# How Do I Create an Attribute MSA Report in Excel Using SigmaXL?

Attribute MSA is also known as Attribute
Agreement Analysis. Use the Ordinal option if the assessed result is
numeric ordinal (e.g., 1, 2, 3, 4, 5). There must be at least 3
response levels in the assessed result, otherwise it is binary.
Examples of ordinal responses used elsewhere in this workbook
include:

*Customer Loyalty –Likely to Recommend*score which contains ordinal integer values from 1 to 5, where a 1 indicates that the customer is very unlikely to recommend and a 5 indicates that the customer is very likely to recommend.- Taste Score on a scale of 1-7 where 1 is "awful" and 7 is "delicious." This is used in the cake bake taste test Design of Experiments.

An Ordinal Attribute MSA study should be
done prior to formal ordinal data collection for use in hypothesis
testing, regression or design of experiments.

- Open the file
**Attribute MSA – Ordinal.xlsx.**This is an Ordinal MSA example with 50 samples, 3 appraisers and 3 trials. The response is 1 to 5, grading product quality. One denotes “Very Poor Quality,” 2 is “Poor,” 3 is “Fair,” 4 is “Good” and a 5 is “Very Good Quality.” The Expert Reference column is the reference standard from an expert appraisal. Note that the worksheet data must be in stacked column format and the reference values must be consistent for each sample. - Click
**SigmaXL > Measurement Systems Analysis > Attribute MSA (Ordinal)**. Ensure that the entire data table is selected. Click**Next**. - Select
*Sample No., Appraiser, Assessed Result and Expert Reference*as shown. Check**Report Information**and enter*Attribute MSA Ordinal*for**Product/Unit Name**. Select**Percent Confidence Interval Type – Wilson Score**:

- Click
**OK.**The Attribute MSA Ordinal Analysis Report is produced.

**Tip:** While this report is quite extensive, a
quick assessment of the attribute measurement system can be made by
viewing the** Kendall Concordance** and **Kendall Correlation** color
highlights: **Green** - very good agreement; **Yellow** - marginally
acceptable, improvement should be considered; **Red** - unacceptable.
Further details on the Kendall Coefficients are given below.

Tip: Fleiss’ Kappa and Percent Agreement are included in the report
for completeness but not recommended for use with Ordinal response
data because they treat each response level as nominal. Kendall’s
Concordance and Correlation take the order of the data into account,
so a deviation of 1 is not as bad as a deviation of 2 or more. See
Attribute MSA – Nominal for a discussion of the Fleiss’ Kappa
report.

**Tip: Fleiss’ Kappa** and
**Percent Agreement** are included in the report for
completeness but not recommended for use with Ordinal response data
because they treat each response level as nominal. Kendall’s
Concordance and Correlation take the order of the data into account,
so a deviation of 1 is not as bad as a deviation of 2 or more. See
**Attribute MSA – Nominal** for a discussion of the**
Fleiss’ Kappa** report.

**Kendall’s Concordance/CI Within Appraiser Agreement Graph:**

**Within Appraiser Agreement Table:**

**Between Appraiser Agreement Table:**

**Kendall's Coefficient of Concordance** (Kendall's W) is a measure of association for discrete ordinal data, used for assessments that do not include a known reference standard. Kendall’s coefficient of concordance ranges from 0 to 1: A coefficient value of 1 indicates perfect agreement. If the coefficient = 0, then the agreement is random, i.e., the same as would be expected by chance.** “Rule-of-thumb” interpretation guidelines: >= 0.9 very good agreement (green); 0.7 to < 0.9 marginally acceptable, improvement should be considered (yellow); < 0.7 unacceptable (red)**.

**Kendall's Concordance P-Value**:
H0: Kendall's Coefficient of Concordance = 0. If P-Value < alpha
(.05 for specified 95% confidence level), reject H0 and conclude
that agreement is not the same as would be expected by chance.
Significant P-Values are highlighted in red. See Appendix Kendall’s Coefficient of Concordance for further details on the Kendall Concordance calculations and “rule-of-thumb” interpretation guidelines.

