How to Measure the Difference Between National and Local Chains

erik

The recent question on the table has been about how to quantify the regionality of different store chains.  One possible way to do this, and probably the most simple, is the chi square test.  There are certain drawbacks to the simplicity of the method, but it should work for general purposes. 

The chi square test involves comparing what we would expect to observe against what we actually observe.  In looking at the distribution of a given store chain, a perfectly national store chain would match the population distribution.  A simple approximation of the population distribution would be the 210,000 discover ATM locations.  If we divide the country into its 206 Designated Market Areas (DMAs), we can calculate the proportions per DMA.  Then we see how each list compares to those proportions, and we end up with a chi square statistic.  The idea is that the closer to zero the chi square statistic is, the more regional.  The higher the chi square statistic, the more it’s deviating from the national distribution, thus being more local.   

Doing the math, here’s what we get for US restaurants that have more than 100 locations (top and bottom 15):

NAME

LOCATIONS

CHI SQUARE

Mcdonalds

13811

0.070046944

Subway

24105

0.103919262

Burger King

7034

0.119288867

Godiva

3679

0.150437442

KFC

4655

0.152629049

Dominos

4830

0.18811625

Applebees

1867

0.203611562

Bolthouse Farms

20408

0.210399793

Taco Bell

6076

0.217482468

Wendy's

5795

0.219231556

Olive Garden

784

0.222174748

Pizza Hut

6530

0.257761281

Chucke Cheese

529

0.274454515

Papa Johns

2835

0.291444446

Red Lobster

679

0.293296582

   

   

Bob's Big Boy

124

21.35187178

Taco Bueno

177

21.49879157

Taco Time

234

21.6098216

Vocelli

101

22.02710021

ABC Wine and Spirits

135

22.69824962

Taco Del Mar

121

23.79662662

Sharis

102

26.50148421

Braum's

279

27.26602181

Mountain Mike's

150

29.9897022

Tedeschi

177

38.50929883

Cousin Subs

140

40.21931153

Skyline Chili

130

40.32505047

Mazzio's

153

48.41473573

Honey Dew Donuts

142

51.92285407

Dutch Brother's

169

64.00169676

It’s no surprise here that the most national stores have the most locations and the most local stores have the least.  Of course if a store has more locations, it’s more likely to be spread out.  But it’s interesting to note the chains that are in the top 15 that have a lot fewer locations than the others, specifically Olive Garden, Chuckie Cheese, and Red Lobster.

Olive Garden has approximately 784 locations, with a chi square of .22.  Whataburger has approximately 733 locations, which is fairly close to Olive Garden, but it has a chi square of 10.62.  We can see the difference graphically:

Olive Garden:

Whataburger:

The map of Olive Garden shows more red in all of the major city centers of the US, while Whataburger is clearly marketing to Texas and the South.  Now let’s take a look at the most local chain on the list, Dutch Brothers:

Dutch Brothers has a chi square of 64, even though it may appear to have a similar distribution as Whataburger, which had a chi square six times lower.  The difference is first the fact that Dutch Brothers has a lot fewer locations.  The second reason, and the primary reason, is that it is focused on parts of the US that are less populated than Whataburger.  Texas has huge cities, so a Texas based chain will be closer to the distribution of the population than a chain in less populated areas.  As you can see on the map, Dutch Brothers is focused on the west coast, but not the most populated parts of the west coast.  They cover eastern Washington, Idaho, and Oregon, making the distribution lopsided.  Thus, Dutch Brothers is a solidly local chain.