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Statistics

Sign-flip Simpson: order size and fill quality

simpsons-paradoxconfoundingregression

Pooling all your trades, a scatter of order size against fill quality slopes upward: larger orders are associated with better fills (lower cost per share). But when you split trades by the stock's liquidity tier, within every tier the slope is downward: larger orders get worse fills.

Reconcile the positive pooled slope with the negative within-tier slopes. Which relationship should guide how you size an order?

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