## How to extend the AHP Excel Template for more Participants?

As I received many requests to extend the number of participants in my AHP excel template, here a short information how to use it for more than 20 participants. There are two possibilities

• Use my AHP online Software.
• Use several templates, each  of them for up to 20 participants, and then combine the consolidated results in an additional summary template.
• Modify the template.

As the template is quite complex, I strongly recommend to use the first possibility. But if you really want to modify the template itself, follow the step-by-step instruction below. This instruction does not include the AHP consensus indicator calculation.

1. Unprotect sheet In20; create a copy of the sheet In20 and rename to In21.
2. Go to “Formulas – Name Manager” and delete name Matrix20 with scope In21.
Mark matrix cells of the decision matrix in In21 (C79:L88), and define new name Matrix21 with scope workbook.
Go to Sheet multInp, unprotect sheet. Add additional matrix, e.g. copy/paste from matrix 20 (2 matrices per rows, same structure as for matrix 1-10).
Mark content cells of new matrix and define new name “m_p21
Set it {=Matrix21} ( {} = array function, see below).
Mark the consolidated matrix (B9:K18), and modify the formula
{=(M9:V18*B22:K31* …*B74:K83)^(1/N4)} to include the added participant’s matrix.
3. Go to sheet Summary, unprotect sheet.
Mark matrix starting at line 38, and add new matrix m_p11 in the formula: {=IF(p_sel>0;CHOOSE(p_sel; m_p1; m_p2; … ; m_p20; m_p21);MatrixC)}.
Select field C7 (number of participants). Menu “Data – Data Validation”:
change range from 1 to 20 to 1 to 21.
4. Continue in the same way for additional participants.

Note:  {} is the Excel array function: mark cell area, and use Ctrl-Shift-Enter.

All matrices in the input sheets are named Matrixn, n = 1 to max. number of participants. (Matrix1, Matrix2, etc.)
The matrices in the multInp sheet are named “m_pn” (m_p1, m_p2, etc.)

## Diversity Calculator Excel – BPMSG

The diversity calculator is an excel template that allows you to calculate alpha-, beta- and gamma diversity for a set samples (input data), and to analyze similarities between the samples based on partitioning diversity in alpha and beta diversity.

The template works under Windows OS and Excel 2010 (xlsx extension). No macros or links to external workbooks are necessary. The workbook consists of an input worksheet for a set of data samples, a calculation worksheet, where all necessary calculations are done, and a result worksheet “beta” displaying the results.

## Applications

The template may be used to partition data distributions into alpha and beta diversity, it can be applied in many areas, for example

• Bio diversity – local (alpha) and regional (beta) diversity
• AHP group consensus – identify sub-goups of decision makers with similar priorities
• Marketing – cluster analysis of similarities in markets
• Business diversification over time periods
• and many more.

Let me know your application! If you just need to calculate a set of diversity indices, you can use my online diversity calculator.

## Calculations and results

Following data will be calculated and displayed:

• Shannon Entropy H (natural logarithm) alpha-, beta- and gamma, and corresponding Hill numbers (true diversity of order one) for all samples
• Homogeneity measure
1. Mac Arthur homogeneity indicator M
2. Relative homogeneity S
3. AHP group consensus S* (for AHP priority distributions)

• Table 1: Shannon alpha-entropy, Equitability, Simpson Dominance, Gini-Simpson index and Hill numbers for each data sample

• Table 2: Top 24 pairs of most similar samples
• Page 2: Matrix of pairs of data samples
• Diagram 1: Gini-Simpson index and Shannon Equitability
• Diagram 2: Average proportional distribution for all classes/categories
• Diagram 3: Proportional distribution sorted from largest to smallest proportion (relative abundance)

Limitations:

• Maximum number of classes/categories: 20
• Maximum number of samples: 24

Description of the template:  BPMSG-Diversity-Calc-v14-09-08.pdf

Other posts explaining the concept of diversity

BPMSG Diversity Calculator Excel Template Version 2020-07-05 (zip)

As this version is the first release, please feedback any bugs or problems you might encounter.

## Updated AHP Excel Template Version 08.02.13

An updated version of my AHP Excel template for multiple inputs is now available as version 08.02.13. Beside the extension from 8 to 10 criteria and from 7 to 20 participants some new features have been added. In the past it was sometimes difficult for participants to achieve a low consistency ratio. Now inconsistent comparisons in the input sheet will be highlighted, if the required consistency level is exceeded.  The level of consistency needed (“alpha” in the summary sheet) can also be changed from 0.1 (standard rule of thumb from Saaty) to higher values, for example 0.15 or 0.2. In addition another scale for the judgment can be chosen. For my projects I made good experience with the balanced scale.

