Podcast
Questions and Answers
What is the purpose of maximizing SS Regression in a regression analysis?
What is the purpose of maximizing SS Regression in a regression analysis?
What does the R2 coefficient represent in a regression model?
What does the R2 coefficient represent in a regression model?
What is the purpose of standardizing coefficients in a regression model?
What is the purpose of standardizing coefficients in a regression model?
What does the semi-partial correlation measure in a regression model?
What does the semi-partial correlation measure in a regression model?
Signup and view all the answers
What is the purpose of regression diagnostics?
What is the purpose of regression diagnostics?
Signup and view all the answers
What is an outlier score in a regression analysis?
What is an outlier score in a regression analysis?
Signup and view all the answers
What is the purpose of studentized residuals in a regression analysis?
What is the purpose of studentized residuals in a regression analysis?
Signup and view all the answers
What is partial correlation in a regression model?
What is partial correlation in a regression model?
Signup and view all the answers
What is the main purpose of Cook's Distance?
What is the main purpose of Cook's Distance?
Signup and view all the answers
What is the reason for excluding a data point from the analysis?
What is the reason for excluding a data point from the analysis?
Signup and view all the answers
What does a high score on Cook's Distance indicate?
What does a high score on Cook's Distance indicate?
Signup and view all the answers
What is the purpose of a semi-partial correlation?
What is the purpose of a semi-partial correlation?
Signup and view all the answers
What is the definition of leverage?
What is the definition of leverage?
Signup and view all the answers
Why may there be a significant association in an IV and DV in Pearson's Correlation, but not in multiple regression analysis?
Why may there be a significant association in an IV and DV in Pearson's Correlation, but not in multiple regression analysis?
Signup and view all the answers
What does a standardized regression coefficient provide?
What does a standardized regression coefficient provide?
Signup and view all the answers
What is the main assumption of regression?
What is the main assumption of regression?
Signup and view all the answers
What is the purpose of the Mahalanobis distance?
What is the purpose of the Mahalanobis distance?
Signup and view all the answers
What happens to the sum of squares (SSregression) when the predicted inattention scores vary widely?
What happens to the sum of squares (SSregression) when the predicted inattention scores vary widely?
Signup and view all the answers
What is the reason for the uniquely explained variance being small in the model?
What is the reason for the uniquely explained variance being small in the model?
Signup and view all the answers
What is the purpose of entering IVs in a specific order in hierarchical regression?
What is the purpose of entering IVs in a specific order in hierarchical regression?
Signup and view all the answers
What is the purpose of using tolerance in regression analysis?
What is the purpose of using tolerance in regression analysis?
Signup and view all the answers
What is the advantage of using standard multiple regression?
What is the advantage of using standard multiple regression?
Signup and view all the answers
What is multicollinearity, and what problem does it cause in regression models?
What is multicollinearity, and what problem does it cause in regression models?
Signup and view all the answers
What is the purpose of using R squared change in hierarchical regression?
What is the purpose of using R squared change in hierarchical regression?
Signup and view all the answers
Why is it important to enter IVs in a specific order in hierarchical regression?
Why is it important to enter IVs in a specific order in hierarchical regression?
Signup and view all the answers
What is the difference between hierarchical regression and statistical regression?
What is the difference between hierarchical regression and statistical regression?
Signup and view all the answers
What is the purpose of using variance inflation factor (VIF) in regression analysis?
What is the purpose of using variance inflation factor (VIF) in regression analysis?
Signup and view all the answers
What is the advantage of using hierarchical regression?
What is the advantage of using hierarchical regression?
Signup and view all the answers
What is the primary reason why the Sobel Test is not recommended?
What is the primary reason why the Sobel Test is not recommended?
Signup and view all the answers
What is the purpose of a factor loading in Principal Components Analysis?
What is the purpose of a factor loading in Principal Components Analysis?
Signup and view all the answers
What is the goal of factor rotation in Principal Components Analysis?
What is the goal of factor rotation in Principal Components Analysis?
Signup and view all the answers
What is the characteristic of components after an orthogonal rotation?
What is the characteristic of components after an orthogonal rotation?
Signup and view all the answers
What is the purpose of examining the component matrix in Principal Components Analysis?
What is the purpose of examining the component matrix in Principal Components Analysis?
Signup and view all the answers
What is the advantage of using Varimax rotation?
What is the advantage of using Varimax rotation?
