An estimate is not its uncertainty
A mean and a standard error answer different questions. Identify the population quantity, sampling process, dependence and units before choosing a formula.
Worked example: paired observations
For 25 paired differences with mean 2 and sample standard deviation 5, the standard error is 5/√25 = 1. The t statistic against zero is 2. Use the variation of the differences rather than treating the two groups as independent.
This does not prove a trading signal. Inspect pairing, independence, prespecified hypotheses and how many alternatives were tried.
Study progression
- Mean, variance, covariance and scaling.
- Sampling variation and interval interpretation.
- Conditional expectation and total variance.
- Regression, serial correlation and multiple testing.
Common traps
Do not confuse standard deviation with standard error. Do not interpret a confidence interval as posterior probability without a Bayesian model. Do not annualize performance blindly under autocorrelation. State the model behind every shortcut.
Two Sigma’s guidance identifies statistics and open-ended analysis as relevant to QR. Rehearse the reasoning aloud as well as numerically.
Try a fresh question
This optional exercise uses the actual parameterized bank.
Worked method
Keep the practice connected
Train Statistics & Inference · Follow the Quant Path · Evidence standard