- 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 central

tendency 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.

Our CTO and Co-Founder, John Noguera, regularly hosts free Web Demos featuring SigmaXL and DiscoverSim**Click here to view some now!**

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