Signup and view all the answers
What is the primary purpose of hierarchical model testing?
What is the primary purpose of hierarchical model testing?
Signup and view all the answers
What type of effect occurs when the effect of one predictor on an outcome is explained or partially explained by a second predictor?
What type of effect occurs when the effect of one predictor on an outcome is explained or partially explained by a second predictor?
Signup and view all the answers
What is the purpose of calculating the communality (h2) in Principal Components Analysis?
What is the purpose of calculating the communality (h2) in Principal Components Analysis?
Signup and view all the answers
What is the condition required for a mediator to precede the DV?
What is the condition required for a mediator to precede the DV?
Signup and view all the answers
What is the criterion for excluding items in Principal Components Analysis?
What is the criterion for excluding items in Principal Components Analysis?
Signup and view all the answers
What type of research is required to establish causation?
What type of research is required to establish causation?
Signup and view all the answers
What is the purpose of naming factors in Principal Components Analysis?
What is the purpose of naming factors in Principal Components Analysis?
Signup and view all the answers
What is the result of an orthogonal rotation on the component matrix?
What is the result of an orthogonal rotation on the component matrix?
Signup and view all the answers
What is the purpose of Path A in the Classic Mediation model?
What is the purpose of Path A in the Classic Mediation model?
Signup and view all the answers
What is the condition required for a mediating effect to be significant?
What is the condition required for a mediating effect to be significant?
Signup and view all the answers
What is the formula to obtain the total effect of the mediating pathway?
What is the formula to obtain the total effect of the mediating pathway?
Signup and view all the answers
What type of effect occurs when the effect of an IV on a DV is explained by a common cause?
What type of effect occurs when the effect of an IV on a DV is explained by a common cause?
Signup and view all the answers
What is the purpose of Path C' in the Classic Mediation model?
What is the purpose of Path C' in the Classic Mediation model?
Signup and view all the answers
What type of data is used in cross-sectional modeling?
What type of data is used in cross-sectional modeling?
Signup and view all the answers
What is the purpose of Kaiser-Meyer Olkin measure of sampling adequacy?
What is the purpose of Kaiser-Meyer Olkin measure of sampling adequacy?
Signup and view all the answers
What is the purpose of Bartlett's test of sphericity?
What is the purpose of Bartlett's test of sphericity?
Signup and view all the answers
What is the purpose of the Anti-Image Matrices?
What is the purpose of the Anti-Image Matrices?
Signup and view all the answers
What is the main goal of Principal Components Analysis (PCA) and Factor Analysis (FA)?
What is the main goal of Principal Components Analysis (PCA) and Factor Analysis (FA)?
Signup and view all the answers
What does the Pattern matrix provide?
What does the Pattern matrix provide?
Signup and view all the answers
What is the purpose of reliability analysis in research?
What is the purpose of reliability analysis in research?
Signup and view all the answers
What is the main difference between Principal Components Analysis (PCA) and Factor Analysis (FA)?
What is the main difference between Principal Components Analysis (PCA) and Factor Analysis (FA)?
Signup and view all the answers
What is the minimum number of response options required for items in PCA/FA?
What is the minimum number of response options required for items in PCA/FA?
Signup and view all the answers
What is the purpose of orthogonal rotation in Factor Analysis?
What is the purpose of orthogonal rotation in Factor Analysis?
Signup and view all the answers
What is the purpose of inspecting item distributions?
What is the purpose of inspecting item distributions?
Signup and view all the answers
What is a complex item in Factor Analysis?
What is a complex item in Factor Analysis?
Signup and view all the answers
What is the purpose of varimax rotation in Factor Analysis?
What is the purpose of varimax rotation in Factor Analysis?
Signup and view all the answers
What is the internal consistency of components measured by?
What is the internal consistency of components measured by?
Signup and view all the answers
What is the minimum acceptable internal consistency for research?
What is the minimum acceptable internal consistency for research?
Signup and view all the answers
What is the difference between orthogonal and oblique rotation in Factor Analysis?
What is the difference between orthogonal and oblique rotation in Factor Analysis?
Signup and view all the answers
What happens if Bartlett's test of sphericity is not significant?
What happens if Bartlett's test of sphericity is not significant?
Signup and view all the answers
What is the purpose of communalities in Factor Analysis?
What is the purpose of communalities in Factor Analysis?
Signup and view all the answers
What is the advantage of using Principal Components Analysis (PCA) over Factor Analysis (FA)?
