What's Cohen's d and why compute it here?

Cohen's d is the standardized mean difference between two groups: d = (mean_A − mean_B) / s_pooled, where s_pooled is the sqrt of the weighted-average within-group variance. It's the two-group analogue of Cohen's f (Stats #24) and η² (Stats #24) which were multi-group effect sizes. On today's US CPI × GBPUSD 5-bucket sample, pairwise Cohen's d tells you HOW BIG the between-bucket differences are in units of within-bucket noise — same interpretation as an effect size in a psych experiment, just applied to macro-event buckets.

The worked-example numbers?

big_miss n=13 mean=+33.12p sd=38.19; in_line n=75 mean=+2.06p sd=25.32. s_pooled = sqrt(((13−1)·38.19² + (75−1)·25.32²) / (13+75−2)) = sqrt((12·1458.24 + 74·641.05) / 86) = sqrt(755.08) = 27.48p. d = (33.12 − 2.06) / 27.48 = 31.07 / 27.48 = +1.131. Same computation for the other 3 buckets vs in_line: big_miss +1.13, small_miss +0.45, small_beat -0.71, big_beat -0.56. Tail-to-tail big_miss vs big_beat: mean diff = 33.12 − (−11.64) = 44.76p, s_pooled = 30.75p, d = 44.76 / 30.75 = +1.51.

Why is big_beat only medium when big_miss is large?

Because the tails are asymmetric in mean AND in variance. big_miss n=13 mean +33.12p sd 38.19; big_beat n=15 mean -11.64p sd 19.33. The big_miss magnitude (33.12) is nearly 3× the big_beat magnitude (11.64) — so the numerator (mean vs in_line's +2.06p) is much bigger on the miss side than the beat side. And the DENOMINATOR is smaller for big_beat because big_beat's within-bucket SD (19.33) is HALF the big_miss SD (38.19), which partly compensates — hence big_beat isn't tiny (d = -0.56 is still MEDIUM by Cohen 1988), it's just meaningfully smaller than big_miss's +1.13.

small_beat vs big_beat d = -0.22 — is that the bucket-boundary artefact?

Yes. small_beat n=35 mean -19.35p; big_beat n=15 mean -11.64p. The 'bigger' beat bucket has a SMALLER-magnitude mean, which flips the sign of the adjacent-bucket Cohen's d. Same shape as the bucket-boundary artefact this ledger has documented on AUD Employment × GBPAUD (2026-08-28) and today's slot 5 EURAUD post — a small-n bucket (n=15) with dampeners (2 flat COVID-era big-beat prints and 1 early-sample print) pulls the big_beat mean toward zero. Median walk (which is robust to outliers) doesn't show the flip; only the mean-based Cohen's d does.

Tail-to-tail d = +1.51 — what does that mean for trading?

The two tail buckets (big_miss vs big_beat) are separated by 44.76 pips of mean move, and the pooled within-bucket noise is 30.75 pips. So a bucket-filter strategy that trades only the tail buckets — long GBPUSD on big_miss, short on big_beat — is buying a directional signal that's 1.51 SDs bigger than the noise. Rule-of-thumb: at d = 1.5, roughly 93% of the two tail distributions don't overlap (Cohen 1988 Table 2.2). That's the effect size actually available to you if you filter by bucket; the overall r = -0.30 across all 196 releases (with in_line and small_* buckets included) is misleadingly modest because it dilutes the tail signal with the 75 in_line prints where there's nothing to trade.

How does this connect to Stats #24 (Cohen's f and η²)?

Cohen's f is the multi-group generalization: f = sqrt(η² / (1 − η²)), where η² is the between-group share of total variance from one-way ANOVA. Stats #24 (2026-08-24) computed f = 0.4925 on the CAD CPI × USDCAD 5-bucket sample (η² = 0.1952). Cohen's d is the two-group case: given only two groups, f collapses to d/2 (up to sign). For the same ANOVA-style sample, pairwise Cohen's d values are the fine-grained pairwise-comparison version of what η² summarized in a single number. Today's Stats #30 is the natural pairwise sibling of Stats #24's overall effect-size result.