**Kendall's Concordance LC** (Lower Confidence) limit and
**Kendall's
Concordance UC** (Upper Confidence) limit cannot be solved
analytically, so are estimated using bootstrapping. Interpretation Guidelines:
Concordance lower confidence limit >= 0.9: very good agreement.
Concordance upper confidence limit < 0.7: the attribute agreement is
unacceptable. Wide confidence intervals indicate that the sample
size is inadequate.

The **Within Appraiser Agreement** for Joe is marginal, Moe is
unacceptable and Sue is very good.

The **Between Appraiser Agreement** is unacceptable.

**Kendall’s Correlation/CI Each Appraiser vs. Standard
Effectiveness Graph:**

**Each Appraiser vs. Standard Agreement Table:**

**All Appraisers vs. Standard Agreement Table:**

**Each Appraiser vs. Standard Effectiveness Table:**

**Kendall's Correlation Coefficient** (Kendall's tau-b) is a measure
of association for discrete ordinal data, used for assessments that
include a known reference standard. Kendall’s correlation
coefficient ranges from -1 to 1: A coefficient value of 1 indicates
perfect agreement. If the coefficient = 0, then the agreement is
random, i.e., the same as would be expected by chance. A coefficient
value of -1 indicates perfect disagreement. **“Rule-of-thumb”
interpretation guidelines: >= 0.8 very good agreement (green); 0.6
to < 0.8 marginally acceptable, improvement should be considered
(yellow); < 0.6 unacceptable (red)**.

**Kendall's Correlation P-Value: H0:**
Kendall's Correlation Coefficient = 0. If P-Value < alpha (.05 for
specified 95% confidence level), reject H0 and conclude that
agreement is not the same as would be expected by chance.
Significant P-Values are highlighted in red.

**Kendall's Correlation LC**
(Lower Confidence) and **Kendall's Correlation UC**
(Upper Confidence) limit use a normal approximation. Interpretation
Guidelines: Correlation lower confidence limit >= 0.8: very good
agreement. Correlation upper confidence limit < 0.6: the attribute
agreement is unacceptable. Wide confidence intervals indicate that
the sample size is inadequate.

**Tip**: Kendall’s Correlation
values in the Effectiveness tables are very similar to those in the
Agreement tables (the slight difference is due to average Kendall
for unstacked versus Kendall for stacked data). This is why the
**Kendall’s Correlation/CI Each Appraiser** **vs.
Standard Agreement** graph is not shown. It would essentially
be a duplicate of the **Kendall’s Correlation/CI Each
Appraiser vs. Standard Effectiveness **graph.

Appraiser Joe has marginal agreement versus
the standard values. Appraiser Moe has unacceptable agreement to the
standard. Sue has very good agreement to the standard.

Overall, the appraisers have marginal
agreement to the standard.

Note that the Percent Agreement results in
**All Appraisers vs. Standard Agreement** **Table**
show only 2% agreement! This is due to the requirement that all
appraisers agree with the standard across all trials for a 5 level
response, which is very unlikely to occur. This highlights the
problem with using Percent Agreement in an Ordinal MSA. Kendall’s
coefficients are the key metric to assess an Ordinal MSA.

**Effectiveness and Misclassification
Summary** is a summary table of all appraisers’ correct
rating counts and misclassification counts compared to the known
reference standard values.

**Attribute MSA Data** is a summary showing the original data in
unstacked format. This makes it easy to visually compare appraiser
results by part. If a reference standard is provided, the cells are
color highlighted as follows: absolute deviation = 0 (green);
absolute deviation = 1 (yellow); absolute deviation >=2 (red):

In conclusion, this measurement system is marginal and should be improved. Appraiser Moe needs training and Appraiser Joe needs a refresher. Sue has very good agreement based on Kendall’s Concordance and Correlation, but would have been considered marginal based on Kappa (< .9) and Percent Effectiveness (< 95%). As discussed above, Kappa and Percent Effectiveness do not take the order of the response data into account, so are not as useful as Kendall’s coefficients in an Ordinal MSA study.

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