What is the advantage of using Principal Components Analysis (PCA) over Factor Analysis (FA)?
Signup and view all the answers
What is the purpose of factor loadings in Factor Analysis?
What is the purpose of factor loadings in Factor Analysis?
Signup and view all the answers
What is the purpose of using Cronbach's alpha in testing internal consistency?
What is the purpose of using Cronbach's alpha in testing internal consistency?
Signup and view all the answers
What is the advantage of using components/factors in other analyses?
What is the advantage of using components/factors in other analyses?
Signup and view all the answers
What is the purpose of reporting the number of items included in the final solution?
What is the purpose of reporting the number of items included in the final solution?
Signup and view all the answers
What is the main difference between principal components analysis and factor analysis?
What is the main difference between principal components analysis and factor analysis?
Signup and view all the answers
What is the purpose of using orthogonal rotation in principal components analysis?
What is the purpose of using orthogonal rotation in principal components analysis?
Signup and view all the answers
What is the advantage of using varimax rotation in principal components analysis?
What is the advantage of using varimax rotation in principal components analysis?
Signup and view all the answers
What is the purpose of using direct oblimin rotation in principal components analysis?
What is the purpose of using direct oblimin rotation in principal components analysis?
Signup and view all the answers
What is the advantage of using factor scores in analysis?
What is the advantage of using factor scores in analysis?
Signup and view all the answers
What is the purpose of reporting the percentage of variance accounted for in each component?
What is the purpose of reporting the percentage of variance accounted for in each component?
Signup and view all the answers
What is the purpose of using Bartlett's test of sphericity?
What is the purpose of using Bartlett's test of sphericity?
Signup and view all the answers
What does an eigenvalue of 1 represent in a factor?
What does an eigenvalue of 1 represent in a factor?
Signup and view all the answers
What is the role of a moderator in a statistical analysis?
What is the role of a moderator in a statistical analysis?
Signup and view all the answers
What is the purpose of using covariates in an analysis?
What is the purpose of using covariates in an analysis?
Signup and view all the answers
What is the difference between a mediator and a moderator?
What is the difference between a mediator and a moderator?
Signup and view all the answers
What happens to the total variance when a rotated factor matrix is used?
What happens to the total variance when a rotated factor matrix is used?
Signup and view all the answers
What does an eigenvalue of 1 represent in a factor?
What does an eigenvalue of 1 represent in a factor?
Signup and view all the answers
What is the role of a moderator in a statistical analysis?
What is the role of a moderator in a statistical analysis?
Signup and view all the answers
What is the purpose of controlling for covariates in a regression analysis?
What is the purpose of controlling for covariates in a regression analysis?
Signup and view all the answers
What is the role of a mediator in a statistical analysis?
What is the role of a mediator in a statistical analysis?
Signup and view all the answers
What is the definition of a dependent variable in a regression analysis?
What is the definition of a dependent variable in a regression analysis?
Signup and view all the answers
What is the purpose of rotating a factor matrix?
What is the purpose of rotating a factor matrix?
Signup and view all the answers
What is the definition of unique variance in multiple regression?
What is the definition of unique variance in multiple regression?
Signup and view all the answers
What is the goal of standard multiple regression?
What is the goal of standard multiple regression?
Signup and view all the answers
What type of regression model is used when the researcher wants to determine the importance of different constructs and test the significance of individual IVs?
What type of regression model is used when the researcher wants to determine the importance of different constructs and test the significance of individual IVs?
Signup and view all the answers
What is the purpose of using tolerance in regression analysis?
What is the purpose of using tolerance in regression analysis?
Signup and view all the answers
What is the result of a high score on Cook's Distance?
What is the result of a high score on Cook's Distance?
Signup and view all the answers
What is the purpose of using R squared change in hierarchical regression?
What is the purpose of using R squared change in hierarchical regression?
Signup and view all the answers
What is the assumption of homoscedasticity in regression analysis?
What is the assumption of homoscedasticity in regression analysis?
Signup and view all the answers
What is the purpose of using standard multiple regression?
What is the purpose of using standard multiple regression?
Signup and view all the answers
What is the result of multicollinearity in regression models?
What is the result of multicollinearity in regression models?
Signup and view all the answers
What is the purpose of using partial correlation in regression analysis?
What is the purpose of using partial correlation in regression analysis?
