Plain-English Statistics
Statistics for People Who Came Here for the Psychology
Whether you're choosing a method for your research question, decoding a result in a paper or reviewing for an exam: plain-English guides to the statistical methods psychology uses. Each one follows one example from start to finish, with the math worked step by step and every calculated result recomputed from the data.
72 methods · 316 terms · chosen from what psychology journals actually publish (Blanca et al., 2018).
Students slept less than the recommended minimum of 7 hours a night, t(39) = −2.64, p = .012, d = −0.42.
- t(39) = −2.64
- Our students' average sat 2.64 standard errors below 7 hours.
- p = .012
- If students really averaged 7 hours, a gap this big would turn up about 1 time in 80.
- d = −0.42
- About four-tenths of a standard deviation: a small effect by Cohen's benchmarks.
Where Are You Starting?
Pick Your Way In
Start from whatever you have in front of you: a result in a paper, a research question, a description of your study, a kind of analysis, a method's name or a term you've just run into.
Result Decoder
You have a result from a paper:
…anxiety differed across the three groups, F(2, 87) = 4.12, p = .020, η2p = .09.
Paste it as printed. The decoder explains each number, names the methods that could have produced it and checks that the p-value fits.
Decode It →Your Research Question
You have a question you want answered:
“Do students who sleep less score lower on exams?”
23 kinds of research question, grouped by goal, each with the methods that answer it.
Find Your Question →Describe Your Study
You have a study design, but no method yet:
Three groups · different people in each · one score out of 100
Answer a few questions, one at a time, and watch the methods that don't fit grey out.
Describe Your Study →A Kind of Analysis
You have a rough idea of the analysis:
“It's some kind of correlation.”
Start from a family, like comparing groups, relating variables or checking agreement, and narrow down to the method.
Browse by Kind →All Methods
You have a method's name:
“My advisor said to run a mixed ANOVA.”
All 72 methods, searchable, each with when to use it, the math on one example and how to run it in R, Python and SPSS.
Find the Method →Glossary
You have a term you don't recognize:
“What's a Greenhouse-Geisser correction?”
All 316 terms and symbols on the site, defined once, with the labels SPSS, R and Python print for them.
Look It Up →What Makes It Different
Explanations You Can Actually Follow
One Study, Start to Finish
Every page follows one realistic study: the question, the data, the math and the write-up, all from the same study, so nothing stays abstract for long.
Green always means the example, so you can find it on any page at a glance.
Do undergraduates sleep less than the recommended 7 hours a night? Forty students logged their sleep for a week, and each student's nightly average is one score.
Napkin Math, Step by Step
Each formula is broken into steps with plain-English headings. Read just the headings and you have the story; open a step and a handwritten note plugs in the example's numbers.
The reaction we're after: “Oh, that's all we're doing? Okay, now show me the equation.”
1. Find the Difference between What We Observed and What We Expected
\bar{x} is our students' average, 6.50 hours. \mu_0 is the 7 hours we're testing against. 6.50 − 7 = −0.50 hours.
2. Figure Out How Much People's Scores Naturally Vary
x_i is each student's score and \sum means “add them all up.” So find each student's distance from 6.50, square it, add up all 40, divide by n - 1 = 39, and take the square root. That's 1.20 hours.
3. Figure Out How Precisely Our Sample Estimates the Population Average
s is that 1.20-hour spread and n is our 40 students. 1.20 ÷ √40 (about 6.32) = 0.19 hours, roughly 11 minutes.
Benchmarks, with the Caveats
Know what counts as small, medium or large, and what those labels can't tell you. Every page reports results in the same order: what was found, how big it is, how sure we are, then whether it's significant.
Common mistakes come as a don't and an instead, so you learn the fix along with the error.
Benchmarks Effect Size (Cohen's d)
Don'tRead p = .06 as “no effect.”
InsteadReport the effect size and its confidence interval, and say what they show.
Every Method Page
The Same Six Parts, in the Same Order
Learn one page and you know where to look on all of them.
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1
The Basics
When to use it, the vocabulary you need, and the assumptions, each with what to do if it's violated.
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2
Limitations
When it's not your test, what it can't tell you, and the most common mistakes.
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3
Result Decoder
Guidelines for reading the result, how it's reported, and what each number means.
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4
Calculations
The running example, Napkin Math step by step, and how to run it in your software.
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5
Impact
Effect size, significance or uncertainty, and how to plan your sample size, with a calculator for many methods.
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6
Other Info
Follow-up and post hoc tests, related methods, and the references behind it all.
Who It's For
For Everyone Who Reads Psychology Research
Students
Undergraduate stats, research methods and the night before the exam.
“What's the difference between SD and SE, again?”
Researchers
Planning a study, choosing the analysis and writing it up in APA style.
“How many participants do I need to detect a medium effect?”
Clinicians
Reading the evidence behind a treatment without a statistics degree.
“Is a d of 0.3 worth changing my practice for?”
Instructors
Pages to assign that explain it the way you would in office hours.
“Read the Napkin Math before Thursday.”
Stop Guessing. Start Understanding.
Tell us what you're trying to find out, and we'll show you the right method and walk you through it.