Lecture 9: Statistical Inference — Vocabulary

Vocabulary flashcards covering key concepts from Lecture 9 on statistical inference.

Intercept

The predicted value of the response when all predictors are zero; for categorical predictors, corresponds to the reference (baseline) category.

Slope

The change in the response for a one-unit change in a numeric predictor; in additive models, slopes are the same across groups.

Null model

An intercept-only model with no explanatory variables; estimates the overall mean and is analogous to a one-sample t-test.

Categorical explanatory variable

A qualitative predictor with distinct categories (e.g., penguin species) used in regression.

Dummy variables

0/1 indicators used to encode categorical predictors so each non-reference category has its own intercept.

Reference category

The baseline level of a categorical predictor against which other levels are compared in the model.

Additive model

A regression model where the effects of predictors add up with a common slope across groups; lines are parallel.

Interaction model

A model that includes interaction terms, allowing slopes to differ by category; lines are not parallel.

Dummy coding

Encoding scheme using 0/1 variables to represent categories and enable group-specific intercepts.

Linear model (LM)

A regression framework modeling a continuous response as a linear combination of predictors; t-tests and ANOVA are special cases.

ANOVA

A method to test for differences among means and to compare nested models in regression.

AIC (Akaike Information Criterion)

A model quality metric that balances goodness-of-fit with model complexity; lower is better; differences >~4 suggest meaningful improvement.

Parsimony

Preference for simpler models that sufficiently explain the data, balancing fit and complexity.

Confidence interval

A range around a parameter estimate that would contain the true parameter in repeated samples; a single study’s interval either contains it or not.

Shapiro-Wilk test

A normality test for residuals, used as an alternative or complement to QQ plots.

QQ plot

A diagnostic plot comparing observed quantiles to theoretical quantiles to assess normality of residuals.

Residuals

Differences between observed values and model-predicted values, used to assess fit and detect patterns or outliers.

Log transformation

Applying a logarithm to data to stabilize variance or meet model assumptions; not always effective.

Back-transformation

Transforming predictions from a transformed scale (e.g., log) back to the original scale for interpretation.

Non-independence

A violation of the assumption that observations are independent; may require alternative tests or models.

Population parameter

The true value of a quantity in the population (e.g., the true mean); estimated from sample data.

Point prediction

A single predicted value from the regression equation for a given set of predictor values.

Hypothesis testing

A framework for deciding if data provide evidence against a null hypothesis, often using p-values.