Often when we make a survey to compare various products (or vendors, companies, brands) the results are in the following format:
Now, we can visualize such data in several ways. One of the obvious ways to visualize is to make a stacked bar chart. But it results in poor representation of values as we cannot easily compare ratings of one vendor to another. This is where a panel chart would help. A sample panel chart for above data can be like this:
A panel chart (often called as trellis display or small-multiples) shows data for multiple variables in an easy to digest format. It lets users compare in any way and draw conclusions with ease.
Today, I want to discuss how the principles of panel chart can be applied to visualize a complex set of survey results. For this we will use the recent survey conducted by Gartner on how various customers use BI (Business Intelligence) tools. The folks at Tableau have done good analysis of this data and presented the results in this format:
While the above chart is ok, it doesn’t let you compare vendors very well. We can only compare them on first usage, “viewing static management reports”. For everything else, the base line changes, so it is difficult to draw meaningful conclusions if, for example, you want to know which software is getting used more for “doing complex adhoc analysis”.
Jon Peltier has done beautiful analysis of this chart and presented various alternatives in his post yesterday. One of his recommendations is, of course, making a panel chart like this:
While, Jon’s Panel Chart greatly improves the readability of these survey results, I have 2 problems with it.
- Making such a panel chart in Excel is like baking your own bread. If you are like me, after few hours, you would run to bakery both hungry and frustrated. Panel Charts are not native in Excel. That means, we have to bribe, coax, threaten, protest and bend over backwards to prepare something like this in Excel. Thankfully people have already done that. So we can follow the examples and learn from their lead. [here is a panel chart tutorial from Jon]. However, the point still remains that, creating a panel chart in excel is a pain.
- Once such a panel chart is constructed, it is still pretty rigid. For eg. if you are interested in knowing how IBM as a BI vendor fares, you would like to have the results sorted by IBM’s BI Usages, but doing that in this carefully weaved panel set up means going to square 1 with less dough. So, we are stuck with a panel chart where the values cannot be sorted by any one vendor.
Is there a simpler way to construct panel charts in Excel?
So, I wondered, “is there a better and simpler way to make this chart that would still let me compare values (by BI vendor or BI Usage), let me sort and still save me enough time to drive down to one of the best bakeries in town to get a nice fluffy donut?“.
Of course there is…
The trick is to use Incell Charts. Ahem!
Instead of carefully tweaking chart options, adding dummy series and hiding them in the charts, we can just use incell charts with REPT formula and then align them in the cells. Since Excel naturally has the grid layout, creating panels (or small multiples) is as easy as snapping your fingers. (pls. note, this method of panel chart is only applicable for bar / column charts. If you need panels of line charts or scatter charts, you still need to use the methods suggested by Jon.)
We can also easily add a sorting option and use the lovely LARGE formula to sort the results based on selected vendor.
Here is what I prepared using the above recipe and it took me less than 20 minutes to set this up.
[click here for larger version of this]
How is the above incell panel chart constructed?
I am sure you are eager to know how this chart is constructed. Here is the secret:
- I took the raw data from Jon’s site and then Pivoted it so that we get the survey results in a table (with vendors on top and usages on left).
- I have dedicated a cell to let user select the sort order. Let us call this cell as “K3”
- Based on the vendor selected in K3, I have sorted the entire raw data using LARGE formula (and generous use of MATCH, INDEX, OFFSET formulas as well – examples here and here).
- Then I used the REPT formula to plot the incell bar charts (and the font “play bill” so that the bars look thick and nice).
- I have topped this with conditional formatting so that sorted vendor can be highlighted in different color.
Download the Incell Panel Chart Workbook
Download the Incell Panel chart workbook to play with it. I am sure you will find something useful and fun in that. [mirror download link]
How would you chart survey results?
There are still few problems with this approach though (for eg. adding labels can be a pain), but all in all, this simplifies the charting task and leaves room for adding extra features like sorting, conditional formatting.
Here is a open invitation. We have a long weekend coming up, thanks to Easter. So go ahead and download the original data here. And make your own charts for this survey data. The objective is that we should be able to compare vendors with each other with ease. Save your charts as images and upload them somewhere. Then leave a comment here with that URL so that we all can know how you would chart survey results.