Signup and view all the answers
What is the purpose of using variance inflation factor (VIF) in regression analysis?
What is the purpose of using variance inflation factor (VIF) in regression analysis?
Signup and view all the answers
What is the goal of regression analysis?
What is the goal of regression analysis?
Signup and view all the answers
What is the primary goal of Mediated Regression Analysis?
What is the primary goal of Mediated Regression Analysis?
Signup and view all the answers
What is a characteristic of a Parallel Mediator Model?
What is a characteristic of a Parallel Mediator Model?
Signup and view all the answers
What is the purpose of bootstrapping in Mediated Regression Analysis?
What is the purpose of bootstrapping in Mediated Regression Analysis?
Signup and view all the answers
What is the difference between a moderator and a mediator?
What is the difference between a moderator and a mediator?
Signup and view all the answers
What is the formula to calculate the total effect of the mediating pathway?
What is the formula to calculate the total effect of the mediating pathway?
Signup and view all the answers
What is the purpose of the Sobel test?
What is the purpose of the Sobel test?
Signup and view all the answers
What is a characteristic of an Interactive Model?
What is a characteristic of an Interactive Model?
Signup and view all the answers
What is the purpose of using unstandardized regression coefficients in Moderated Regression Analysis?
What is the purpose of using unstandardized regression coefficients in Moderated Regression Analysis?
Signup and view all the answers
What is the definition of a Conditional Effect?
What is the definition of a Conditional Effect?
Signup and view all the answers
What is the purpose of a Simple Slope Analysis?
What is the purpose of a Simple Slope Analysis?
Signup and view all the answers
What is the main purpose of using variable centring in moderated regression?
What is the main purpose of using variable centring in moderated regression?
Signup and view all the answers
What is the minimum recommended sample size for conducting a power analysis in moderated regression?
What is the minimum recommended sample size for conducting a power analysis in moderated regression?
Signup and view all the answers
What is the purpose of a covariate in moderated regression?
What is the purpose of a covariate in moderated regression?
Signup and view all the answers
What is the difference between a main effect and an interaction in factorial ANOVA?
What is the difference between a main effect and an interaction in factorial ANOVA?
Signup and view all the answers
What is the purpose of an omnibus test in ANOVA?
What is the purpose of an omnibus test in ANOVA?
Signup and view all the answers
What is the difference between a between-subjects design and a within-subjects design in ANOVA?
What is the difference between a between-subjects design and a within-subjects design in ANOVA?
Signup and view all the answers
What is the purpose of the F-statistic in ANOVA?
What is the purpose of the F-statistic in ANOVA?
Signup and view all the answers
What is the purpose of the degrees of freedom in ANOVA?
What is the purpose of the degrees of freedom in ANOVA?
Signup and view all the answers
What is the difference between an ordinal interaction and a disordinal interaction?
What is the difference between an ordinal interaction and a disordinal interaction?
Signup and view all the answers
What is the purpose of a contrast in ANOVA?
What is the purpose of a contrast in ANOVA?
Signup and view all the answers
What is the purpose of including a control variable in a regression analysis?
What is the purpose of including a control variable in a regression analysis?
Signup and view all the answers
What is the primary difference between a moderator and a mediator?
What is the primary difference between a moderator and a mediator?
Signup and view all the answers
What is the purpose of factor rotation in Principal Components Analysis?
What is the purpose of factor rotation in Principal Components Analysis?
Signup and view all the answers
What is the purpose of calculating the communality in Principal Components Analysis?
What is the purpose of calculating the communality in Principal Components Analysis?
Signup and view all the answers
What is the condition required for a mediating effect to be significant?
What is the condition required for a mediating effect to be significant?
Signup and view all the answers
What is the purpose of using hierarchical regression?
What is the purpose of using hierarchical regression?
Signup and view all the answers
What is the purpose of using Varimax rotation in Principal Components Analysis?
What is the purpose of using Varimax rotation in Principal Components Analysis?
Signup and view all the answers
What is the primary assumption of multiple regression?
What is the primary assumption of multiple regression?
Signup and view all the answers
What is the primary purpose of using partial correlation in multiple regression analysis?
What is the primary purpose of using partial correlation in multiple regression analysis?
Signup and view all the answers
Which of the following assumptions of regression is most closely related to the concept of homoscedasticity?
Which of the following assumptions of regression is most closely related to the concept of homoscedasticity?
Signup and view all the answers
What is the primary advantage of using hierarchical regression over standard multiple regression?
