Vijayakumar PVijayakumar P
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#hypothesis-testing

5 posts tagged with "hypothesis-testing".

Stylised illustration of a tea stall — Vijay stands centre behind his counter looking up at a long chalked diagram on the back wall titled `degrees of freedom = n − 1 = 7`. Eight large round tokens are chalked in a row: seven of them have a `?` inside (free), the eighth has a small chalked padlock (spent). A brace under the seven free tokens reads `free to vary`; the eighth is labelled `spent`. On the far left a woman in warm orange holds a fan of blank slips each marked with a `?`. On the far right a man in graphite-blue holds a brass padlock with a small paper tag reading `x̄`.

Analytics

Degrees of Freedom Walks Into a Tea Stall

Vijay's calculator keeps using n − 1 instead of n. He doesn't know why. Two strangers — one with a fan of blank slips, one with a brass padlock — explain why every parameter you estimate costs you one of your data points.

Vijayakumar P 11 min read
Stylised illustration of a tea stall — Vijay stands centre behind his counter looking up at a wooden two-armed signpost mounted on the back wall. The left arm is grey, points left and reads `H₀ : NO CHANGE`. The right arm is warm orange, points right and reads `H₁ : SOMETHING CHANGED`. On the far left a calm man in plain grey holds up a small clipboard with `STATUS QUO` written across the top. On the far right a curly-haired man in warm orange holds up a magnifying glass.

Analytics

Null and Alternative Hypothesis Walk Into a Tea Stall

Vijay started serving fresh ginger biscuits this month. His daily mean rose from 87 to 91. Real effect or noise? Two strangers explain why every test is a courtroom — and which side is presumed innocent.

Vijayakumar P 11 min read
Stylised illustration of a tea stall — Vijay stands centre behind his counter looking up at a long chalked bell-curve diagram on the back wall titled `WHERE DOES α LIVE?`. The curve has shaded rejection regions: a heavy orange shade on the right tail, lighter teal shading on both tails, with critical values −1.96, 1.645, 1.96 chalked along the baseline. On the far left a focused man in warm orange holds a single arrow pointing right toward the orange right tail. On the far right a calm man in teal holds two arrows pointing in opposite directions.

Analytics

One-tailed and Two-tailed Tests Walk Into a Tea Stall

Vijay added cardamom to his tea. Mean rating rose from 3.8 to 4.0. He's about to run the t-test, and the software asks him a question he's never thought about — one-sided or two? Two strangers, one with a single arrow and one with two, explain why it matters.

Vijayakumar P 11 min read
Stylised illustration of a tea stall — Vijay stands behind his counter looking down at a paper card on the counter that asks 'is the cousin right?' with cousin's claim 100 on the left, his notebook's mean 87 on the right, and a big red question mark between them. A confident woman holding a printed σ = 14 card stands on the left; a careful man holding a fan of bell-curve cutouts and a small calculator showing −5.31 stands on the right.

Analytics

t-test and z-test Walk Into a Tea Stall

Vijay's cousin keeps claiming he should average 100 customers a day. The notebook says 87. Two strangers turn up to test it — one needs to know sigma, the other doesn't.

Vijayakumar P 9 min read
Stylised illustration of a tea stall — Vijay stands centre behind his counter looking up at a chalkboard 2x2 matrix mounted high on the back wall labelled Type I (top-left, red), Power (top-right, green), Correct (bottom-left, green), Type II (bottom-right, red). On the far left a confident woman in red holds a handbell mid-ring with BING! BING! sound waves. On the far right a calm man in navy wears a sleep mask, snoring Zzz, his own bell silent at his side.

Analytics

Type I and Type II Errors Walk Into a Tea Stall

Vijay's last 7 days dropped from his usual 87 to 75. The t-test rejects. Two strangers turn up — one rings a bell at every shadow, the other sleeps through real wolves — and explain what could go wrong with that verdict.

Vijayakumar P 10 min read

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