Also, share your opinion on this type of panel charts. What is your experience with them? Do you like / hate panel charts?
20 Responses to “Simulating Dice throws – the correct way to do it in excel”
You have an interesting point, but the bell curve theory is nonsense. Certainly it is not what you would want, even if it were true.
Alpha Bravo - Although not a distribution curve in the strict sense, is does reflect the actual results of throwing two physical dice.
And reflects the following . .
There is 1 way of throwing a total of 2
There are 2 ways of throwing a total of 3
There are 3 ways of throwing a total of 4
There are 4 ways of throwing a total of 5
There are 5 ways of throwing a total of 6
There are 6 ways of throwing a total of 7
There are 5 ways of throwing a total of 8
There are 4 ways of throwing a total of 9
There are 3 ways of throwing a total of 10
There are 2 ways of throwing a total of 11
There is 1 way of throwing a total of 12
@alpha bravo ... welcome... 🙂
either your comment or your dice is loaded 😉
I am afraid the distribution shown in the right graph is what you get when you throw a pair of dice in real world. As Karl already explained, it is not random behavior you see when you try to combine 2 random events (individual dice throws), but more of order due to how things work.
@Karl, thanks 🙂
When simulating a coin toss, the ROUND function you used is appropriate. However, your die simulation formula should use INT instead of ROUND:
=INT(RAND()*6)+1
Otherwise, the rounding causes half of each number's predictions to be applied to the next higher number. Also, you'd get a count for 7, which isn't possible in a die.
To illustrate, I set up 1200 trials of each formula in a worksheet and counted the results. The image here shows the table and a histogram of results:
http://peltiertech.com/WordPress/wp-content/img200808/RandonDieTrials.png
@Jon: thanks for pointing this out. You are absolutely right. INT() is what I should I have used instead of ROUND() as it reduces the possibility of having either 1 or 6 by almost half that of having other numbers.
this is such a good thing to learn, helps me a lot in my future simulations.
Btw, the actual graphs I have shown were plotted based on randbetween() and not from rand()*6, so they still hold good.
Updating the post to include your comments as it helps everyone to know this.
By the way, the distribution is not a Gaussian distribution, as Karl points out. However, when you add the simulations of many dice together (i.e., ten throws), the overall results will approximate a Gaussian distribution. If my feeble memory serves me, this is the Central Limit Theorem.
@Jon, that is right, you have to nearly throw infinite number of dice and add their face counts to get a perfect bell curve or Gaussian distribution, but as the central limit theorem suggests, our curve should roughly look like a bell curve... 🙂
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I'm afraid to say that this is a badly stated and ambiguous post, which is likely to cause errors and misunderstanding.
Aside from the initial use of round() instead of int(),.. (you've since corrected), you made several crucial mistakes by not accurately and unambiguously stating the details.
Firstly, you said:
"this little function generates a random fraction between 0 and 1"
Correctly stated this should be:
"this little function generates a random fraction F where 0 <= F < 1".
Secondly, I guess because you were a little fuzzy about the exact range of values returned by rand(), you have then been just as ambiguous in stating:
"I usually write int(rand()*12)+1 if I need a random number between 0 to 12".
(that implies 13 integers, not 12)
Your formula, does not return 13 integers between 0 to 12.
It returns 12 integers between 1 and 12 (inclusive).
-- As rand() returns a random fraction F where 0 <= F < 1, you can obviously can only get integers between 1 and 12 (inclusive) from your formula as stated above, but clearly not zero.
If you had said either:
"I usually write int(rand()*12) if I need a random number between 0 to 11 (inclusive)",
or:
"I usually write int(rand()*12)+1 if I need a random number between 1 to 12 (inclusive)"
then you would have been correct.
Unfortunately, you FAIL! -- repeat 5th grade please!