What is the primary advantage of using hierarchical regression over standard multiple regression?
Signup and view all the answers
What is the purpose of using standardized coefficients in multiple regression analysis?
What is the purpose of using standardized coefficients in multiple regression analysis?
Signup and view all the answers
What is the primary purpose of using cooks distance in multiple regression analysis?
What is the primary purpose of using cooks distance in multiple regression analysis?
Signup and view all the answers
What is the primary advantage of using statistical regression analysis over hierarchical regression?
What is the primary advantage of using statistical regression analysis over hierarchical regression?
Signup and view all the answers
What is the primary purpose of using leverage in multiple regression analysis?
What is the primary purpose of using leverage in multiple regression analysis?
Signup and view all the answers
What is the primary purpose of using Mahalanobis distance in multiple regression analysis?
What is the primary purpose of using Mahalanobis distance in multiple regression analysis?
Signup and view all the answers
What is the primary purpose of using variance inflation factor (VIF) in multiple regression analysis?
What is the primary purpose of using variance inflation factor (VIF) in multiple regression analysis?
Signup and view all the answers
What is the purpose of variable centring?
What is the purpose of variable centring?
Signup and view all the answers
What is the minimum sample size recommended for conducting a moderated regression?
What is the minimum sample size recommended for conducting a moderated regression?
Signup and view all the answers
What is the purpose of the omnibus test in ANOVA?
What is the purpose of the omnibus test in ANOVA?
Signup and view all the answers
What is the definition of a simple effect in a factorial ANOVA design?
What is the definition of a simple effect in a factorial ANOVA design?
Signup and view all the answers
What is a three-way interaction in a factorial ANOVA design?
What is a three-way interaction in a factorial ANOVA design?
Signup and view all the answers
What is an ordinal interaction in a factorial ANOVA design?
What is an ordinal interaction in a factorial ANOVA design?
Signup and view all the answers
What is the purpose of a contrast in a factorial ANOVA design?
What is the purpose of a contrast in a factorial ANOVA design?
Signup and view all the answers
What is the formula for the t-statistic in a t-test?
What is the formula for the t-statistic in a t-test?
Signup and view all the answers
What is the purpose of the degrees of freedom in ANOVA?
What is the purpose of the degrees of freedom in ANOVA?
Signup and view all the answers
What is the difference between a between-groups design and a repeated-measures design in ANOVA?
What is the difference between a between-groups design and a repeated-measures design in ANOVA?
Signup and view all the answers
In Mediated Regression Analysis, what is the requirement for the mediator to precede the DV?
In Mediated Regression Analysis, what is the requirement for the mediator to precede the DV?
Signup and view all the answers
What is the purpose of Path A in the Classic Mediation model?
What is the purpose of Path A in the Classic Mediation model?
Signup and view all the answers
In Moderating Regression Analysis, what is the coefficient b3?
In Moderating Regression Analysis, what is the coefficient b3?
Signup and view all the answers
What is the difference between a mediated and a moderated regression model?
What is the difference between a mediated and a moderated regression model?
Signup and view all the answers
What is the purpose of the parallel mediator model?
What is the purpose of the parallel mediator model?
Signup and view all the answers
What is the formula to obtain the total effect of the mediating pathway?
What is the formula to obtain the total effect of the mediating pathway?
Signup and view all the answers
What is the result of a statistically significant moderator term in Moderated Regression Analysis?
What is the result of a statistically significant moderator term in Moderated Regression Analysis?
Signup and view all the answers
What is the purpose of using unstandardized regression coefficients in Moderated Regression Analysis?
What is the purpose of using unstandardized regression coefficients in Moderated Regression Analysis?
Signup and view all the answers
What is the difference between an additive and an interactive model?
What is the difference between an additive and an interactive model?
Signup and view all the answers
What is the purpose of the Pick-a-Point Technique in Moderated Regression Analysis?
What is the purpose of the Pick-a-Point Technique in Moderated Regression Analysis?
Signup and view all the answers
Study Notes
Regression Analysis
- Variance: The goal is to maximize SS Regression and minimize SS Error.
- Regression Coefficient (R2): Represents the proportion of variance in the dependent variable explained by independent variables, ranging from 0 (not explained) to 1 (explains all variability).
- Standardized Coefficients (Beta): Allows comparison of different predictors, generally ranging from -1 to +1.