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Statistics30 August 2026· 5 min read

Statistics for Traders #30: Cohen's d on today's slot-1 US CPI × GBPUSD sample — big_miss vs in_line is d = +1.13 (LARGE by Cohen 1988), big_beat vs in_line is only d = -0.56 (MEDIUM), and the miss-side effect is 2× the beat-side effect in effect-size language

Q: Hedges' g small-sample correction — how big does it matter?

Hedges' g = d · (1 - 3 / (4·(n_A + n_B) - 9)). For big_miss (n=13) vs in_line (n=75): correction = 1 - 3/343 = 0.9913, so g = +1.1207 vs d = +1.1306 — 0.87% shrinkage. For tail-to-tail big_miss vs big_beat (n=13 vs n=15): correction = 1 - 3/103 = 0.9709, so g = +1.470 vs d = +1.514 — 2.90% shrinkage, the biggest of the pairwise pairs because both samples are small. Hedges (1981) proved this correction removes the positive bias in d as a small-sample estimator of the population effect size δ. At n ≥ 40 per group the correction is under 0.5% and rarely worth reporting; at n = 13/15 it's material.

Cohen’s d for the 5 buckets of today’s slot-1 sample — US CPI m/m × GBPUSD 15m, n=196. Pairwise bucket-vs-in_line effect sizes: big_miss +1.13, small_miss +0.45, small_beat -0.71, big_beat -0.56. Tail- to-tail big_miss vs big_beat d = +1.51 (VERY LARGE by Cohen 1988). The miss and beat tails are asymmetric even in effect-size language, not just in median/pct-up — miss-side effect is roughly 2× the beat-side effect.

Directly builds on Stats #24 (one-way ANOVA, R², η², Cohen’s f): today’s pairwise Cohen’s d values are the fine-grained pairwise-comparison sibling of Stats #24’s multi-group summary. Grounded in today’s slot 1 so you can see the exact sample the numbers came from.

Horizontal bar chart of Cohen's d values for 5 pairwise bucket comparisons on the US CPI m/m × GBPUSD 15m sample. The chart has a central vertical zero line with reference marks at ±0.2, ±0.5, and ±0.8 (Cohen 1988 thresholds). Five bars extend from the zero line: big_miss vs in_line +1.13 (green, extends right, LARGE), small_miss vs in_line +0.45 (green, small-medium), small_beat vs in_line -0.71 (coral/red, extends left, medium-large), big_beat vs in_line -0.56 (coral, medium), and big_miss vs big_beat +1.51 (green, VERY LARGE, extends furthest right). Each bar is labelled with its d value and Cohen 1988 magnitude classification. Footer legend: Cohen 1988 conventions |d| < 0.2 negligible, 0.2 small, 0.5 medium, 0.8 large. — Pairwise Cohen’s d on the 5 buckets of today’s slot-1 US CPI × GBPUSD sample (n=196). Miss side ~2× the beat side in effect-size magnitude.

The formula

Cohen’s d is the standardized mean difference between two groups:

d = (mean_A − mean_B) / s_pooled, where s_pooled = sqrt( ((n_A − 1)·s_A² + (n_B − 1)·s_B²) / (n_A + n_B − 2) ).

It reports the between-group mean difference in units of the within-group standard deviation. Interpretation matches every other standardized effect size: |d| = 1 means the two group means are one pooled-SD apart. Cohen 1988 conventions: |d| < 0.2 negligible; 0.2 small; 0.5 medium; 0.8 large.

Worked example: big_miss vs in_line

big_miss n=13 mean=+33.12p sd=38.19; in_line n=75 mean=+2.06p sd=25.32.

s_pooled = sqrt(((13−1)·38.19² + (75−1)·25.32²) / (13+75−2)) = sqrt((12·1458.24 + 74·641.05) / 86) = sqrt(755.08) = 27.48p.

d = (33.12 − 2.06) / 27.48 = 31.07 / 27.48 = +1.131— LARGE by Cohen 1988 (> 0.8).

