Are these brokerages really any better or worse than each others?

 Globe and Mail ranked Canadian brokerages by the following table:

Rank	Broker	Costs (/25)	Trading (/25)	Tools (/20)	Account Info (20)	Innovation (/10)	Total (/100)
1	Qtrade Investor	16	21	15	18	7	77
2	Virtual Brokers	23.5	18.5	11	10	8	71
3	BMO InvestorLine	10	16.5	16.5	18.5	6.5	68
4	Scotia iTrade	18	16.5	13	13	7	67.5
5	RBC Direct Investing	10	17.5	18	16	5	66.5
6	Credential Direct	12.5	16	14.5	18	5	66
7	TD Waterhouse	10	17	18	11	4.5	60.5
8	CIBC Investor's Edge	14.5	13.5	15	8	6	57
9	Disnat (Classic)	10.5	11.5	15	15	3.5	55.5
10	Questrade	16	13.5	10.5	9	6.5	55.5
11	National Bank Direct Brokerage	8.5	10.5	14	16.5	3.5	53
12	HSBC InvestDirect	10	13	6	10	1	40

If the Globe and Mail scores are representative of the collective opinions of the traders and investors, are any of the brokerages any better or worse than the others?


In other words, are the scores really different? Let's put all scores in one column and the brokerage name in the other, and use Tukey's multiple comparison test to find out. Actually, let's use all 3 -- Bon Ferroni, Tukey and Scheffe.


Save the above table as z:\brokers.csv, and run the following SAS code. We found all 3 tests put all the brokerages into a single group. They are all the same by standards of Globe and Mail.



filename in 'z:\brokers.csv';
data mydata.brokers;
length broker $32;
infile in dsd dlm="," missover firstobs=2;
input Rank Broker $ Costs Trading Tools AcctInfo Innovation total;
run;


data mydata.brokers2(drop= Costs Trading Tools AcctInfo Innovation i);
set mydata.brokers(drop=rank total);
array attrs (*) _numeric_;
do i=1 to dim(attrs);
score=attrs(i);
output;
end;
run;


proc glm data=mydata.brokers2;
class broker;
model score = broker /solution e;
means broker /bon tukey scheffe alpha=0.05 ;
run;