Category Archives: Data analysis

Tornado Charts in Excel 2007/2010 Update

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Tornado diagrams are a classic tool of sensitivity analysis to provide decision makers a quick overview of the risks involved.  A tornado chart to show a financial analysis for a project may look like this:

Tornado chart - a sensitivity analysis tool

In this particular case, we are assuming that the tornado shows the NPV of a project. We expect the project can be valued at $7 billion (the point where the vertical axis crosses), subject to uncertainties.

The tornado helps visualize these uncertainties. In the example, Conversion (i.e. how many of the people that shop for our product become a customer) is the largest uncertainty. We believe 35% of the shoppers would convert. If only 25% convert, the project’s NPV would drop to $4 billion, from the base case, $7 billion. On the other hand, if 45% convert, we have a large upside and the NPV would be $12 billion.

Next in relevance would be pricing, $25,500 in the base case. If it goes down to $20,500 the NPV would reduce to $5 billion. If we can raise price up to $29,500 due to a favorable competitive environment, then the upside is $4 billion from the base case.

By now, you can follow the logic of the chart, with the other variables.  Do you still have questions?  Go ahead and drop us a line.  We are happy to help.

Tornado diagrams are not used as frequently as one would expect, given how clearly they help showing the impact of different variables on a geven outcome. As suggested by Ted Eschenbach on a recent article of Engineering Economist, (issue of 06/22/2006), perhaps this is due to difficulties in constructing them.

Sensitivity analysis is needed to address the inherent uncertainty in engineering economy applications because (1) time horizons are measured in years or decades and (2) much economic analysis is done at the feasibility and preliminary design stages. This is often shown using relative sensitivity analysis charts or spiderplots, which have a long and rich history in practice and texts (they are described in 10 of 18 texts reviewed, including Blank and Tarquin (2002), Canada et al. (1996), Eschenbach (2003), Lang and Merino (1993), Park (2002, 2004), Sullivan et al. (2003), Thuesen and Fabrycky (2001), White et al. (1998), Young (1993). Tornado diagrams are not new, but they have not been used nearly as frequently. Only one of the 18 texts included a tornado diagram (Eschenbach, 2003)–

 

Searching Google on how to make tornado charts, you’ll get many results, most of them requiring you to download an add-in. Keep reading to see how you can create tornado charts with plain Excel in just 5 steps… very easy and straightforward!!

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Harmonic Averages

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This is a short note to talk about Harmonic Averages. Most people are familiar with Weighted Averages, as they are a valuable tool for aggregation. For instance, with the data below, the average profitability (~1735) can be easily calculated using weighted averages.

Avg_Profit = (1000*1200 + 200*300 + 500*2500 + 10*600 + 100*300) / (1000 + 200 + 500 + 10 + 100)

or

Avg_Profit = SUMPRODUCT(UnitsSold,ProfitPerUnit)/SUM(UnitsSold)

I’m using Excel notation, and assuming it is clear from the context that UnitsSold is a range that covers the second column, for all models, etc.

A less known way of averaging are Harmonic Averages. It is relevant when the data to aggregate is actually a ratio whose denominator is proportional to the weighting factor. A typical case is miles per gallon (MPG) for a bunch of vehicles. Gas consumption is directly proportional to the number of units.

Let’s add some MPG data to the table above.

Using Weighted Averages for an inverse ratio like MPG is plain wrong (24.3 MPG is NOT the average fuel economy)

The right thing is to use Harmonic Average:

Harm_Avg_MPG = (1000 + 200 + 500 + 10 + 100) / (1000/22.5 + 200/15.0 + 500/32.0 + 10/12.0 + 100/24.0)

As Excel doesn’t have a similar function to SUMPRODUCT for adding 1000/22.5, 200/15.0, etc. I will not use Excel notation, but plain math notation:


UPDATED formula

If you have to deal with Harmonic Averages, you may find interesting this note on how to do PivotTable Multidimensional Analysis with Harmonic Averages. There’s a similar one for Weighted Averages as well.

Let me know what you think.

