Constructing a chi-square test as a gate for two-way market records

Treat the test as a gate

TradersWeek editorial: the chi-square construction is a gate, not a garnish. A two-way market tally is unfinished until observed counts are forced through a Yates-corrected, one-degree-of-freedom comparison with a written expected-rate baseline.

A two-way record is a tally limited to a pair of mutually exclusive outcomes, such as rise versus decline. That record can be tested for chance with a chi-square test, a one-degree-of-freedom comparison of observed two-way counts with the counts implied by a stated baseline.

Write expected counts from the baseline

An expected count is the count implied for one outcome after the baseline rate is applied to that bucket's total.

When the overall sample is not split evenly between the two outcomes, each bucket's expected counts should be the sample-wide outcome rates times that bucket's total, not an even split.

Apply the Yates correction

The Yates correction is a half-count adjustment applied to the absolute observed-minus-expected gap before that gap is squared.

The Yates-corrected construction takes the absolute gap between an observed count and its expected count, subtracts 0.5, squares the remainder, and divides by each of the two expected counts.

A shorter form when the baseline is even money

An even-money baseline is the special case in which the two outcomes are treated as equally likely, allowing a shorter form of the same test.

If the baseline can be treated as even money, the same test reduces to one less than the absolute gap between the two outcome counts, squared and divided by their combined total.

Read the statistic as a confidence level

A confidence level is a conventional label for how rarely a result at least as large as the computed statistic would appear if the baseline were true.

After the statistic is computed, conventional cutoffs treat a result above 3.84 as 95 percent confidence, above 6.64 as 99 percent, and above 10.83 as 99.9 percent.

Those three confidence cutoffs correspond to a chance repeat about once in 20 repetitions, once in 100 repetitions, and once in 1,000 repetitions.

Weekday rise and decline counts

The weekday illustration uses a long lookback of ordered daily rise and decline counts and a sampling interval of one weekday, then compares each day's observed mix with the sample-wide expected mix.