A new feature is the consensus index. If you have more than 1 participant and do the group aggregation (select participant “0”), the consensus index is an indicator, how homogenous the judgment within the group was done. Zero percent means no consensus, all participants put their preference on different criteria;  100% means full consensus. Here the changes in detail:

## Summary sheet

• Number of criteria increased from 8 to 10
• Number of participants increased from 7 to 20
1. Linear standard scale
2. Log
3. Sqrt
4. InvLin
5. Balanced
6. Power
7. Geom.
• Alpha – allows to adjust consistency threshold (0.1 default)
• Consensus indicator for group aggregation added
• Geometric Consistency Index CGI added

## Input sheets

• Consistency ratio is calculated on each input sheet.
• Priorities are calculated and shown based on RGMM (row geometric mean method)
• Top three inconsistent pairwise comparisons highlighted (if CR>alpha)

## Known Issues

Thanks to feedback from Rick, sometimes there seems to be a problem with the correct display of weights beside the criteria in the summary sheet. If you face this problem, unprotect sheet summary. Select weigths (O18:O27). Click “conditional formating”, “clear rules”,”clear rules from selected cells”. Then the values will be displayed correctly, and you can format them in the way you want. It is a strange effect; it only appears on one of my PCs, on the other it works fine. I uploaded a modified version, but not sure whether it works for everyone.

## Diversity Calculation in Excel – Diversity Indices and True Diversity

In my video “Diversity Index as Business KPI – The Concept of Diversity” I explain the mathematical concept of diversity introducing the Simpson Index λ and its complement (1-λ) as a measure of product diversification in markets.

Beside the Simpson Index there are many other indices used to describe diversity. I have developed a simple Diversity Excel template to calculate a couple of diversity indices for up to 20 categories. The following diversity indices are calculated:

• Richness
• Shannon entropy
• Shannon equitability
• Simpson dominance
• Gini-Simpson Index
• Berger-Parker Index
• Hill numbers (“true diversity”) and Renyi entropy of order one to four

For a quick calculation of diversity indices you might also use my online calculator

For calculation of Shannon entropy and its partitioning into independent alpha and beta components  see here.

Any feedback is welcome!

## Welcome to BPMSG – Dec 2012

Dear Friends, dear Visitors,

yesterday I realized 10000 visits on my website since April 2012, when I implemented the Piwik web statistics. Over the last couple of months the daily visitor frequency was actually increasing, doubling within the last 3 months. On my youtube channel http://www.youtube.com/bpmsg I am now slowly reaching 100,000 video views.

So first to all of you a big thank you, showing interest in the topics of bpmsg.com, and especially to those of you,  giving me feedback, as I can learn and progress from there. For me it also means to stay committed and keep the content interesting and updated.

The topic with the highest interest is AHP – the analytic hierarchy process, and many of you downloaded my AHP excel template. Actually, here I would really like even more feedback about your applications, just to get an idea, in what other areas my template is used. Some of them, as I received, are:

• Asset management prioritisation
• BPMSG AHP template as a teaching tool
• Weights of textual elements that affect difficulty of a given text
• Environmental quality
• Green supply chain

In my last update of the template  I improved the accuracy of calculation  significantly, so please always use the latest version, and revisit the site from time to time, to get the latest update. Alternatively you might subscribe to the bpmsg newsfeed; the link is given in the footer of the page.

My latest topic “Diversity index as business KPI – the concept of diversity” seems also to gain some interest. My video on youtube  got in a short time more viewers than the previous video about operational and strategic business performance. For me it was intersting to apply the diversity concept in business performance, as I haven’t seen this before, and the mathematical concept, to measure diversity of species in a habitat (biodiversity), is quite well established . I am thinking to publish a second video, showing more practical applications of the diversity concept in a business context.

After starting my youtube channel in 2009, I gained more and more experience in making videos. You can  clearly see the difference, comparing one of my older videos with the latest ones. Now my camcorder – a Canon XA10 – is with me most of the time on my business trips or vacations. Therefore you also find some video travel impressions on this web site under the topic “others”. My last trip was to the Philippines showing the nice island of Bohol, as well as one of the world’s largest crater lakes on a lake on an island – Lake Taal.

Klaus Goepel,
Singapore, Dec 2012

BPMSG stands for Business Performance Management Singapore. As of now, it is a non-commercial website, and information is shared for educational purposes. Please see licensing conditions and terms of use. Please give credit or a link to my site, if you use parts in your website or blog.

## Updated AHP Excel Template Version 11.12.12

Due to feedback from several users, I revised the implementation of the power method for the calculation of the Eigenvector and Eigenvalue to improve the accuracy of my AHP excel template. The calculation sheet ‘8×8 in the workbook was completely reworked. My tests show a significant increase in accuracy. As an example see my updated post AHP template – numerical accuracy.