Market partition – Mekko chart in Excel, no add-ins

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Mekko charts are two dimensional graphs that analyze how data is partitioned against two variables, the X and Y axes. The width of the columns is proportional to data represented by the columns. Individual segment height is a percentage of the respective bar total value.

Yet another in-cell Excel bar chart technique

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Two improvements over the technique described by Juice Analytics and posted in Lifehacker: better resolution and solid-looking bars that show better at different font sizes.

If your values are integers in a range 0-9 or so, you can use the REPT formula as presented there, and perhaps you like the dashed type bars, so the formula as shown would work perfectly for you. If not, keep reading.
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Math on the simplified market adoption s-curve for Excel

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I’ve got a number of questions on the simplified Excel s-curve formula I published some time ago, so here are more details for those interested in the math behind it. The previous posting focused on how business analysts sometimes need to model market adoption, and provided a simple and easy to maintain formula to do so in Excel.

The formula =saturation/(1 + 81^((hypergrowth + takeover/2 – year)/takeover)) suggested for Excel is a simplification of the formula for a sigmoid function (See the Wikipedia article)

Sigmoid Formula

The graphic below shows the shape of both functions is identical. The saturation parameter just scales the function to a desired value, instead of going from 0 to 1. The factor 81 on the Excel formula determines how “sharp” the curve is, in this particular case, reaching 0.1 at the period hypergrowth and 0.9 at hypergrowth + takeover. Note that 81^x can be re-written as e^(ln(81)*x), so whatever factor is used there is simply going to affect the shape by compressing or expanding it horizontally.

Sigmoid math

This is how the scaling factor can be computed. Let’s say we want the penetration to be 5% at the period specified by hypergrowth. We can work out the solution off the second function. We need to solve for 1/(1+e^(-x) == 0.05, which gives x=-2.94444. Since the function is symmetrical, we also know for x=2.94444 P(x) == 0.95.

Since factor^((hypergrowth + takeover/2 – year)/takeover)) can be re-written as e^(ln(factor)*(hypergrowth + takeover/2 – year)/takeover)), we can solve ln(factor)*(hypergrowth + takeover/2 – (hypergrowth + takeover))/takeover == 2.94444. Reducing all the math, we arrive to
1/(1 + e^(-0.5*ln(factor))) == 0.95, and factor would be 361. If the desired penetration at hypergrowth is 20%, then we solve 1/(1 + e^(-0.5*ln(factor))) == 0.80, leading to factor == 16

Modeling market adoption in Excel with a simplified s-curve

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UPDATE 10/31/2007: Here is a screencast for this model

Often business analysts need to model the adoption of a new product or service for financial planning. There are several approaches, but a common one is the s-curve (see Wikipedia article). Here is a simple implementation in Excel that can be easily added to your spreadsheets. It reduces all the math to just three parameters:

  • saturation – What is the maximum expected penetration after the product becomes mainstream? i.e. what is the value that the top of the s-curve will reach?
  • start of fast growth – By this year, the penetration will be 10% of the saturation value, and it will start to grow rapidly. 10% was an arbitrary choice to simplify the model, and by doing some math you could change the formula to any value. It is a reasonable choice in most cases. We’ll call this parameter hypergrowth
  • takeover time – How long it will take for the product to “catch on”? – The operational assumption in the formula is that this number of years after the start of fast growth, the product would have reached 90% of the saturation value and will start to slow down. Again, 90% is an arbitrary value I chose.

The s-curve model focuses in the early phases of the product lifecycle, until maturity is reached. Penetration decay is NOT covered by this model.

The formula for each year’s penetration would simply be:
=saturation/(1+81^((hypergrowth+takeover/2-year)/takeover))

See it in action:

s curve example

In the sample spreadsheet above, look at cell B8 where you can see the formula in use. It is the same for all row 8.

saturation, hypergrowth and takeover are names defined for the parameters on rows 2 to 5 (you use names in your models instead of plain cell references, don’t you?)

Very simple, easy to maintain, light on calculation times… happy market adoption modeling!

