---
title: "90 % of the t distribution"
url: https://daily.dev/posts/90-of-the-t-distribution-zxfso0ftw
source_url: https://entropicthoughts.com/ninety-percent-of-the-t-distribution
type: article
source: "Programming Digest"
published: 2026-08-10T03:41:07.220Z
updated: 2026-08-10T03:41:34.924Z
tags: ["data-analysis", "statistics"]
reading_time: 4
upvotes: 0
comments: 0
language: en
---

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# 90 % of the t distribution

**[Programming Digest](https://daily.dev/sources/programmingdigest)** · 4 min read · 0 upvotes · 0 comments

## Summary

William Sealy Gosset (publishing as 'Student') developed the t-distribution to correct confidence intervals when sample sizes are small. Using a normal distribution assumption with a sample standard deviation produces intervals that are too narrow. A practical correction table is provided: multiply the standard deviation by 4× for 2 samples, 2× for 3, 1.5× for 4, 1.3× for 5, 1.2× for 6–8, and 1.1× for 9–20 samples, then multiply by 1.645 for a 90% interval. Beyond 20 samples, the naive estimate suffices. A bonus technique: the standard deviation estimated from just two values equals roughly 1.3 times the distance between them, enabling quick sanity checks on whether a result is truly unusual.

## Full article

daily.dev links to this article rather than hosting it. Read it at the original source: <https://entropicthoughts.com/ninety-percent-of-the-t-distribution>

## Questions this post answers

### How much wider should a 90% confidence interval be when I only have 5 samples instead of assuming a normal distribution?

With 5 samples, multiply your estimated standard deviation by 1.3× before computing the 90% confidence interval. The full procedure: multiply the sample standard deviation by the correction factor (4× for 2 samples, 2× for 3, 1.5× for 4, 1.3× for 5, 1.2× for 6–8, 1.1× for 9–20), then multiply by 1.645. Above 20 samples, no correction is needed.

_Teams doing small-sample analysis track these kinds of statistical gotchas on daily.dev._

### How do I estimate standard deviation from just two data points?

Multiply the absolute difference between the two values by 1.3 to get a rough but t-corrected estimate of the standard deviation. This works because the sample standard deviation of two values corresponds to a t-score of 1.846, and rounding the combined constant gives the 1.3 multiplier. It is a quick sanity check, not a substitute for more data.

_Developers and analysts doing back-of-envelope estimates share practical tricks like this on daily.dev._

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Tags: [#data-analysis](https://daily.dev/tags/data-analysis), [#statistics](https://daily.dev/tags/statistics)

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