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Statistical Inference Methods Cheat Sheet

The core ideas of Statistical Inference Methods distilled into a single, scannable reference — perfect for review or quick lookup.

PiqCue — piqcue.com/statistical-inference-methods/cheatsheet

Quick Reference

Sampling Distribution

The distribution of a statistic computed from all possible samples of a given size. The CLT describes how sampling distributions become approximately normal as sample size increases.

Central Limit Theorem

For large samples, the sampling distribution of the sample mean is approximately normal regardless of population shape. For proportions, np >= 10 and n(1-p) >= 10 must hold.

Confidence Interval for a Proportion

Interval estimate: p-hat +/- z* sqrt(p-hat(1-p-hat)/n). Conditions: random, Large Counts, 10% condition.

Confidence Interval for a Mean

Interval estimate using t-distribution: x-bar +/- t* (s/sqrt(n)) with df = n-1. Used when population SD is unknown.

Hypothesis Test

Formal procedure: state H0 and Ha, compute test statistic, find p-value, conclude in context.

Chi-Square Test

Test for categorical data. GOF checks observed vs expected frequencies. Independence checks association between variables. Statistic: sum((O-E)^2/E).

Inference for Regression Slope

Testing whether slope beta = 0. Uses t = b/SE_b with df = n-2. CI: b +/- t* SE_b.

Power of a Test

Probability of correctly rejecting a false H0: Power = 1 - beta. Increases with larger n, larger effect, higher alpha.

Key Terms at a Glance

Sampling Distribution:The probability distribution of a statistic from all possible samples of a given size.
Confidence Interval:An interval estimate for a population parameter with a specified confidence level across repeated sampling.
Margin of Error:Critical value times standard error. Half the CI width.
Null Hypothesis (H0):Statement of no effect/difference/association. The default claim to test.
Alternative Hypothesis (Ha):The claim contradicting H0. Can be one-sided or two-sided.
P-Value:Probability of a test statistic as extreme as observed, assuming H0 is true.
Significance Level (alpha):Threshold below which H0 is rejected. Equals probability of Type I error.
Type I Error:Rejecting a true H0 (false positive). Probability = alpha.
Type II Error:Failing to reject a false H0 (false negative). Probability = beta. Power = 1-beta.
Power:Probability of correctly rejecting a false H0. Power = 1-beta.
Chi-Square Statistic:X2 = sum((O-E)^2/E). For GOF and independence/homogeneity tests.
Degrees of Freedom:Independent pieces of information. GOF: k-1. Independence: (r-1)(c-1). t-test: n-1 or n-2.
Standard Error:SD of sampling distribution. Means: s/sqrt(n). Proportions: sqrt(p-hat(1-p-hat)/n).
Pooled Proportion:p-hat_c = (x1+x2)/(n1+n2). Used in two-proportion z-tests under H0.
10% Condition:n < 0.10N ensures approximate independence when sampling without replacement.

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Statistical Inference Methods Cheat Sheet - Quick Reference Guide | PiqCue