PS: The chart shown is NeoOffice, an open source alternative to Excel for Macintosh users, based on OpenOffice

Presenting time series of market participation

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One very common need in almost any industry is to show a given market, its size, the key participant and how all has evolved over the last few years. I have used since a few years a technique I like, and yesterday I read on Juice Analytics’ weblog an article describing basically the same approach. By the way, these guys have an interesting blog.

In their sample chart, there’s only one bar and one line, so many people may ask “why bother?” — it’s not that confusing to have the overlay in the default way Excel will leave the combination chart.

The chart below is a good example of why the technique is powerful. Click to see full size. Disclaimer: as this is an excerpt from a slide, the sample is missing a lot of must-have elements of a good chart, like units, meaningful title, etc.
Sample chart market share

When showing a market and how it is partitioned across players, there are some useful elements you’d like to show:

  • Is it a growing, stable or shrinking overall market?
  • What is our share? Is it growing?
  • How are competitors doing? Are there changes that merit closer understanding?

Most common charts I’ve seen people use for the problem are:

  • One pie chart with the last year figures. Ok, but you miss the interesting historical perspective
  • Two pie charts side by side. That one hurts my eyes! There are many reasons it’s a bad representation. People are not intuitively good at comparing areas. Requires a lot of effort to follow where in each chart is each player, and how is it doing relatively to competition… enough said!
  • Stacked column charts. This is a reasonable approach. Shows the trends nicely. It is hard for people to judge the relative percentage of the bar segments, so sometimes people end up with the percentages annotated in each segment, and in that case the chart is very busy
  • Lines showing the share. Basically, the bottom part of the chart shown. It is a nice approach, you can follow what happened to the market players along time. In stable markets, may be all what is needed. The chart may be misleading though in growing markets because it loses the overall market size.

The combination of a bar chart to show the overall picture, plus lines to show the individual player trends has the best mix of good features I’ve found. I’d love to hear suggestions on other ways to approach the problem. It is not easy to spot growth in absolute volume for a given player, but in this is not usually a major drawback. If you are happy with your 3% growth and the market has been growing at 45% you’ll be soon out of business. Talk about charting failure :)

Where is the source file of that data?

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On my job I usually have to present data-rich slides that are the result of analysis on sets of data. One of my pet peeves on this types of slides is the omission of the data source. As I always point out to analysts in training, *please* do yourself a favor: put the footnote with the source. You’ll be happy when 5 months later you are asked to support some results of your analysis.

That answers the question “What is the source of your data?”. More often than not, when you have to support your analysis, its also handy to know “Where is the source of my data?”. My recommendation decks are usually in Powerpoint, and I only sparringly use Office’s embedded file feature, so what is on the slide is just a picture of the spreadsheet, chart or table.

My source notes usually look as shown below:

Example footnote with file name in Excel

The way I recommend analysts in training to do it is through the CELL function in Excel.

=CELL("filename")

The formula above will print the whole path and filename of the file. If you want only the filename, you can use

MID(LEFT(CELL("filename",A1), FIND("]", CELL("filename", A1))- 1), FIND("[",CELL("filename", A1))+1, 255)

Easy creation of tornado charts in Excel – 5 steps, no add-ins

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UPDATE: A newer post is available, with Excel 2007 instructions and a screencast.

Normalize Excel tables

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Business data is quite often expressed across many dimensions. The profitability equation in a company is very simple in concept, but in practice those revenues come across regions, product lines, products etc., making them in fact multidimensional data.

Users of OLAP systems are very aware of multidimensional data. However, many spreadsheet users are not, so they manage to flatten the data the best they can, using pages or subtotals for dimensions beyond the second one.

Modern spreadsheets have “PivotTable” capabilities, which makes easier to deal with multidimensional data. To feed these pivot tables, the information has to be normalized. This post explains how to normalize data from non-normal representation, using a Visual Basic macro

If you are familiar with OLAP and normalized data, skip to the code. I’ll show samples of non-normalized data, how the same data would look normalized, and why this recipe is useful.

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