By default the number of iterations is now set to 12.  The check value in sheet ‘8×8 cell B33 shows the sum of all matrix elements solving the Eigenvalue equation (AI*λ) x = 0 with A the Decision matrix, λ = estimated principal Eigenvalue and x = estimated Eigenvector. The ideal check value is zero. With the example numbers given in the template the result is 5E-08.

Please let me know, if  you find any problems in the new version.

## AHP template – numerical accuracy

Thanks to feedback from Mihail, here a few words about the numerical accuracy when using the AHP excel template.

AHP requires the calculation of the principal Eigenvalue, the weights are derived from the Eigenvector.  In my calculations I use the power method.  It is an iterative method, and  only one of several techniques that can be used to approximate the eigenvalues of a matrix.

## Update 11.12.12

The whole calculation is shown in work sheet ’10×10′. I use 12 iterations; at the end of the sheet I do a check (the reverse calculation), using the Eigenvalue equation: (Aλ IX = 0,  with A the AHP matrix; λ the principal Eigenvalue, and X the estimated Eigenvector. The resulting check value in cell B33 shows the sum of all matrix element of the Eigenvalue equation using the iterated Eigenvector and Eigenvalue. Ideally it should be zero.

## Update 9.5.14

From version 2014-05-09 onward the template shows the convergence of the power method, when calculating the eigenvalue. In the summary sheet a threshold (squared Euclidean distance d2) can be set, to show how many iterations it takes, until the change of the approximated eigenvector is below the given threshold. By default the value is set to Thresh: 1E-07. As the number of iterations in the template is fixed to 12, care should be taken if the value reaches 12.

## Examples

Here a practical example comparing the results from the power method, as now implemented in my template, with  an example (7 criteria) given by Saaty in Int. J. Services Sciences, Vol. 1, No. 1, 2008 (p 86, table 2). The AHP matrix is:

 1 9 5 2 1 1 1/2 1/9 1 1/3 1/9 1/9 1/9 1/9 1/5 3 1 1/3 1/4 1/3 1/9 1/2 9 3 1 1/2 1 1/3 1 9 4 2 1 2 1/2 1 9 3 1 1/2 1 1/3 2 9 9 3 2 3 1

The result according Saaty is
(0.177,  0.019, 0.042, 0.116, 0.190, 0.129, 0.327) with consistency ratio of 0,022

The result from my AHP Excel template is
(0.1775, 0.0191, 0.0418, 0.1164, 0.1896, 0.1288, 0.3268) with CR 0f 0.022
exactly the same. The check value in sheet ‘8×8 is 4E-12.

More examples

## Update AHP Excel Template Version 16.10.12

Thanks to the feedback from Pascal a bug is corrected, when you select the results of individual participants in the summary sheet. Selection/display  of results from participant 4 to 7 was not shown correctly.

## New AHP Excel template with multiple inputs

The AHP Excel template works under Office Libre and Excel version MS Excel 2013. The workbook consists of 20 input worksheets for pair-wise comparisons, a sheet for the consolidation of all judgments, a summary sheet to display the result, a sheet with reference tables (random index, limits for geometric consistency index GCI, judgment scales) and a sheet for solving the eigenvalue problem when using the eigenvector method (EVM). Latest version: 2022-07-08.

Alternative for complex AHP projects: AHP free online software.

### Excel Template

• Within the input worksheets (questionnaires) priorities are calculated using the row geometric mean method (RGMM).
• Three consistency indices (the consistency ratio CR, the geometric consistency index GCI and overall dissonance Psi) are calculated. The level of consistency needed (α) is implemented as a variable input field in the summary sheet, and can be set between zero and one.
• If CR exceeds α, the top 3 inconsistent pair-wise comparisons on the input sheets are highlighted, to allow the participants an adjustment of their judgments. The judgment resulting in lower inconsistency is proposed.
• Final priorities are shown in a summary sheet; their calculation is based on the eigen vector method (EVM). For the solution of the eigenvalue problem the power method algorithm is applied with a fixed number of 20 iterations.
• Different judgment scales are implemented.
• Errors of the EVM and RGMM are show beside the calculated priorities.
• Either individual participants, or an aggregation of individual judgments (AIJ) based on the weighted geometric mean of all participants’ judgments can be selected.

Limitations

• The template does not include the hierarchy of the decision problem and the final aggregation of weights, i.e. it is only suitable for finding the weights in each category or sub-category. For the definition of a hierarchy and evaluation of alternatives see here.
• Sensitivity analysis of the final result is not included.

### Reference

When you use the template for your research, please make a reference to the author’s paper.

```Klaus D. Goepel, (2013). Implementing the Analytic Hierarchy Process as a Standard Method for Multi-Criteria Decision Making In Corporate Enterprises – A New AHP Excel Template with Multiple Inputs, Proceedings of the International Symposium on the Analytic Hierarchy Process, Kuala Lumpur 2013. DOI: https://doi.org/10.13033/isahp.y2013.047```