Two execution algos on the same names: pair the test

Question

You run two execution algorithms on the same $40$ stocks on the same day and record each algo's slippage in basis points per stock. Algo A averages $5.0$ bps, Algo B averages $4.4$ bps. The per-stock difference $d = A - B$ has mean $\bar d = 0.6$ bps and sample standard deviation $s_d = 1.8$ bps.

Test whether the algos differ. Which test should you use, and is the difference significant?

Accepted Answer

Choose the test. Both algos ran on the same 40 stocks, so the two measurements per stock are paired, and the large stock-to-stock variation is common to both. An unpaired test would treat that shared variation as noise and drown the signal. Use the paired t-test: a one-sample t-test on the differences. Compute. t = \frac{\bar d}{sd / \sqrt{n}} = \frac{0.6}{1.8 / \sqrt{40}} = \frac{0.6}{1.8 / 6.325} = \frac{0.6}{0.2846} \approx 2.11, with 	ext{df} = n - 1 = 39. Decide. The two-sided 5\% critical value at 39 df is about 2.02. Since 2.11 2.02 (p-value \approx 0.04), we reject: the algos differ …

Two execution algos on the same names: pair the test

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