10 Replies Latest reply on May 30, 2015 6:45 PM by Susan Baier

# Help with Standard Deviation

OK. I'm sure this is fairly straightforward but I've been struggling with it and can't figure it out.

I have set of data reporting appeal of various features and benefits, showing average responses on a Likert scale for each of three different segments within the respondent group (blue, green and orange). (It's proprietary so I can't attach the workbook, but I've included a screen shot.)

I want somehow to give people an easy "handle" with which to evaluate whether the responses between segments on a particular items are statistically different. It seems that showing a representation of each response +/- one-half a standard deviation would be fine in this regard, but I can't figure out how to show that.

The measure being used here is AVG(Response).

Could I show a range (like a bar) with each dot showing its +/- standard deviation limits?

Susan

• ###### 1. Re: Help with Standard Deviation

Hi Susan,

Working with survey data makes a nice break from counting how many patients who have COPD have been readmitted in the last 6 months, here goes one attempt:

Fortunately when it comes to Likert scales and survey data we do have a sample data set that we can use, I'm using the data that Steve Wexler used in his visualizing survey data posts, in particular this one: Using Tableau to Visualize Survey Data — Part 3: Dealing with Multiple Memberships for Respondents » Data Revelations

[end of digression]

I took the raw data and pivoted the questions in v9 to make a tall data set, and renamed the pivot field names Question and the pivot field values Response. Then I filtered the data for 3 Generations (the segment) and a few of the answers. Here's a worksheet that duplicates the look of yours:

We could add a reference band for +/- 1 standard deviation but that has three problems: The first is that the SD would be computed for each Question (cell), not for each Generation within the cell. The second problem is that reference lines & bands are computed as an aggregation on the pill (e.g. AVG(Response)), not the underlying data (e.g. the Response for each ID). The third is that a single reference line/band has only one set of colors, whereas we might want to color each line/band based on the Mark color and not have to add a new line/band every time there's a segment.

One way to hack this would be to create a dual axis, on the second axis add the respondent ID to Level of Detail of the view, use table calculations or LOD expressions to compute the overall average to draw those Marks, create three additional calculations to return the Response per Generation, and then use those three calcs to make 3 reference bands with the right colors. But that's doing a lot of hard coding and making Tableau pull data for every ID from the data source which can impact performance.

A more elegant solution is to do our own calcs and then draw the bands on a secondary axis. Gantt marks are great for this, the continuous used on Rows/Columns for Gantt marks sets the start of the mark, then whatever is on the Size Shelf sets the length of the mark.

Here's the Gantt Start calc:

AVG([Response]) - (STDEV([Response]) * [# of SD])

It's taking the AVG(Response) and subtracting the STDEV(Response) * a # of SD factor that is a parameter (more on that below). We're using the AVG() aggregation at the same level of detail as the STDEV() so the results will be accurate, avoiding problem #2 with the reference lines/bands. In addition, this avoids problem #1 because the aggregations are computed at the level of detail of the view, which is Question & Generation.

Then the length (Size) of the Gantt bar is:

STDEV([Response]) * 2 * [# of SD]

Here's the start of the view, the only change was to make the Color for the Gantt marks slightly transparent.

And here's the view after synchronizing the axes:

The overlapping bars make the view harder to read, however clicking on a mark will highlight the entire bar:

If there are new generations added or removed there's no work to be done, the workbook will automatically adjust. Plus there's only standard aggregations used in the view, so the work Tableau and the data source have to do are much simpler.

Now for the bit on standard deviation and why I used a parameter. In the original post the goal was to show a 1 standard deviation range. Given a normal distribution, that only covers 68% of the data. A more common definition of outlier is to show 2SD (95%) or 3SD (99.7%), so I used the parameter to set that so you can see the difference. In practice I'd fix the number in the calcs and avoid the parameter, that way Tableau can do more caching and get more performance.

An alternative view would be to use a dashboard, I set up the original circle plot and then used a modified view with the Generations as separate rows and the Gantt marks. A Filter Action on Question connects the two:

Hope this helps!

Jonathan

[Edited 20150521 to fix the calcs per Steve Wexler's note below, change the screenshot to reflect that and post a revised packaged workbook]

1 of 1 people found this helpful
• ###### 2. Re: Help with Standard Deviation

Dear Jonathan,

First of all, THANK YOU! This is exactly what I needed, and I am so grateful to you for taking the time to post such a detailed and helpful response.

Second of all, THANK YOU for your absolutely appropriate digression about the lack of a sample workbook. You're completely right, and I was being lazy by not going to the effort to include one. I am properly chastised, and won't let it happen again. :-)

I'm gonna apply this to my workbook and let you know how it works. Again, appreciate your prompt and helpful response. You're a peach. :-)

Susan

• ###### 3. Re: Help with Standard Deviation

Hi Jonathan,

I've created a sample workbook with my data, and tried your approach but I can't seem to get the GANTT bars right -- they're clearly not in the right place, and don't have any width at all. Would you mind taking a look and seeing if you can figure out what I'm doing wrong? I'd be grateful. Thank you.

Susan

• ###### 4. Re: Help with Standard Deviation

Hi Susan, I'll get a chance to check tomorrow morning.

Jonathan

• ###### 5. Re: Help with Standard Deviation

Thanks so much Jonathan.

Susan

On Wed, May 20, 2015 at 2:56 PM, Jonathan Drummey <

• ###### 6. Re: Help with Standard Deviation

Ha! Never mind! I figured it out! (Didn't have Gantt Size on the Size pill, it was on the Label pill - DUH.) Thanks so much Jonathan!

Susan

• ###### 7. Re: Help with Standard Deviation

Great!!

• ###### 8. Re: Help with Standard Deviation

Jonathan,

I took a different approach where my single STDDEV matches your two levels of STDDEV.

I placed all the responses on the viz and then used the undocumented RANDOM() function to jitter the responses.  I used a reference line to show average response and a reference band to show STDDEV.

I tend to like to see the marks to see how things cluster and if there are lots of outliers or not.  One could also make the marks very subtle and replace the reference line with a big circle using a dual axis chart.

Any thoughts on why my -1, 1 STDDEV is equal to your -2, 2?

Steve

• ###### 9. Re: Help with Standard Deviation

Hi Steve,

Jittering is a great way to deal with the limited number of discrete values, I like it! As I'm looking at yours, nother way could be to use a vertical bar chart on one axis and the ref line on the other.

Thanks for checking out what I'd posted, I'd built the function with one idea in mind (the parameter being the range of SD) and described it with another (the parameter being the +/- SD). I've fixed the workbook and edited my post to reflect that.

Jonathan

• ###### 10. Re: Help with Standard Deviation

Jonathan Drummey I wanted to show you what I ended up with (attached). This allows me to eyeball the extent to which the average ratings on these items are (or aren't) half a standard deviation apart from other ratings. The bar is set to 1 standard deviation, giving me .5 SD to either side of the mean. Very helpful in my situation, where I need to see the difference relative not to one other mean, but 2 or 3 others. What do you think? I'm grateful for your help and Steve Wexler's in getting me to this!

Susan