Statistics: T and F Tests

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Questions and Answers

What is the primary purpose of including control variables in a multiple regression model?

To calculate the unique variance explained by each independent variable

To increase the number of independent variables in the model

To identify the dependent variable

To reduce the effect of extraneous variables on the relationship between independent and dependent variables (correct)

What is the difference between the observed value and the true value in a regression analysis?

Unique variance

Error (correct)

Shared variance

Residual

In a multiple regression model, what is the term for the variability in the dependent variable that is explained by multiple independent variables simultaneously?

Total variance

Unique variance

Residual variance

Shared variance (correct)

What is the purpose of the best fitting line in a regression analysis?

To show the relationship between the independent and dependent variables Signup and view all the answers

What is the range of the regression coefficient R2?

0 to 1 Signup and view all the answers

What is the term for the change in the dependent variable for one unit change in the independent variable, holding other independent variables constant, excluding shared variance?

Unstandardized slope Signup and view all the answers

What is the equation for the General Linear Model (GLM)?

data = model + error Signup and view all the answers

What is the primary difference between unique variance and shared variance?

Unique variance is explained by a single independent variable, while shared variance is explained by multiple independent variables Signup and view all the answers

What is the primary purpose of standardized coefficients in regression analysis?

To express the slopes of the regression line in standard deviation units Signup and view all the answers

Which type of correlation measures the relationship between a predictor variable and the outcome variable while controlling for the shared variance with other predictors?

Partial correlation Signup and view all the answers

What is the purpose of the p-value in regression analysis?

To test whether the R-squared value is different from 0 Signup and view all the answers

What is the primary goal of selecting the 'best' model in regression analysis?

To minimize the residual mean square Signup and view all the answers

What is the main difference between hierarchical and stepwise regression models?

The order of entry of the predictor variables Signup and view all the answers

What is the purpose of the Mahanobalis and Leverage measures in regression analysis?

To identify influential observations Signup and view all the answers

What is the assumption of homoscedasticity in regression analysis?

The variance of the residual is the same for any value of the independent variable Signup and view all the answers

What is the purpose of the R-change value in hierarchical regression analysis?

To measure the added variance explained by each predictor variable Signup and view all the answers

What is the primary goal of mediated regression analysis?

To explain how the predictor variables influence the dependent variable Signup and view all the answers

What is the requirement for the mediating variable in mediated regression analysis?

The mediating variable must precede the dependent variable in time Signup and view all the answers

What is the purpose of bootstrapping in testing the significance of a mediated pathway?

To calculate the confidence interval of the mediated pathway Signup and view all the answers

What is the implication of a non-significant mediator term in a parallel mediation model?

The mediator has no individual influence on the outcome Signup and view all the answers

What is the purpose of a moderator variable in a moderating regression analysis?

To determine the conditional effect of the IV on the DV Signup and view all the answers

What is the difference between an additive and interactive model?

Additive models have slopes that are the same, while interactive models have slopes that differ Signup and view all the answers

What is the purpose of variable centring in moderated regression?

To create a mean of 0 Signup and view all the answers

What is the implication of a statistically significant moderator term in a moderating regression analysis?

The relationship between the IV and DV is conditional on the moderator variable Signup and view all the answers

What is the purpose of the Johnson-Neyman test in moderating regression?

To determine the region of significance for the moderator variable Signup and view all the answers

What is the minimum sample size required for moderating regression analysis?

150 participants Signup and view all the answers

What is the purpose of a covariate in moderating regression?

To add variance to the explanation of the outcome variable Signup and view all the answers

What is the primary purpose of F statistics in ANOVA?

To calculate the ratio of the model to its error Signup and view all the answers

What is the degree of freedom for SS total in ANOVA?

N-1 Signup and view all the answers

What type of ANOVA design is used when there are two experimental conditions and the same people take part in both conditions?

Repeated measures Signup and view all the answers

What is the main effect of an independent variable in a factorial ANOVA?

The influence of one IV on the score of the DV, ignoring the other IV Signup and view all the answers

What type of interaction occurs when the effect of one IV differs at different levels of the second IV, and the direction of the effect differs?

Disordinal interaction Signup and view all the answers

What is the purpose of a contrast in ANOVA?

To evaluate the effects of two IVs for different levels of a third IV Signup and view all the answers

What is the assumption of sphericity in ANOVA?

The assumption that the variance is equal across all groups Signup and view all the answers

What is the purpose of the omnibus test in ANOVA?

To test for an overall experimental effect Signup and view all the answers

What is the formula for calculating the t-test in ANOVA?

