General Statistics & Hypothesis Testing Flashcards

Flashcards containing key terms and definitions related to general statistics and hypothesis testing.

Population

The complete set of subjects or observations about which we want to draw conclusions.

Sample

A subset of the population used to make inferences about the population.

Null Hypothesis (H₀)

A default statement to be tested, often representing 'no effect' or 'no difference.'

Alternative Hypothesis (Hₐ or H₁)

A statement contradicting H₀, representing the effect or difference we suspect exists.

Test Statistic

A calculated value (e.g., z-score, t-score) used to determine whether to reject H₀.

Critical Value

A threshold value from a distribution (e.g., t-distribution) that defines the rejection region for H₀.

p-value

The probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming H₀ is true; Reject H₀ if p-value < α.

Significance Level (α)

The probability of rejecting H₀ when it is true (Type I error). Common values: 0.01, 0.05, 0.10.

Type I Error

Incorrectly rejecting a true H₀ (false positive).

Type II Error

Failing to reject a false H₀ (false negative).

One-Sided Test

Tests for an effect in one direction (e.g., Hₐ: μ > μ₀).

Two-Sided Test

Tests for any difference (Hₐ: μ ≠ μ₀).

Regression

A statistical method to model the relationship between a dependent variable (Y) and one or more independent variables (X).

Line of Best Fit (OLS Regression Line)

The line that minimizes the sum of squared residuals in a scatterplot. ( \hat{Y} = \hat{\beta}0 + \hat{\beta}1 X ).

Slope (β̂₁)

The estimated change in Y for a one-unit increase in X.

Intercept (β̂₀)

The predicted value of Y when X = 0. May not always have a meaningful interpretation.

Residual (êᵢ)

The difference between the observed (Yi) and the predicted (\hat{Y}i).

Sum of Squared Residuals (SSR)

A measure of how well the regression line fits the data: ( \sum \hat{e}_i^2 ).

R-squared (R²)

The proportion of variance in Y explained by X. Range: 0 (no fit) to 1 (perfect fit).

Homoskedasticity

Constant variance of residuals across all X values. Violation: Heteroskedasticity (uneven spread).

Simple Linear Regression Model

Assumes: ( Y = \beta0 + \beta1 X + \varepsilon ), where ( \mathbb{E}(\varepsilon|X) = 0 ).

Causal Inference

Requires the SLR assumptions to interpret (\beta_1) as the causal effect of X on Y. Challenge: Omitted variable bias.

ANOVA (Analysis of Variance)

Tests whether group means differ by comparing between-group and within-group variability.

MSTR (Mean Square Treatment)

Measures variation between sample means.

MSE (Mean Square Error)

Measures variation within samples.

Pooled-Variance t-test

Compares two means assuming equal variances.

Unequal-Variance t-test (Welch’s Test)

Compares two means without assuming equal variances.

Excel’s Analysis ToolPak

Used to perform regression, ANOVA, and hypothesis tests. Output Includes: Coefficients, standard errors, t-stats, p-values.

Confidence Interval

A range of values likely to contain the population parameter (e.g., slope).

Sampling Variation

Random fluctuations in sample statistics due to drawing different samples. Even if H₀ is true, sample results vary.