143 Questions
What is the purpose of standard regression?
To predict a dependent variable using two or more independent variables simultaneously
What is the best-fitting line in regression analysis?
The line that shows the relationship between dependent and independent variables
What is the definition of error in regression analysis?
The difference between the observed value and the true value
What is unique variance in multiple regression?
Variability in a DV uniquely explained by specific IV(s) in multiple regression
What is the concept of shared variance in multiple regression?
Variability in a DV explained by multiple IVs simultaneously
What is the general linear model in regression and ANOVA?
Data = model + error
What is the standardised slope in regression analysis?
Change in DV for one unit change in IV, holding other IVs constant
What is the regression coefficient R2?
Represents the proportion of variance in the DV that is explained by the IV in the model
What is the primary purpose of using partial correlation?
To measure the correlation between a predictor variable and outcome variable while controlling for the effects of other predictors.
What is the primary difference between a mediated regression model and a hierarchical regression model?
The order of entry of predictor variables.
What is the primary purpose of using tolerance and variance inflation factor (VIF)?
To identify multicollinearity between predictor variables.
What is the primary assumption of the standard multiple regression model?
The relationship between the predictor variables and the outcome variable is linear.
What is the primary purpose of using bootstrapping in mediated regression?
To test the significance of the mediated pathway.
What is the primary purpose of including a covariate in an analysis?
To reduce error by accounting for extraneous variables
What is the primary difference between a moderated regression model and an additive model?
The interaction between predictor variables.
What does an omnibus test assess in ANOVA?
The overall experimental effect
What is the primary purpose of using the Johnson-Neyman test?
To identify the region of significance for the moderator variable.
What is the primary assumption of homogeneity of regression?
The variance of the residuals is homogeneous across all levels of the predictor variable.
What is the primary difference between a bivariate correlation and a semi-partial correlation?
The control for other independent variables in the analysis
What is the primary purpose of using a pick-a-point technique in moderated regression?
To create a graph to describe the association between the predictor variables and the outcome variable.
What is the purpose of Cook's Distance?
To measure the influence of individual data points on the model
What is the primary issue in moderated regression?
Limited power due to small sample size.
What is the primary advantage of using bootstrapping in mediated regression?
Generation of a 95% confidence interval for the mediated effect
What is the purpose of rotating a factor matrix?
To improve the interpretability of the factors
What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
To evaluate the internal consistency of the items on each factor
What is the assumption of homogeneity of regression in ANCOVA?
The relationship between the covariate and dependent variable is the same across all levels of the independent variable
What is the main effect in ANOVA?
The influence of an independent variable on the dependent variable, ignoring other independent variables
What is a studentized residual in regression analysis?
A measure of the discrepancy between the observed and predicted values of the dependent variable
What is the assumption in ANOVA when the association between the covariate and the dependent variable is the same for each group?
The slopes are the same for each group.
What type of effect does an unconditional effect in regression analysis represent?
The influence of each independent variable independent of one another.
What is a characteristic of a balanced design in ANOVA?
Equal numbers of participants in each group.
What is the purpose of Mauchly's test in a study?
To determine whether the variances and covariance matrices are the same across groups.
What does a KMO sampling technique measure in FA/PCA?
The adequacy of the overall items in the solution.
What is the purpose of Bartlett's test of sphericity in FA/PCA?
To determine whether there are groups of independent or semi-independent items.
What is a consequence of an unbalanced design in ANOVA?
The effects are correlated with one another.
When is Mauchly's test not conducted in a study?
When there are only two levels of the repeated factor.
What is the primary purpose of using partial correlation?
To control for the variance shared between other predictors
What does a discrepancy score indicate?
Unusual on the IV and DV
What is the primary purpose of the general linear model in regression and ANOVA?
To represent the data as a combination of the model and error
What is the assumption of homoscedasticity?
The variance of the residual is the same for any value of the IV
What does the standardised slope represent in regression analysis?
The change in the dependent variable for one standard deviation change in the independent variable
What is multicollinearity?
The association between the predictors is dependent
What is the primary purpose of using hierarchical regression?
To determine the theoretical importance of the predictors
What is the difference between unique variance and shared variance in multiple regression?