- Semi-partial Correlation: Measures the unique contribution of a specific independent variable to the dependent variable, controlling for other predictors.
Identifying Unusual Scores
- Regression Diagnostics: Aim for an accurate relationship between predictors and outcomes.
- Outlier Scores: Small data points can have a large influence on the solution.
- Studentized Residual: Measures the difference between the predicted and observed scores.
- Leverage: Measures the influence of each data point on the regression line.
- Cook's Distance: Combines leverage and studentized residual to identify influential data points.
Assumptions of Regression
- Linearity: The relationship between predictors and outcomes should be linear.
- Normality: Residuals should be normally distributed.
- Homoscedasticity: Residuals should have constant variance.
- Independence: Observations should be independent.
Multiple Regression
- Standard Multiple Regression: Used when the combination of predictors explains significant variance in the outcome variable.
- Hierarchical Regression: Used to test theoretical models, entering predictors in a specific order based on theoretical importance.
Mediated Regression Analysis
- Direct Effects: The straight arrow from predictor to outcome variable.
- Indirect Effects: The arrow from predictor to mediator to outcome variable.
- Mediating Variables: Explain how predictor variables influence the outcome variable.
- Fully Mediated Effects: When the predictor variable influences the outcome variable only through the mediator.
Factors and Principal Components
- Principal Components Analysis (PCA): Reduces a large number of items to a smaller number of components, interested in all variance.
- Factor Analysis (FA): Interested in the common variance, what is shared among items (co-variance).
- Orthogonal Rotation: Produces independent components, maintaining independence between components.
Let me know if you'd like me to clarify anything!### Factor Analysis
- Deliberate mind wandering: enjoying mind wandering, thoughts wander on purpose, becoming absorbed in pleasant fantasy, and mind wandering to cope with boredom
- Types of mind wandering: deliberate and spontaneous
Principal Axis Solutions
- Uses a 2-factor solution
- FA eigenvalues are lower than PCA because PCA uses 100% of the variance, while FA only uses shared variance
- Scree plot is used to determine the number of factors to extract
- Factor matrix: all 8 items have strong loadings, but item 2 has a mix, which is not desirable
- Varimax rotation can improve the factor matrix
Complex Items
- Items that correlate more than 0.35 on more than one component in the rotated solution
- May be part of a general construct only and not explanatory when searching for independent dimensions
- Solution: exclude the item (if there is one), or if many, components are not independent; use an oblique solution to allow for correlations between components
Oblique Rotation
- Components are not independent; correlations between them
- Independent (varimax) - angle = 90 degrees
- Oblique (not independent) - each axis moves separately
- Not independent < 90 degrees
Pattern Matrix and Structure Matrix
- Pattern matrix: provides factor loadings that are unique (excludes shared variance)
- Structure matrix: factor loadings are higher than the pattern matrix and include shared variance (variance counted twice)
- Factor correlation matrix: gives the correlation between the two matrices
Writing Up an Oblique Solution
- Report total % of variance accounted for
- Describe factors using factor loadings
- Report correlation between factors produced
Assumptions of Analysis
- Bartlett's test of sphericity: determines whether there are factors/components in the correlation matrix
- Kaiser-Meyer-Olkin measure of sampling adequacy: describes the proportion of variance that might be described by underlying factors
Distribution of Items
- Scales suitable for PCA/FA: non-discriminating items (same score), extreme scores
- Bartlett's test: determines whether there are factors/components in the correlation matrix
- Kaiser-Meyer-Olkin measure of sampling adequacy: describes the proportion of variance that might be described by underlying factors
Strategy Analysis
- Inspect item distributions
- Correlation matrix: exclude items with correlations < 0.3 with at least one other
- Assess sampling adequacy
- Determine how many components to extract
- Remove variables that need to be discarded
- Perform rotations
Reliability Analysis
- Internal consistency of components: correlation between item and component
- Cronbach's alpha: measures the extent to which different items on a scale are measuring the same construct
- Good reliability: does not necessarily mean the instrument is valid
Testing Internal Consistency Factors
- Use items with high loading on each scale
- Reliability statistic: using Cronbach's alpha
- Item-total statistics: Cronbach's alpha if an item is deleted, corrected item-total correlation, and squared multiple correlation
Using Components in Other Analyses for Validity
- Can be saved and components/factors used in other analyses - added to data file
- Uses linear combination produced based on rotation used for each component/factor
Reporting Results
- Number of items included in final solution (as well as how many excluded)
- Assumptions
- % variance accounted for overall and how many components included in final solution
- If orthogonal rotation, % accounted for each component
- Use final solution (e.g., varimax), tell reader
- Final solution based on theoretical meaningfulness of outcome, not entirely statistics
- Table with all items on each component and loading
- Describe each component and name it
- Coefficient alpha (α) for each component
Factor Analysis
- Eigenvalue determines the percentage of variance accounted for in a factor
- An eigenvalue of 1 equals the proportion of variance of one item
Moderation and Mediation
- Moderator: a conditional/dependent effect where the influence of the independent variable (IV) on the dependent variable (DV) depends on the score of the moderator
- Example: years in education (IV), gender (moderator), and salary (DV)
- Mediator: a pathway or chain of events where the IV influences the mediator, which in turn influences the score on the DV
- Example: years in education (IV), beginning salary (mediator), and salary (DV)
Covariates
- Should be used in an analysis when you want to control for error to better explain the association between the IV and DV
Regression Basics
- Standard multiple regression predicts a dependent variable (DV) using two or more independent variables (IVs) simultaneously.
