Comprehensive Guide to One-Way and Repeated-Measures ANOVA, T-Tests, and Correlation in Psychology and Statistics

What does ANOVA stand for?

Analysis of Variance

What is the purpose of a one-way ANOVA?

To find associations between variables by comparing 2 or more means.

What type of outcome variable is used in one-way ANOVA?

Interval or ratio.

What types of predictor variables can be used in one-way ANOVA?

Binary, nominal, or ordinal.

What is the assumption of homogeneity of variance in one-way ANOVA?

The variances among the groups should be equal.

Which test is used to check for homogeneity of variance?

Levene's test.

What does a p-value less than 0.05 indicate in Levene's test?

Reject the null hypothesis; variances are not equal.

What is the significance of the Shapiro-Wilk test in one-way ANOVA?

It checks the normality of residuals.

What does η2 (eta-squared) estimate in ANOVA?

The effect size, indicating the strength of the relationship between the predictor and outcome.

What does an η2 value greater than 0.14 indicate?

A large effect size.

What should be done if the ANOVA indicates rejecting the null hypothesis?

Conduct post hoc tests to explore specific differences between categories.

What is the Holm correction used for in post hoc tests?

To guard against type I errors (false positives).

What does a significant F-value (e.g., F = 960, p < 0.001) indicate?

The outcome means are significantly different between categories of the predictor.

What is the role of QQ plots in one-way ANOVA?

To visually assess the normality of residuals.

What is the consequence of violating the normality assumption in ANOVA?

You can still use ANOVA if the sample size is large and residuals fit closely to the normal line.

What is the relationship between a binary predictor and a t-test in one-way ANOVA?

A one-way ANOVA with a binary predictor works the same as a t-test.

What is the importance of checking assumptions before running a one-way ANOVA?

To ensure the validity of the ANOVA results.

What does a p-value of 0.004 indicate regarding normality of residuals?

Reject the null hypothesis; the residuals are non-normal.

What is the first step in running a one-way ANOVA in Jamovi?

Check homogeneity and normality assumptions.

What is the significance of the estimated means table in post hoc results?

It suggests which groups have significant differences in means.

What is a repeated-measures one-way ANOVA used for?

It is used when the same participants are in each group.

What type of outcome variable is required for repeated-measures ANOVA?

The outcome variable must be interval or ratio.

What types of predictor variables can be used in repeated-measures ANOVA?

The predictor variable can be binary, nominal, or ordinal.

What is the assumption of sphericity in repeated-measures ANOVA?

Sphericity means equal variances among differences between all pairs.

What is Mauchly's W-test used for in repeated-measures ANOVA?

It tests the sphericity assumption.

What should you check if your sphericity assumption is not met?

Use a correction based on the Greenhouse-Geisser value.

What should be done if the ANOVA results indicate to reject the null hypothesis?

Conduct post hoc comparison tests to explore specific differences between categories.

What is the purpose of using Holm correction in post hoc tests?

To guard against 'p-hacking' and reduce the chances of a type I error.

What does a p-value greater than 0.05 indicate in the context of sphericity?

It indicates that the sphericity assumption is met.

What does F = 6.93 (p = 0.013) indicate in ANOVA results?

It indicates that the outcome means are significantly different, allowing rejection of the null hypothesis.

What is the first step when running a repeated-measures ANOVA?

Check the sphericity assumption.

What happens if p < 0.05 in the sphericity test?

You would reject the null hypothesis and apply a correction.

What is the significance of the estimated effect size (η2) being 0.414?

It indicates large differences in outcome means between the categories.

What should you do if the ANOVA indicates to retain the null hypothesis?

Do not run post hoc tests.

What is the purpose of a t-test?

To test whether associations exist between a binary predictor and an interval or ratio outcome variable.

What are the three types of t-tests?

One-sample t-test, Independent-samples t-test, Paired-samples t-test.

What is a one-sample t-test used for?

To compare the sample mean of an outcome variable to the expected population mean (μ).

What key outputs does a one-sample t-test produce?

t-statistic, degrees of freedom (df), and p-value.

What does the p-value indicate in a one-sample t-test?

The risk of committing a type I error if we reject the null hypothesis.

How do you check for normality in a one-sample t-test?

