MENTAL MODEL · M9929

Goodness-of-Fit Test

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Updated 2026-08-15

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INTRODUCTION

English translation pending.

CORE DEFINITION

A goodness-of-fit test compares observed frequencies with the frequencies expected under a specified distribution, using a statistic such as Pearson's chi-square or the Kolmogorov-Smirnov test. It formalizes the question of whether a model is adequate, replacing visual impression with a decision rule. The core claim is that the discrepancy between observed and expected counts, scaled by the expected counts, has a known distribution under the null hypothesis, so its size can be judged against sampling noise. The qualification is that the answer depends on sample size and on how the data were binned: small samples lack power, while very large samples flag trivial deviations as significant.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

- Test the model: ask whether the fitted distribution could plausibly have produced these data. - Check assumptions: verify residual normality before trusting a regression's standard errors. - Read the bins: confirm the grouping was chosen before seeing results, not to fit them.

anchor

Anchor fast decisions

If the model were correct, observed and expected counts would differ only by sampling noise, and a specific statistic would follow a known distribution. Comparing the statistic against that reference converts an open question about adequacy into a probability. This is why the test flags deviations too small to matter at large samples: the reference distribution narrows as n grows, so the same absolute gap becomes significant. Bin choice intervenes as well, since merging sparse categories changes the statistic without changing the data.

MINIMUM ACTION

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Practice this model in one real situation:

State the theoretical distribution or model whose fit you are testing. 2. Compute expected frequencies for each bin and check that none are too small. 3. Choose the test statistic, chi-square or Kolmogorov-Smirnov, and compute it. 4. Judge the p-value together with the effect size, not on its own.

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en.wikipedia.orghttps://en.wikipedia.org/wiki/Goodness_of_fitZH · Explicit
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