Mean difference divided by the standard error Signup and view all the answers

What type of interaction occurs when there is an interaction effect between three independent variables on a continuous dependent variable?

Three-way interaction Signup and view all the answers

What is homogeneity of regression used for in ANCOVA?

To ensure that the relationship between the independent variable and the dependent variable is the same across all groups Signup and view all the answers

What is the difference between conditional and unconditional design in ANOVA or regression?

Unconditional effects are the influence of one IV on the DV without regard of the other IV's in the analysis. Conditional effect is the influence of one IV on score of DV without considering the other independent variables. Signup and view all the answers

What is the main difference between a balanced and unbalanced design in ANOVA, and what difficulties can an unbalanced design cause?

A balanced design has equal sample sizes, while an unbalanced design has unequal sample sizes, which can cause difficulties in interpretation of results and estimation of variances. Signup and view all the answers

Study Notes

Regression Basics

Standard multiple regression predicts a dependent variable (DV) using two or more independent variables (IVs) simultaneously.
Definitions:
- Variable: Measurable characteristic that varies by groups, individuals, or time.
- Dependent/Outcome Variable (DV): Presumed effect in the analysis.
- Independent/Explanatory Variable (IV): Presumed cause in an analysis.
- Control Variable/Covariate: Variables that are not studied but included in the model/analysis.
Key concepts:
- Best Fitting Line: The most appropriate line showing the relationship between dependent and independent variables.
- Residual: Deviators from the fitted line (estimated value) to the observed values (data point).
- Error: Difference between the observed value and the true value (often unobserved).
- Unique Variance: Variability in a DV uniquely explained by specific IV(s) in multiple regression.
- Shared Variance: Variability in a DV explained by multiple IV(s) simultaneously.

Graphical Representation

Total Variance, explained and error

Regression Results

Regression Coefficient R2: represents the proportion of the variance in the DV that is explained by the IVs.
Unstandardized coefficient: the slope of the regression line reflecting the change in the DV from one-unit change in the IV.
Standardized coefficient: the slope of the regression line expressed in standard deviation units.
Semi-partial correlation (Part)sr2: Correlation between the predictor and outcome variable with variance shared between other predictors controlled.
p-value of the model: tests whether R2 is different from 0.

Identifying Unusual Scores

Influences the way the outcome of the analysis can be interpreted.
Avoid: larger sample size, reliable measure, and pilot test.
Outlier Score: Studentised residual: unusual on IV.
Discrepancy (most unstable): unusual on IV and DV.
Influential: unusual on IV.

Assumptions of Regression

Linearity: The relationship between IV and the mean of DV is linear.
Homoscedasticity: The variance of residual is the same for any IV.
Normality: For any fixed value of IV, DV is normally distributed.
Multicollinearity: Associations between predictors (0) redundant (1) independent.

Selecting the "Best" Model

Goal is to minimize the residual mean square (which maximizes R2) by comparing regression models.

Hierarchical Regression Model

Hypothesis model: determine what happens based on theory.
Entered into the model at different steps, based on theoretical importance or control.
R2 change: Squared semi-partial correlation.

Statistical Regression Analysis (Stepwise)

M - not theory (not recommended) - based on the size of the correlations.

Mediated Regression Analysis (CUE BALL)

Mediating variables theoretically explain how the predictor variables influence the DV.
Steps:
- Path C: statistically significant.
- Path A: statistically significant IV and mediator after controlling for DV.
- Path B: statistically significant mediator and DV after controlling for IV.
- Path c' association of IV and DV after controlling for mediator.

Moderating Regression Analysis

Influence of one IV on DV "changes" based on score on second IV.
Moderator variable: IV that influences the relationship between IV and DV.
Moderator effects: IVs are not independent.
Unconditional: The predictors each add variance to the explanation of the outcome variable.
Conditional: The effect of one predictor variable may depend on the value of another predictor variable.

ANOVA Basics

Are the means different?
Definitions:
- T statistics: Tests whether two group means are significantly different.
- F statistics: The ratio of the model to its error.
- Variability: Between conditions and within conditions.
Degrees of Freedom:
- df for SS between: k-1.
- df for SS within: N-k.
- df SS total: N-1.
Omnibus test: Tests for an overall experimental effect.

Factorial ANOVA

Factorial Designs can show interactions.
Main effect: Influence of IV without regard for other IV's in the analysis.
Interaction: Influence of one IV on score of DV conditional on the other independent variable.
Types of Interactions:
- Three-way interaction.
- Disordinal Interaction.
- Ordinal Interaction.

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Description

Understand the concepts of T statistics and F statistics, including variability, sum of squares, and degrees of freedom in statistical analysis.