Unique variance is the variance explained by a specific independent variable, while shared variance is the variance explained by all independent variables
What is the primary difference between a mediated regression model and a hierarchical regression model?
The order of entering the predictors into the model
What is the purpose of the regression coefficient R2 in regression analysis?
To measure the proportion of variance in the dependent variable explained by the independent variable
What is the difference between the unstandardised coefficient and the standardised coefficient in regression analysis?
The unstandardised coefficient is in original units, while the standardised coefficient is in standard deviation units
What is the purpose of using the Sobel test?
To test the significance of the mediated pathway
What is the purpose of SS regression in regression analysis?
To measure the difference between the predicted score and the mean score
What is the primary purpose of using moderated regression analysis?
To examine the interaction between the IV and the moderator
What is the primary purpose of using the Johnson-Neyman test?
To describe the association between the continuous moderator and the DV
What is the difference between SS total and SS residual in regression analysis?
SS total is the total variance in the dependent variable, while SS residual is the unexplained variance
What is the purpose of semi-partial correlation in regression analysis?
To measure the proportion of variance in the dependent variable explained by a specific independent variable
What is the primary difference between conditional and unconditional effects in regression analysis?
Unconditional effects represent the influence of an IV on the DV, regardless of other IVs.
What is the main consequence of an unbalanced design in ANOVA?
It makes it difficult to isolate independent effects.
What is the primary purpose of Mauchly's test in a study?
To test for sphericity in a repeated-measures design.
What is the primary purpose of the KMO sampling technique in FA/PCA?
To determine the adequacy of the solution.
What is the primary purpose of Bartlett's test of sphericity in FA/PCA?
To determine if the correlation matrix is an identity matrix.
What is a characteristic of a balanced design in ANOVA?
Equal number of participants in each group.
What is the primary difference between a conditional and an unconditional effect in ANOVA?
A conditional effect is the influence of an IV on the DV, considering other IVs.
When is Mauchly's test not conducted in a study?
When there are only two levels of the repeated factor.
What is the primary requirement for a covariate to be included in an analysis?
The covariate must be associated with the dependent variable but not the independent variable.
What is the primary purpose of using a semi-partial correlation?
To examine the unique variance explained by each independent variable.
What is the primary difference between a between-subjects and a within-subjects design in ANOVA?
The level of experimental control.
What is the primary purpose of using bootstrapping in mediated regression?
To generate a confidence interval for the mediated effect.
What is the primary assumption of homogeneity of regression in ANCOVA?
The association between the covariate and the dependent variable must be the same for each group.
What is the primary purpose of rotating a factor matrix?
To produce more coherent factors with different items loading on different factors.
What is the primary purpose of using Cook's Distance?
To examine the influence of individual data points on the regression model.
What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
To determine the internal consistency of the items on each factor.
What is the primary difference between an omnibus test and a main effect in ANOVA?
The omnibus test examines the overall effect, while the main effect examines the effect of each independent variable.
What is the primary purpose of using an F statistic in ANOVA?
To determine the ratio of the model to its error.
In a partial correlation, what is removed from the predictor variable?
Shared variance with other predictors
What is the primary assumption of the standard multiple regression model?
Independence of predictor variables
What is the purpose of using tolerance and variance inflation factor (VIF) in regression analysis?
To detect multicollinearity between predictor variables
What is the primary purpose of using mediated regression analysis?
To analyze the indirect effect of a predictor on an outcome variable through a mediator
What is the primary advantage of using bootstrapping in mediated regression?
It provides a more precise estimate of the standard error
What is the primary purpose of using moderated regression analysis?
To analyze the conditional effect of a predictor on an outcome variable
What is the primary difference between an interactive model and an additive model?
The slopes of the predictors are different in an interactive model
What is the primary purpose of using a pick-a-point technique in moderated regression?
To plot the interaction effect of two predictors
What is the primary assumption of homogeneity of regression?
The variance of the residuals is constant across all levels of the predictor variable
What is the primary purpose of the general linear model in regression and ANOVA?
To separate the variance in the dependent variable into explainable and unexplainable components
What is the primary issue in moderated regression?
Power, with a minimum of 150 participants required
Which of the following statements is true about the standardized slope in regression analysis?
It represents the change in the dependent variable for one standard deviation change in the independent variable, while holding other variables constant
What is the difference between unique variance and shared variance in multiple regression?
