Editor’s Note: This monthly blog from Scott Wise, JMP Principal Engineer, seeks to find interesting uses of statistical discovery to solve deep questions dealing with business, economics, sports, health, food, history and psychology. In this addition, we will tackle one of the biggest problems of dining out around Austin, Texas…mainly where is the best place to get your BBQ!
The classic 60’s rock band The Lovin’ Spoonful sang “Did you ever have to make up your mind? You pick up on one and leave the other one behind. It's not often easy and not often kind. Did you ever have to make up your mind?” Or in my case as designated concierge and chauffer for my hungry family, how do you best pick a place to eat that will keep the troops satisfied? It is not as simple as saying just go get the best food in town that money can buy! This is a problem that can involve multiple criteria, especially when the cries of hunger start coming from the back seat! So let’s do a study involving where to find the best of one of the culinary delicacies in Central Texas…mainly BBQ!
First off we need to explain what is Texas BBQ and why we selected it for our study. Texas BBQ usually refers to beef brisket that is smoked over a wood fire pit (often using hickory, pecan, oak or mesquite). Not only is it delicious but there are literally huge numbers of places to get BBQ around every corner. And of course any good Texan has their favorites and will not hesitate to offer their opinion on where you should go! But we will instead use some hard data on BBQ around Austin, TX to allow us to utilize statistical analysis to help make the best selections! Borrowing a page from the home shopping giant QVC, we will look for data that addresses three key dimensions of selection criteria…namely Quality, Value and Convenience!
While there are numerous dining apps (such as Yelp, etc.) that offer user ratings of restaurants, we found that most of these rely on simple categorical rating systems that don’t offer much separation from restaurant to restaurant (such as always getting a large grouping of places getting four stars out of five)! Luckily Zagat offers dining food ratings using a continuous 30 point scale (https://www.zagat.com) for 23 BBQ restaurants throughout Central Texas. This site also gives a comparable estimate of the price of a BBQ meal as well. That just leaves us to get a measure of convenience. Since you go to a BBQ joint more for the food than the ambiance, we just used the distance from my house to the restaurant locations.
For our statistical analysis, we asked JMP to help select the dominant points in the data that best fit the most desirable features we want to see in a BBQ restaurant. Mainly we want to see those locations that would offer the highest food rating, at the lowest costs, with the shortest travel distances. We marked in red the rows for these selected restaurants and gave them a value of one in new indicator column labeled “Dominant.” See below for a snapshot of our collected datatable with dominant points indicated.
The first issue we encounter is deciding on the best way to visualize the data. As we have three dimensions of criteria (quality, value and convenience) our first choice was to look at graphs that could present things in a 3-D format. Using a 3-D Scatterplot, you can see below that there does seem to be a group of dominant points in red that stand out from the other ones. We included transparent Contour Ellipsoids to give us some further evidence of the grouping of these selected points. However, without being able to click on and interact with the graph directly in JMP, it is hard to use this as a decision tool. Our eyes have trouble seeing with this graph where exactly the points are located within the three scales!
So let’s make our graphs work a little harder. Using the very flexible Graph Builder in JMP, we created the one below. We plotted the food rating on the Y axis and drew in some dashed lines to create three grouping zones (poorly rated meals under 22, medium rated meals, from 22 to 26, and highly rated meals above 26). We next put distance in miles on the X axis and again created three grouping zones (local places less than 10 miles away, downtown locations 10 to 30 miles away, and out of town locations over 30 miles away). Then we were able to create trellis (panel) groupings by the cost, choosing three levels (cheaper meals $10-$18, medium meals $18-$22 and expensive meals $22 to $36). Now we have a graph that can help us make a much better decision!
If we zoom into the first panel of BBQ meals with costs (from $10 to $18), we can see that there are three dominant points in red. The one which is the closest drive and cheapest in price is the Green Mesquite, but it doesn’t carry a very high food rating. The next red point has a higher food rating but requires more of a drive…in this case to Elgin, TX to go to Meyer’s. Lastly the highest rated but still inexpensive meal would require a very long drive to Snow’s in the small town of Lexington, TX. So if I want to stay local and get just an average BBQ meal, then the Green Mesquite may fit the bill. However, a little longer drive to Meyer’s in Elgin would provide a better quality BBQ meal still at a very reasonable price!
If we look at the next two price point panels, we can see how we can make better decisions if we are willing to pay more for a higher quality meal. For a little more expense (from $18-$22) there are great highly rated options like Black's BBQ in the downtown Austin area. On the most expensive meal end of the chart (from $22-$36) we see two points of interest. The Franklin Barbecue is world famous and is the most highly rated BBQ place in our study. However, while it is just a little more expensive, it also is so popular that large lines form early in the morning just to get inside as once they run out of a limited amount of BBQ meat they close for the day (often a little bit after lunch time). Contrast this with one of the non-dominant choices on the graph, the swanky and new Lamberts Downtown Barbecue. It boasts the highest BBQ meal price tag, but with only a poor food quality rating to show for it! Given all the options above, a visit to Black’s would definitely be the most convenient and best quality BBQ for the money!
Lastly we can turn back to another 3D graph in JMP called a Ternary Plot used to show interplay of mixture percentages. With a little practice we can use this much the same way we did with the graphs above, but this time we must first decide on the relative percentage of cost, distance and quality that we want in order to find a good selection. Once again the dominant (best) selections are in red. Looking below, if I don’t mind a long drive (high on the distance mixture percentage) and want the cheapest meal (low on the average cost mixture percentage), but want the best quality BBQ (highest on the average food rating mixture), then Snow’s in Lexington, TX would be well worth the longer drive!
So the next time you are having to choose between things involving multiple options, don’t be afraid to address it in three dimensions…whether it is for deciding where to drive to eat...or even for some other big decision. Lastly as local Central Texas Troubadour Robert Earl Keen sings, “If you're feelin' puny, you don't know what to do. Treat yourself to some meat, get some barbecue!”
You must be a registered user to add a comment. If you've already registered, sign in. Otherwise, register and sign in.