in this case. If interpolated, the result will be an interpolated estimate of the
specified confidence level (typically 95.0%) and is the recommended setting. See Appendix
Percentile (Nonparametric)Confidence and Tolerance Intervals for further details.
- If the Confidence Interval or Tolerance Interval cannot be computed due to inadequate sample
size, a minimum sample size is reported.

- The
**Outlier (Boxplot Rules)**Tests are: Potential 1.5(IQR), Likely 2.2(IQR), Extreme 3.0(IQR).

**Grubbs Outlier Test**is more powerful at detecting a single outlier as maximum or minimum but assumes that the remainder of the data are normally distributed.

- The
**Randomness Runs Test**is a nonparametric exact runs test.

- The Outlier and Randomness Tests use the same Green, Yellow,
Red highlight given in the
automatic assumptions report that are included in t-tests and
ANOVA.

- Click
**Recall SigmaXL Dialog**menu or press**F3**to recall last dialog. Click**Options**. Uncheck**Select All**to clear the selections and check**Percentile Confidence Intervals**, select Exact and Percentile. Check**Percentile Tolerance Intervals**, and select**Exact**as shown:

- Click
**OK**. The Percentile Confidence Intervals and Tolerance Intervals are displayed:

- The specified 95% is a guaranteed minimum. The exact confidence level is given with each reported interval.

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