Do Apparel Stores Have a Higher Return on Equity (ROE) than Department Stores?

My population is the return on equity in all years for all apparel stores and return on equity in all years for all department stores. The parameters are the mean return on equity for all apparel stores and the mean return on equity for all department stores. The samples are 51 apparel stores and 30 department stores from Yahoo Finance on November 6, 2013. I eliminated stores for which Yahoo did not have a ROE or that had negative ROE. The statistics are the mean return on equity for 51 apparel stores which was 19.30and the mean return on equity for 30 department stores which was 16.47%.

Presentation of the data:

Department Store / ROE % / cumulative
lower / upper / midpoint / width / frequency / percent / frequency / percent
0.00 / 5.00 / 2.50 / 5.00 / 5 / 16.7 / 5 / 16.7
5.00 / 10.00 / 7.50 / 5.00 / 4 / 13.3 / 9 / 30.0
10.00 / 15.00 / 12.50 / 5.00 / 7 / 23.3 / 16 / 53.3
15.00 / 20.00 / 17.50 / 5.00 / 7 / 23.3 / 23 / 76.7
20.00 / 25.00 / 22.50 / 5.00 / 3 / 10.0 / 26 / 86.7
25.00 / 30.00 / 27.50 / 5.00 / 1 / 3.3 / 27 / 90.0
30.00 / 35.00 / 32.50 / 5.00 / 0 / 0.0 / 27 / 90.0
35.00 / 40.00 / 37.50 / 5.00 / 0 / 0.0 / 27 / 90.0
40.00 / 45.00 / 42.50 / 5.00 / 1 / 3.3 / 28 / 93.3
45.00 / 50.00 / 47.50 / 5.00 / 1 / 3.3 / 29 / 96.7
50.00 / 55.00 / 52.50 / 5.00 / 0 / 0.0 / 29 / 96.7
55.00 / 60.00 / 57.50 / 5.00 / 1 / 3.3 / 30 / 100.0
30 / 100.0

Department Store
ROE %
count / 30
mean / 16.41727
sample standard deviation / 12.64181
sample variance / 159.81544
minimum / 0.599
maximum / 55.215
range / 54.616
Apparel stores / ROE % / cumulative
lower / upper / midpoint / width / frequency / percent / frequency / percent
0.00 / 10.00 / 5.00 / 10.00 / 12 / 23.5 / 12 / 23.5
10.00 / 20.00 / 15.00 / 10.00 / 22 / 43.1 / 34 / 66.7
20.00 / 30.00 / 25.00 / 10.00 / 8 / 15.7 / 42 / 82.4
30.00 / 40.00 / 35.00 / 10.00 / 3 / 5.9 / 45 / 88.2
40.00 / 50.00 / 45.00 / 10.00 / 4 / 7.8 / 49 / 96.1
50.00 / 60.00 / 55.00 / 10.00 / 1 / 2.0 / 50 / 98.0
60.00 / 70.00 / 65.00 / 10.00 / 0 / 0.0 / 50 / 98.0
70.00 / 80.00 / 75.00 / 10.00 / 1 / 2.0 / 51 / 100.0
51 / 100.0

Apparel stores
ROE %
count / 51
mean / 19.29759
sample standard deviation / 14.90353
sample variance / 222.11522
minimum / 1.057
maximum / 71.474
range / 70.417

Hypothesis test:

Ho: µAp ≥ µDept or µAp - µDept ≥ 0

HA: µAp < µDept or µAp - µDept < 0

Tcrit = 2.462 ( using α = 0.01 in one tail and df = n – 1 = 30 – 1 =29 using the smaller of the sample sizes) In Excel, t.inv(.99,29)

Fail to reject Ho. The 2.88% difference between the mean return on equity for apparel companies and the mean return on equity of department stores is not sufficient evidence to prove that the apparel companies have a significantly higher return on equity than department stores, on average. There was quite a bit of variation within the two data sets which resulted in me not being confident in the difference I found between the two means. Note that both had distributions that are skewed to the right, but since the sample sizes both exceed 30, I was able to use the normal distribution in the analysis.

Appendix: Data table:

Department Stores / Apparel Stores
ROE % / ROE %
Kirkcaldie & Stains Limited / 0.599 / Ocean Sky International Ltd. / 1.057
Bon-Ton Stores Inc. / 0.616 / Destination XL Group, Inc. / 1.273
Grupo Elektra, S.A. de C.V. / 1.769 / Reitmans (Canada) Limited / 1.437
Saks Incorporated / 3.768 / Reitmans (Canada) Limited / 1.437
Metro Holdings Limited / 4.656 / LeRoi Holdings Ltd. / 2.658
Sears Hometown and Outlet Stor / 7.496 / Etam Developpement SA / 4.509
Grupo Famsa SAB de CV / 7.931 / New York & Company Inc. / 5.409
Lianhua Supermarket / 8.176 / Stage Stores Inc. / 6.578
Organizacion Soriana / 8.846 / Moss Bros Group PLC / 6.944
New World Depa.Store Chin / 10.184 / The Children / 8.954
Sears Canada Inc. / 11.801 / Joyce Boutique Holdings Ltd. / 9.081
Parkson Retail Group Ltd. / 11.987 / Jos. A Bank Clothiers Inc. / 9.744
David Jones Limited / 12.073 / Shoe Carnival Inc. / 10.13
Wing On Company Inter / 14.091 / Evergreen International / 10.507
Century Ginwa Retail / 14.306 / Ascena Retail Group Inc. / 10.713
Intime Department Store Group / 14.585 / Stein Mart Inc. / 11.616
Springland International / 15.368 / The Men's Wearhouse, Inc. / 11.701
Kohl's Corp. / 15.848 / I.T Ltd. / 12.178
Services / 16.887 / Trinity Ltd. / 12.875
Marks & Spencer Group PLC / 17.397 / Genesco Inc. / 13.012
Dillard's Inc. / 18.037 / Premier Investments Limited / 13.683
Debenhams PLC / 18.201 / Abercrombie & Fitch Co. / 14.525
Patagonia / 19.034 / The Cato Corporation / 14.8
Macy's, Inc. / 23.354 / Luxottica Group S.p.A. / 14.812
Lifestyle International / 23.667 / Luxottica Group SpA / 14.812
Ashley (Laura) Holdings PLC / 24.18 / Goldlion Holdings Ltd. / 15.036
Golden Eagle Retail Group Ltd. / 25.666 / Guess' Inc. / 15.107
Warehouse Group Limited (The) / 41.039 / Kathmandu Holdings Limited / 15.396
China Seven Star Shopping Ltd. / 45.741 / Chico's FAS Inc. / 15.435
The TJX Companies, Inc. / 55.215 / DSW Inc. / 15.884
Xtep International / 15.929
American Eagle Outfitters, Inc / 16.762
OrotonGroup Limited / 17.265
Urban Outfitters Inc. / 19.715
Specialty Fashion / 21.308
Destination Maternity Corporat / 21.362
Marisa Lojas SA / 22.836
Casual Male Retail Group, Inc. / 25.52
ANN INC. / 25.902
Tilly's, Inc. / 25.966
Hallenstein Glasson Limited / 27.969
Giordano International Ltd. / 29.615
Industria De Diseno Textil SA / 30.974
Express Inc. / 36.534
Nordstrom Inc. / 39.255
The Gap, Inc. / 40.749
The Buckle, Inc. / 44.135
Ross Stores Inc. / 46.945
Cherokee Inc. / 47.444
TJX Companies / 55.215
Francesca's Holdings Corporati / 71.474