Our World Statistics Day conversations have been a great reminder of how much statistics can inform our lives. Do you have an example of how statistics has made a difference in your life? Share your story with the Community!
In 1962, a psychological experiment was performed on 30 students. Thankfully, no one was delivering or receiving electric shocks (as in the famous Milgram experiment that was carried out in 1961). Instead, each student was asked to look at pictures of a woman making faces and rate the facial expression dissimilarities in terms of emotion and content.
Now I am a numbers girl myself (although I admit to a dark past that includes a minor in psychology), and I find it intriguing how psychologists can make inferences and conclusions from qualitative, inexact information. You may think I am the pot calling the kettle black since the field of statistics is often accused of being inexact. But I think a better way to interpret statistics is as a science that embraces randomness and inexactness to elucidate systematic patterns. Psychologists likely understand this better than most and rely heavily of statistical methods.
One popular method that is perfect for turning students’ impressions of pictures into quantifiable data is Multidimensional Scaling (MDS), a multivariate technique similar to Principal Components Analysis that falls in the class of dimension reduction methods. MDS takes a set of dissimilarities between several objects and finds the best representation of the objects as coordinates, like in a two-dimensional map for example. A classic example is pairwise distances between cities. When MDS is applied to the distances, the result is coordinates for each city that corresponds very closely with their actual locations on a map. MDS has become a popular method in fields such as psychology, ecology, spatial statistics and genetics, to name a few.
Now back to our facial expressions example. We have pairwise dissimilarities between 13 different faces made by the woman:
1. Grief at death of mother
2. Savoring a Coke
3. Very pleasant surprise
4. Maternal love, baby in arms
5. Physical exhaustion
6. Something wrong with plane
7. Anger at seeing dog beaten
8. Pulling hard on seat of chair
9. Unexpectedly meets old boyfriend
11. Extreme pain
12. Knows plane will crash
13. Light sleep
I want to use MDS to try to understand how these emotions are perceived, but JMP doesn’t have a platform to perform MDS. There is, however, an MDS procedure in SAS as well as MDS packages in R, and JMP integrates with both of these!
Luckily for me, some brilliant statistician who happens to share my name has already written a JMP add-in that I can get from the JMP File Exchange to run MDS either via SAS or R. I download the add-in and quickly install it (much like an R package works), and I’m in business! (You can download the add-in, too; it's free, but you'll need a SAS login to get it.)
I have R installed on my machine, which means JMP can connect to R, send data and submit R code, and I can get my results back in JMP to use some dynamic interactive tools. All I need to do is open up my data table and go to the Add-Ins menu and pick the Multidimensional Scaling command that was created by the add-in. I launch a dialog (shown below), fill in the dissimilarities I want to run MDS on, set up some options and click Run.
JMP connects to R (or SAS), and a few seconds later I get results! The first plot that’s launched tells me how well the data fit into coordinates for a series of dimensions. I decide I want to see the MDS results in two dimensions, so I select the point corresponding to 2 on the graph and click the button below the graph to display the MDS results.
The display below now tells me a lot of information about how the students perceived the woman’s emotional faces. In the graph below, points that are closer together mean that those facial expressions portrayed more similar emotions. The expressions are colored based on clustering the coordinates to give an idea of how they may group together into a general class of emotion.
Some things are predictable, like the patterns in Pain, Grief, and Revulsion, while for others we might learn something interesting. I myself would NOT have associated meeting an old boyfriend with maternal love and a pleasant surprise, but I guess the lady making the faces has had better experiences!
One thing I have definitely learned is that using JMP in conjunction with SAS or R provides limitless possibilities for analysis and data exploration. Thanks to the new add-in architecture in JMP, users can extend their analyses in this way, and I encourage all JMP scripters, SAS programmers and R experts out there to submit your own add-ins to the JMP File Exchange so others can benefit from your research and experience!
To learn more about JMP add-ins and SAS or R integration, check out some of the papers and talks for SAS Global Forum, the upcoming user group meetings in Las Vegas.