- A variable is a measurable characteristic that varies (by groups, individuals, or time).
- Dependent/Outcome Variable (DV) is the presumed effect in the analysis.
- Independent/Explanatory Variable (IV) is the presumed cause in an analysis.
- Control Variable/Covariate is a variable that is not studied but included in the model/analysis.
Regression 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 in both multiple regression and Pearson's correlation.
General Linear Model (GLM)
- GLM: date = model + error (regression and ANOVA).
Regression Results
- Regression Coefficient R2: represents the proportion of the variance in the dependent variable that is explained by the independent variables in the model.
- Ranges from 0 (not explained) to 1 (explains all variability).
- Unstandardized coefficient: the slope of the regression line reflecting the change in the DV from one-unit change in the IV, whilst holding all other variables constant (B).
- Standardized coefficient: the slopes of the regression line expressed in standard deviation units (generally -1 to +1); making it comparable with other standardized coefficients.
- Semi-partial correlation (Part)sr2: Correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
- p-value of the model: It tests whether R2 is different from 0. A value less than 0.05 shows a statistically significant relationship.
Identifying Unusual Scores
- Influences the way the outcome of the analysis can be interpreted.
- Outlier Score: Studentised residual: unusual on IV.
- Discrepancy (most instable): unusual on IV and DV.
- Influential: unusual on IV: Mahanobalis and Leverage.
Assumption of Regression
- Linearity: The relationship between IV and the mean of DV is linear.
- Homoscedasticity: The variance of residual is the same for any of 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 – we determine what happens based on theory.
- Entered into the model at different steps, based on theoretical importance or control.
Reporting
- R2 change = Squared semi-partial correlation.
- How much added variance in DV explained each step.
- Report significance of F change.
- Change for individual IVs not always significant.
Mediated Regression Analysis
- Mediating variables theoretically explain how the predictor variables influence the DV (outcome).
- The IV should precede the mediator in time, and the mediator should precede the DV.
Moderated Regression Analysis
- Influence of one IV on DV "changes" based on the score on the second IV.
- The moderator variable is the IV that influences the relationship between IV and DV, such as direction or strength.
- The IV is no longer independent; it is "conditional" on the moderator.
ANOVA Basics
- Are the means different?
- Definitions and Terms:
- T statistics: Tests whether two group means are significantly different.
- F statistics: The ratio of the model to its error.
Variability
- Between conditions: Explained by our model.
- Within conditions: Unexplained error.
Sum of Squares
- SS Total: Grand Mean.
- SS between: Variance explained by our model.
- SS within: Variance not explained by our model.
Degrees of Freedom
- df for SS between: k-1 (number of conditions/groups minus 1).
- df for SS within: N-k (Number of participants minus the number of groups).
- df SS total: N-1 (number of participants minus 1).
Omnibus Test
- Tests for an overall experimental effect – that the difference lies "somewhere".
ANOVA Designs
- Between groups: Two experimental conditions and different people are assigned to each condition.
- Repeated measures: Two experimental conditions and the same people take part in both conditions.
- Mixed ANOVA: Combination of repeated and independent factors.
Factorial ANOVA
- Factorial Designs can show interactions.
- The impact of one independent variable (IV) ignoring the presence of any other IV included in the design.
