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Advanced Statistics — Inference and Modeling

Hypothesis testing, regression, and Bayesian methods

P
posterior_prob 24 terms Feb 12, 2026
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Terms 24

1
Null Hypothesis (H₀)
Default claim of no effect or no difference; tested against alternative hypothesis
2
Alternative Hypothesis (H₁)
Claim of an effect or difference; what researcher hopes to support
3
Type I Error (α)
Rejecting H₀ when it is true; false positive; set by significance level
4
Type II Error (β)
Failing to reject H₀ when it is false; false negative; power = 1 − β
5
p-value
Probability of observing result at least as extreme as data, given H₀ is true
6
Statistical Power
Probability of correctly rejecting false H₀; depends on effect size, n, and α
7
Effect Size
Magnitude of difference independent of sample size; Cohen's d, r, η²
8
Confidence Interval
Range containing true parameter value with specified probability (e.g. 95%) over repeated sampling
9
t-test
Tests difference between means; one-sample, two-sample independent, or paired
10
ANOVA
Analysis of Variance; tests if means of 3+ groups differ; F = between/within group variance
11
Chi-Square Test
Tests association between categorical variables or goodness of fit to expected distribution
12
Simple Linear Regression
ŷ = β₀ + β₁x; minimizes sum of squared residuals; assumes linearity, homoscedasticity, independence
13
Multiple Regression
ŷ = β₀ + β₁x₁ + ... + βₙxₙ; controls for multiple predictors; multicollinearity a concern
14
R² (Coefficient of Determination)
Proportion of variance in y explained by regression model; 0 to 1
15
Logistic Regression
Models binary outcome; log(p/1−p) = Xβ; outputs probability via sigmoid function
16
Maximum Likelihood Estimation
Finds parameter values maximizing probability of observing the data
17
Bayesian Inference
P(θ|data) ∝ P(data|θ)·P(θ); updates prior belief with likelihood to get posterior
18
Prior Distribution
Probability distribution encoding beliefs about parameter before seeing data
19
Likelihood Function
P(data|θ); probability of observed data as function of parameter θ
20
Posterior Distribution
P(θ|data); updated belief about parameter after incorporating data
21
Markov Chain Monte Carlo (MCMC)
Sampling algorithm for complex posteriors; chain of samples approximates distribution
22
Bootstrap
Resampling observed data with replacement to estimate sampling distribution and uncertainty
23
Bonferroni Correction
Adjusts significance threshold for multiple comparisons: α' = α/n tests; reduces Type I errors
24
False Discovery Rate (FDR)
Expected proportion of false positives among rejected hypotheses; Benjamini-Hochberg procedure