module 2 of 7 · 40 min

Statistics

Reason about variability estimates and evidence instead of treating samples as certainty.

Explain Statistics clearlyImplement a small Statistics exampleEvaluate whether Statistics improves a simpler baselineIdentify failure cases and operational constraints
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mental model

start with the idea before the implementation.

Statistics uses samples to make quantified statements about populations under assumptions.
core concepts

the mechanisms you need to reason about.

01

Sampling

Sampling is studied through intuition implementation evidence and trade-offs. The goal is to be able to explain the mechanism and verify it with a concrete test rather than only repeat a definition.

02

Estimation

Estimation is studied through intuition implementation evidence and trade-offs. The goal is to be able to explain the mechanism and verify it with a concrete test rather than only repeat a definition.

03

Confidence intervals

Confidence intervals is studied through intuition implementation evidence and trade-offs. The goal is to be able to explain the mechanism and verify it with a concrete test rather than only repeat a definition.

04

Hypothesis testing

Hypothesis testing is studied through intuition implementation evidence and trade-offs. The goal is to be able to explain the mechanism and verify it with a concrete test rather than only repeat a definition.

engineering lab

turn the lesson into evidence.

LAB 1

simulate sampling distributions

Build the smallest version first. Record the input, expected output, measured result and one failure you discovered.

LAB 2

build an interval

Build the smallest version first. Record the input, expected output, measured result and one failure you discovered.

LAB 3

interpret a p-value carefully

Build the smallest version first. Record the input, expected output, measured result and one failure you discovered.

knowledge checks

prove you can explain and decide.

1

state assumptions

ask cortex to test me →
2

separate effect size from significance

ask cortex to test me →
3

identify selection bias

ask cortex to test me →
failure modes

what usually goes wrong.

risk

p-value worship

Detect this early by defining a baseline, a measurable signal and a condition that would cause you to stop or redesign the approach.

risk

multiple comparisons

Detect this early by defining a baseline, a measurable signal and a condition that would cause you to stop or redesign the approach.

risk

causal claims from correlation

Detect this early by defining a baseline, a measurable signal and a condition that would cause you to stop or redesign the approach.

proof of learning

Create a short Statistics engineering note with one working artifact one metric one failure case and one decision about when you would or would not use it.

Save the result in your portfolio or project repository. A strong learning artifact should make your assumptions, metrics and failure analysis visible.