exss273 test 3 study guide

Q: What is the main goal of inferential statistics?

A: To use sample data to make generalizations about a population and determine whether observed differences are real or due to chance.

Q: What two kinds of differences are most EXSS studies focused on?

A: Group differences (e.g., intervention vs. control) and differences across time (e.g., pre- vs. post-treatment).

Q: What does it mean to "reject the null hypothesis"?

A: Conclude that there is a statistically significant difference between groups or time points.

Q: What does it mean to "fail to reject the null hypothesis"?

A: Conclude that any observed difference could be due to chance; no significant effect.

Q: What is alpha (α)?

A: The preset threshold for significance; commonly 0.05.

Q: What does α = 0.05 indicate?

A: A 5% chance of incorrectly detecting a difference when none exists (Type I error).

Q: What does p < α indicate?

A: Reject the null hypothesis (significant difference).

Q: What does p > α indicate?

A: Fail to reject the null (difference not significant).

Q: What does a lower p-value mean?

A: The observed data is less consistent with the null hypothesis.

Q: What is a Type I error?

A: Rejecting a true null hypothesis (false positive).

Q: What is a Type II error?

A: Failing to reject a false null hypothesis (false negative).

Q: Which error is considered more serious?

A: Type I error.

Q: How do you reduce the likelihood of a Type I error?

A: Decrease α (make significance threshold stricter).

Q: How do you reduce the likelihood of a Type II error?

A: Increase α, increase sample size, or reduce variability.

Q: What is statistical power?

A: The probability of correctly rejecting a false null hypothesis; detecting a true effect.

Q: What is the formula for power?

A: Power = 1 − β (beta = probability of Type II error).

Q: What is the typical target power level?

A: 80% (β = 0.20).

Q: What factors increase statistical power?

A: Higher α, larger sample size, larger effect size, lower variability.

Q: Why can too much power be a problem?

A: It may detect trivial differences that are statistically significant but not meaningful.

Q: What effect size measure is used in ANOVA?

A: Eta squared (η²) or partial eta squared.

Q: How are η² values interpreted?

A: ~.01 minimal, ~.06 moderate, ~.14 substantial.

Q: What does degrees of freedom represent?

A: The number of values free to vary in a calculation before the last one becomes fixed.

Q: df for a single-sample t-test?

A: n − 1.

Q: df for an independent samples t-test?

A: n₁ + n₂ − 2.

Q: df for ANOVA between-groups?

A: k − 1 (k = number of groups).

Q: df for ANOVA within-groups?

A: N − k (N = total participants).

Q: When do you use a chi-square goodness-of-fit test?

A: For categorical data when comparing observed vs. expected frequencies.

Q: What are "observed" frequencies?

A: Actual counts from your sample.

Q: What are "expected" frequencies?

A: Counts based on hypotheses, prior data, or even distribution.

Q: df for chi-square?

A: Number of categories − 1.

Q: What assumptions do t-tests require?

A: Interval/ratio data, normal distribution, appropriate df.

Q: When do you use a single-sample t-test?

A: To compare a sample mean to a known population mean.

Q: When do you use a paired-samples t-test?

A: To compare two related means (e.g., pre/post).

Q: When do you use an independent-samples t-test?

A: To compare means of two different groups.

Q: When is a one-tailed test used?

A: When predicting a specific direction of difference.

Q: When is a two-tailed test used?

A: When testing for any difference, regardless of direction.

Q: When do you use ANOVA instead of multiple t-tests?

A: When comparing 3+ groups or 3+ time points; reduces Type I error.

Q: What does ANOVA evaluate?

A: Differences in variability between and within groups.

Q: What is the F-ratio formula?

A: F = between-group variability / within-group variability.

Q: What does F = 1 mean?

A: Variability between groups equals variability within groups; usually not significant.

Q: What does F > 1 mean?

A: More variability between groups than within; possible significance.

Q: Why do you need post hoc tests?

A: ANOVA tells you a difference exists but not where it exists.

Q: When is Tukey HSD recommended?

A: Equal group sizes, many pairwise comparisons, balanced designs.

Q: When is Bonferroni recommended?

A: Small number of planned comparisons; very conservative; handles unequal sample sizes well.

Q: What does repeated measures ANOVA test?

A: Differences across multiple time points within the same participants.

Q: What does a factorial ANOVA test?

A: Effects of 2+ independent variables and how they interact.

Q: What does a mixed ANOVA include?

A: One between-subjects factor + one within-subjects (usually time).

Q: What is an interaction effect?

A: When the effect of one variable depends on the level of another variable.

Q: What does correlation measure?

A: The strength and direction of a linear relationship between two variables.

Q: Pearson r is used for what type of data?

A: Continuous, normally distributed variables.

Q: Spearman rho is used when?

A: Ordinal data or non-normal variables.

Q: Does correlation imply causation?

A: No — correlation only shows association.

Q: What can distort correlation?

A: Outliers, small samples, nonlinear relationships.

Q: How does regression differ from correlation?

A: Regression predicts an outcome (Y) from a predictor (X) using a line; correlation only measures relationship strength.

Q: Formula for simple regression?

A: Y = bX + a.

Q: What does the slope (b) represent?

A: The change in Y for every one-unit change in X.

Q: What does the intercept (a) represent?

A: Predicted Y when X = 0.

Q: What does the F-statistic indicate in regression?

A: Whether the model explains significantly more variance than error.

Q: What is r²?

A: The proportion of variance in Y explained by the model.

Q: What are residuals?

A: The difference between actual and predicted Y values.

Q: What is the goal of least squares?

A: To minimize the sum of squared residuals.

Q: What is the equation for multiple regression?

A: Y = b₀ + b₁X₁ + b₂X₂ + … + e.

Q: What does each slope (b) represent?

A: The effect of that predictor while holding all other predictors constant.

Q: What indicates multicollinearity?

A: Predictors highly correlating with each other (r > 0.7), unstable coefficients, or signs flipping.

Q: How can multicollinearity be identified?

A: By checking the correlation matrix.