All 5 pairwise Cohen’s d values

Comparison	n_A / n_B	Cohen’s d	Hedges’ g	Cohen 1988
big_miss vs in_line	13 / 75	+1.131	+1.121	LARGE
small_miss vs in_line	58 / 75	+0.447	+0.444	small-medium
small_beat vs in_line	35 / 75	-0.708	-0.702	medium-large
big_beat vs in_line	15 / 75	-0.560	-0.555	MEDIUM
big_miss vs big_beat (tail-to-tail)	13 / 15	+1.514	+1.470	VERY LARGE

The miss-vs-beat asymmetry, in effect-size language

big_miss vs in_line d = +1.13 is LARGE by Cohen 1988. big_beat vs in_line d = -0.56 is only MEDIUM. The miss-side effect is roughly 2× the beat-side effect in standardized-mean-difference units — matches the 15m median asymmetry (+18.5p miss vs -6.4p beat) and the pct-up asymmetry (92.3% vs 26.7%). This is a structural feature of the sample: the miss side has both a bigger mean-shift AND wider variance (sd 38 vs 19), and the two effects partly cancel in the ratio.

The adjacent bucket-boundary artefact, in Cohen’s d language

Adjacent small_beat vs big_beat d = -0.22 — the wrong sign. small_beat n=35 mean -19.35p is MORE NEGATIVE than big_beat n=15 mean -11.64p. Same bucket-boundary artefact this ledger has documented on GBPAUD (2026-08-28) and today’s EURAUD slot 5: a small-n big_beat bucket (n=15) contains dampeners (4 counter-directional prints per slot 1’s release-level inspection) that pull its mean toward zero, making the standardized comparison flip against the adjacent-bucket expected ordering. The median walk (robust to outliers) doesn’t show this flip; only the mean-based Cohen’s d does — one honest reason to prefer median walks over mean walks when reading bucket signal.

The tail-to-tail d as bucket-filter effect size

big_miss vs big_beat d = +1.51 is the effect size actually available to a bucket-filter strategy that trades only the two tail buckets (long GBPUSD on big_miss, short on big_beat). At d = 1.5, roughly 93%of the two tail distributions don’t overlap (Cohen 1988 Table 2.2 — U₃ overlap statistic). By contrast, the overall Pearson r between surprise_z and move_pips across all 196 releases (with in_line and small_* buckets included) is only about -0.30 — misleadingly modest because it dilutes the tail signal with 75 in_line prints where there’s nothing to trade.

Hedges’ g small-sample bias correction

g = d · (1 - 3 / (4·(n_A + n_B) - 9)) — Hedges 1981 proved this correction removes the positive bias in d as a small-sample estimator of the population effect size δ.

For big_miss (n=13) vs in_line (n=75): correction = 1 - 3/343 = 0.9913 (0.87% shrinkage). For tail-to-tail big_miss vs big_beat (n=13 vs n=15): correction = 1 - 3/103 = 0.9709 (2.90% shrinkage — biggest of the pairwise pairs because both samples are small). At n ≥ 40 per group the correction drops below 0.5% and is rarely worth reporting; at n = 13/15 it’s material — the tail-to- tail d = +1.514 becomes g = +1.470, still VERY LARGE, but ~3% smaller.

Verification note

All numbers computed 2026-08-30 in Python numpy against the full 196-release /api/v1/news-impact/releasesresponse for FF:US_CPI_MOM × GBPUSD, non_contaminated, window=15m. Formulas match Cohen (1988) "Statistical Power Analysis for the Behavioral Sciences" §2.2 (d) and Hedges (1981) "Distribution Theory for Glass’s Estimator of Effect Size and Related Estimators" Journal of Educational Statistics 6(2) (g). Chart via a scratch script reusing scripts/insights-charts/svg.ts and theme.ts primitives with sharp rasterization (not committed under scripts/).

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