By running a Shapiro-Wilk normality test.

What does it mean if p > 0.05 in a normality test?

Retain the null hypothesis; the data are normally distributed.

What is the independent-samples t-test used for?

To compare two sample means against each other when there is a binary predictor.

What tests must be performed before running an independent-samples t-test?

Normality test and Levene's test for homogeneity of variance.

What does Levene's test check?

Whether the outcome variable has equal standard deviations across both predictor categories.

What is the paired-samples t-test used for?

To compare observations that are not independent, such as pre- and post-intervention results.

What is Cohen's d?

A measure of effect size for t-tests.

What is the purpose of the Normality Test in t-tests?

To ensure that the data are normally distributed before applying the t-test.

What is the effect of sample size on the t-distribution?

The shape of the t-distribution changes based on the degrees of freedom, which is calculated as sample size - 1.

What is the relationship between the t-statistic and the p-value?

The p-value is calculated based on where the observed t-statistic falls in the t-distribution.

What is correlation?

A bivariate linear association between two interval or ratio variables.

How can we visualize linear correlations?

Using scatterplots where observed values for two variables are plotted as X, Y coordinates.

What is Pearson's r?

A measure of linear correlation between two variables, indicating both direction and magnitude.

What does a positive Pearson's r indicate?

As 'x' increases, 'y' also increases.

What does a negative Pearson's r indicate?

As 'x' increases, 'y' decreases.

What is the outcome variable in linear regression?

The dependent variable that is being predicted.

What are predictor variables in linear regression?

Independent variables used to predict the outcome variable.

What are the five assumptions of linear regression?

1. Linearity, 2. No perfect multicollinearity, 3. Normality of residuals, 4. Constant variance, 5. Independence of residuals.

What is multicollinearity?

When predictor variables are highly correlated with each other.

What is the Variance Inflation Factor (VIF)?

A measure used to detect multicollinearity; VIF < 10 indicates no concern.

What does R² represent in linear regression?

The proportion of variance in the outcome variable explained by the predictor variables.

What is the purpose of the F-test in linear regression?

To determine if the model with predictors is better than random chance.

What is the estimated regression coefficient?

It indicates the expected change in the outcome variable for a one-unit change in the predictor.

What does it mean if the confidence interval for a predictor includes 0?

There is no significant effect of that predictor on the outcome variable.

What is the role of scatterplots in assessing linear regression assumptions?

They help visualize the linearity of relationships between predictors and the outcome.

What is the significance of retaining the null hypothesis in hypothesis testing?

It suggests that the model does not provide a better prediction than random chance.

What should you do before calculating Pearson's r?

Look at the data visually to assess relationships.

What is the importance of checking the normality of residuals?

To ensure that the assumptions of linear regression are met.

What is the estimated value for the outcome variable in linear regression?

The predicted value based on the regression equation.

What does it mean if the p-value for a predictor is greater than 0.05?

We are not confident that this predictor has a significant effect on the outcome.

What is the difference between interval/ratio and binary/nominal predictor variables?

Interval/ratio variables are continuous, while binary/nominal variables are categorical.

What is a p-value?

A p-value indicates the risk of committing a Type I error if we reject the null hypothesis.

What is the typical alpha level used in hypothesis testing?

Typically 0.05 (5%).

What does it mean if p < 0.05?

We reject the null hypothesis (H0).

What does it mean if p > 0.05?

We retain the null hypothesis (H0).

What types of variables can the χ²-test be used for?

Binary, nominal, and ordinal variables.

What is the χ² goodness-of-fit test used for?

It evaluates whether an observed frequency distribution matches an expected frequency distribution.

What are the three key outputs of a χ² goodness-of-fit test?

χ² value, degrees of freedom (df), and p-value.

What does a high p-value indicate in a χ² goodness-of-fit test?

It indicates a high risk of committing a Type I error if we reject the null hypothesis.

What is the purpose of the χ² test of independence?

To test if there is an observable relationship between two variables in a sample.

What is effect size in the context of categorical data analysis?

Effect size measures the strength of association between variables.

What is Phi (ϕ) used for?

To calculate effect size when both variables are binary.

What is Cramér's V used for?

To calculate effect size when at least one variable is nominal or ordinal.