Once a system has been iraded and there is enough data lo give a performance profile, the significance between these actual results and the expected results can be found using the cbi-square test. First, there must be enough data for a relevant answer. From the section on sampling, the formula for error is I n, where yv is the number of items sampled. If there are 25 trades, the expected error in the calculation is 1/V23, or 20%; 100 trades would give results accurate lo 10%.

Assume that the real trading results show a reliability of 20% (1 out of 5) as compared with the expected reliability of 35%. What are the chances of getting these results? The chi-square test is

where Oistheobserved,or actual result, and £ is the expected or theoretical result. Then,

TABLE 23-7 The of a Specific Number of Losses

5Trod« lOTrodes JSTradM

PnAobJrty

, (20-35) (80 - 65) 35 * 65

(-15) (-15) " 35 65

= 9.89

The percentage of actual winning trades is compared with the anticipated winning trades and the losing trades with the expected losing trades. The answer must be found in the first row of Table 23-8. which gives the dishibution ofX.

The probability is dishibuted unequally in the taUe because the results are only significant if the probability is small, showing less likelihood of the results occurring by chance. For this simple twoelement test, the result P is classified as

Highly significant ifP> 10.83 (-1% or 1/1,000) Significant; if P 6.64 (1% or 1/100)

Probably significant if P 3-84 (5% or 1/20)

The answer X = 9.89 is between . lo and lo showing significance. For a large sample, the actual reliability should not have been 20°owhen SSowas expected.

The chi-square test can be used to compare actual price movement with ra appreciable variation. In the section on the Theory of Runs, Table 23-9 showed:

with random pattems to see whether there is

TABLE23-9 Results fi-om Analysis of Runs

Pfiitwbi% of Occurring b, Chance

) eie resuks based on » mull uii4)l»-

Apidying the actual data for runs of one through eight against a random dish-ibution.

(1214-1225) (620-612) (311 - )" (167-153) 1225 612 306 153

(67 - 77) (41-38) (16-19) (13-19)

77 38 19 19

(1) (2) (3) (4) (5)

= .09877 + .10457 + .08169 + 1.2810 + 1.2987

(6) V) (8)

.23684+ .47368+1.8947

Table 23-8 gives the probability of about 550 for 8 cases. The results are not significant; the Theory of Runs shows that all cases taken together give the same patterns as chance movement. Individual runs or sets of two or three adjacent runs can be inspected for distortion, in both cases, the results are further from normal but not mathematically significant. The two runs that differed the most were 4 to 5 days, which showed an 1 lo probability of occurring by chance.

Highly significant price runs can be found in the occurrence of extended runs, for example, 20 dajS, which is experienced occasionally in trending markets. By looking at the asjmmetrj of price movement, where a reverse run of 1 day is of negligible value, the significance of these runs will dramatically increase. Price movement is not a simple matter of random runs and equal payout.