- Main effect: Influence of IV without regard for other IV's in the analysis.
- Interaction: The influence of one IV on the score of DV conditional (dependent) on the other independent variable.
Interaction Contrasts
- Evaluated effects of two IV's for different levels of the third IV.
Types of Interactions
- Disordinal Interaction: Effect of one IV, differs at the level of the second IV & direction or effect differs.
- Ordinal Interaction: Can interpret main effects (further analysis required on statistical interaction).
Regression Basics
- Standard multiple regression predicts a dependent variable (DV) using two or more independent variables (IVs) simultaneously.
- A variable is a measurable characteristic that varies (by groups, individuals, or time).
- Dependent/Outcome Variable (DV) is the presumed effect in the analysis.
- Independent/Explanatory Variable (IV) is the presumed cause in an analysis.
- Control Variable/Covariate is a variable that is not studied but included in the model/analysis.
Regression 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 in both multiple regression and Pearson's correlation.
General Linear Model (GLM)
- GLM: date = model + error (regression and ANOVA).
Regression Results
- Regression Coefficient R2: represents the proportion of the variance in the dependent variable that is explained by the independent variables in the model.
- Ranges from 0 (not explained) to 1 (explains all variability).
- Unstandardized coefficient: the slope of the regression line reflecting the change in the DV from one-unit change in the IV, whilst holding all other variables constant (B).
- Standardized coefficient: the slopes of the regression line expressed in standard deviation units (generally -1 to +1); making it comparable with other standardized coefficients.
- Semi-partial correlation (Part)sr2: Correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
- p-value of the model: It tests whether R2 is different from 0. A value less than 0.05 shows a statistically significant relationship.
Identifying Unusual Scores
- Influences the way the outcome of the analysis can be interpreted.
- Outlier Score: Studentised residual: unusual on IV.
- Discrepancy (most instable): unusual on IV and DV.
- Influential: unusual on IV: Mahanobalis and Leverage.
Assumption of Regression
- Linearity: The relationship between IV and the mean of DV is linear.
- Homoscedasticity: The variance of residual is the same for any of 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 – we determine what happens based on theory.
- Entered into the model at different steps, based on theoretical importance or control.
Reporting
- R2 change = Squared semi-partial correlation.
- How much added variance in DV explained each step.
- Report significance of F change.
- Change for individual IVs not always significant.
Mediated Regression Analysis
- Mediating variables theoretically explain how the predictor variables influence the DV (outcome).
- The IV should precede the mediator in time, and the mediator should precede the DV.
Moderated Regression Analysis
- Influence of one IV on DV "changes" based on the score on the second IV.
- The moderator variable is the IV that influences the relationship between IV and DV, such as direction or strength.
- The IV is no longer independent; it is "conditional" on the moderator.
ANOVA Basics
- Are the means different?
- Definitions and Terms:
- T statistics: Tests whether two group means are significantly different.
- F statistics: The ratio of the model to its error.
Variability
- Between conditions: Explained by our model.
- Within conditions: Unexplained error.
Sum of Squares
- SS Total: Grand Mean.
- SS between: Variance explained by our model.
- SS within: Variance not explained by our model.
Degrees of Freedom
- df for SS between: k-1 (number of conditions/groups minus 1).
- df for SS within: N-k (Number of participants minus the number of groups).
- df SS total: N-1 (number of participants minus 1).
Omnibus Test
- Tests for an overall experimental effect – that the difference lies "somewhere".
ANOVA Designs
- Between groups: Two experimental conditions and different people are assigned to each condition.
- Repeated measures: Two experimental conditions and the same people take part in both conditions.
- Mixed ANOVA: Combination of repeated and independent factors.
Factorial ANOVA
- Factorial Designs can show interactions.
- The impact of one independent variable (IV) ignoring the presence of any other IV included in the design.
- Main effect: Influence of IV without regard for other IV's in the analysis.
- Interaction: The influence of one IV on the score of DV conditional (dependent) on the other independent variable.
Interaction Contrasts
- Evaluated effects of two IV's for different levels of the third IV.
Types of Interactions
- Disordinal Interaction: Effect of one IV, differs at the level of the second IV & direction or effect differs.
- Ordinal Interaction: Can interpret main effects (further analysis required on statistical interaction).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Learn about regression analysis, including maximizing SS regression and minimizing SS error. Understand how R2 represents the proportion of variance explained by independent variables in the model.