Your Fifth Grade Maths Teacher
Idk if I'm on the right forum for this or how soon one can reply, but I'm working on a test using Excel and I have a table set up to get all my answers from BUT I need to generate 10,000 answers from this one table. Every time, I try to do this I get 10,000 duplicate answers. I know there has to be some simple command I have left out or not used at all, any help would be extremely helpful! (And I already have the dice figured out lol)
Roll 4Dice with 20Sides (4D20) if the total < 20 add the sum of a rerolled 2D20. What is the average total over 10,000 turns? (Short and sweet)
Like I said when I try to simulate 10,000turns I just get "67" 10,000times -_- help please! 😀
@Justin
This is a good example to use for basic simulation
have a look at the file I have posted at:
https://rapidshare.com/files/1257689536/4_Dice.xlsx
It uses a variable size dice which you set
Has 4 Dice
Throws them 10,000 times
If Total per roll < 20 uses the sum of 2 extra dice Adds up the scores Averages the results You can read more about how it was constructed by reading this post: http://chandoo.org/wp/2010/05/06/data-tables-monte-carlo-simulations-in-excel-a-comprehensive-guide/
Oh derp, i fell for this trap too, thinking i was makeing a good dice roll simulation.. instead of just got an average of everything 😛
Noteably This dice trow simulate page is kinda important, as most roleplay dice games were hard.. i mean, a crit failure or crit hit (rolling double 1's or double 6's) in a a game for example dungeons and dragons, if you dont do the roll each induvidual dice, then theres a higher chance of scoreing a crit hit or a crit failure on attacking..
I've been working on this for awhile. So here's a few issues I've come across and solved.
#1. round() does work, but you add 0.5 as the constant, not 1.
trunc() and int() give you the same distributions as round() when you use the constant 1, so among the three functions they are all equally fair as long as you remember what you're doing when you use one rather than the other. I've proven it with a rough mathematical proof -- I say rough only because I'm not a proper mathematician.
In short, depending on the function (s is the number of sides, and R stands in for RAND() ):
round(f), where f = sR + 0.5
trunc(f), where f = sR + 1
int(f), where f = sR + 1
will all give you the same distribution, meaning that between the three functions they are fair and none favors something more than the others. However...
#2. None of the above gets you around the uneven distribution of possible outcomes of primes not found in the factorization of the base being used (base-10, since we're using decimal; and the prime factorization of 10 is 2 and 5).
With a 10-sided die, where your equation would be
=ROUND(6*RAND()+0.5)
Your distribution of possible values is even across all ten possibilities.
However, if you use the most basic die, a 6-sided die, the distributions favor some rolls over others. Let's assume your random number can only generate down to the thousandths (0.000 ? R ? 0.999). The distribution of possible outcomes of your function are:
1: 167
2: 167
3: 166
4: 167
5: 167
6: 166
So 4 and 6 are always under-represented in the distribution by 1 less than their compatriots. This is true no matter how many decimals you allow, though the distribution gets closer and closer to equal the further towards infinite decimal places you go.
This carries over to all die whose numbers of sides do not factor down to a prime factorization of some exponential values of 2 and 5.
So, then, how can we fix this one, tiny issue in a practical manner that doesn't make our heads hurt or put unnecessary strain on the computer?
Real quick addendum to the above:
Obviously when I put the equation after the example of the 10-sided die, I meant to put a 10*RAND() instead of a 6*RAND(). Oops!
Also, where I have 0.000 ? R ? 0.999, the ?'s are supposed to be less-than-or-equal-to signs but the comments didn't like that. Oh well.
How do you keep adding up the total? I would like to have a cell which keeps adding up the total sum of the two dices, even after a new number is generated in the cells when you refresh or generate new numbers.
So, how do you simulate rolling 12 dice? Do you write int(rand()*6) 12 times?
Is there a simpler way of simulating n dice in Excel?
I've run this code in VBA
Sub generate()
Application.ScreenUpdating = False
Application.Calculation = False
Dim app, i As Long
Set app = Application.WorksheetFunction
For i = 3 To 10002
Cells(i, 3).Value = i - 2
Cells(i, 4).Value = app.RandBetween(2, 12)
Cells(i, 5).Value = app.RandBetween(1, 6) + app.RandBetween(1, 6)
Next
Application.ScreenUpdating = True
Application.Calculation = True
End Sub
But I get the same distribution for both columns 4 and 5
Why ?
@Mohammed
I would expect to get the same distribution as you have effectively used the same function