Unique variance is the variability in the dependent variable that is explained by a specific independent variable, while shared variance is the variability in the dependent variable that is explained by multiple independent variables simultaneously, but not by a specific independent variable
What is the purpose of the regression coefficient R2 in regression analysis?
To represent the proportion of variance in the dependent variable that is explained by the independent variable
What is the difference between the unstandardized coefficient and the standardized coefficient in regression analysis?
The unstandardized coefficient represents the change in the dependent variable for one unit change in the independent variable, while the standardized coefficient represents the change in the dependent variable for one standard deviation change in the independent variable
What is the primary purpose of using a covariate in an analysis?
To reduce error by controlling for the effects of extraneous variables
What is the primary purpose of SS regression in regression analysis?
To increase the difference between the predicted score and the mean score
What is the difference between a bivariate correlation and a semi-partial correlation?
A bivariate correlation shows the unique variance of one variable, while a semi-partial correlation shows the shared variance between two variables
What is the purpose of the total variance SS total in regression analysis?
To represent the difference between the raw score and the mean score
What is the assumption of homogeneity of regression in ANCOVA?
The relationship between the covariate and the dependent variable is the same for each group
What is the primary purpose of semi-partial correlation in regression analysis?
To represent the proportion of variance in the dependent variable that is explained by a specific independent variable, while controlling for the effects of other independent variables
What is the primary purpose of using bootstrapping in mediated regression?
To test the significance of the mediated effect
What is the difference between a main effect and a simple effect in ANOVA?
A main effect is the overall effect of an independent variable, while a simple effect is the effect of an independent variable at a specific level of a moderator variable
What is Cook's Distance?
A measure of the influence of individual data points on the regression line
What is the primary purpose of rotating a factor matrix?
To simplify the interpretation of the factors
What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
To evaluate the internal consistency of the items loading on each factor
What is a studentized residual?
A measure of the difference between the observed and predicted values of the dependent variable
What is an omnibus test?
A test used to compare the means of three or more groups
What is the primary difference between conditional and unconditional effects in ANOVA or regression?
Unconditional effects represent the influence of an independent variable on the dependent variable, while conditional effects represent the influence of an independent variable on the dependent variable, controlled for other independent variables.
What is the primary consequence of an unbalanced design in ANOVA?
The effects of the independent variables are correlated, making it difficult to isolate independent effects.
What is the purpose of Mauchly's test in a study?
To determine whether the covariance matrices are equal across all groups.
What is the primary purpose of the KMO sampling technique in FA/PCA?
To determine whether the factor solution is viable.
What is the primary purpose of Bartlett's test of sphericity in FA/PCA?
To determine whether the factor solution is viable.
When is Mauchly's test not conducted in a study?
When the study has only two levels of the repeated factor.
What is the primary difference between a balanced and unbalanced design in ANOVA?
A balanced design has equal numbers of participants in each group, while an unbalanced design has different numbers of participants in each group.
What is the primary purpose of using conditional effects in ANOVA or regression?
To examine the influence of an independent variable on the dependent variable, influenced by other independent variables.
What is the primary concept that standard regression predicts?
A dependent variable using two or more independent variables simultaneously
What is the term for the difference between the observed value and the true value in regression analysis?
Error
What is the range of the regression coefficient R2?
0 to 1
What is the purpose of SS regression in regression analysis?
To increase the difference between the predicted score and the mean score
What is the standardised slope in regression analysis?
Change in the dependent variable for one unit change in the independent variable, holding other variables constant
What is the difference between unique variance and shared variance in multiple regression?
Unique variance is the variability in the dependent variable uniquely explained by a specific independent variable, while shared variance is the variability in the dependent variable explained by multiple independent variables simultaneously
What is the general linear model in regression and ANOVA?
Data = model + error
What is the difference between the unstandardised coefficient and the standardised coefficient in regression analysis?
The unstandardised coefficient is in original units, while the standardised coefficient is in standard deviation units
What is the primary purpose of using partial correlation?
To identify the correlation between the predictor and outcome variable while controlling for the effects of other predictors
What is the assumption of homoscedasticity in regression analysis?
The variance of the residual is the same for any value of the predictor variable
What is the primary purpose of using tolerance and variance inflation factor (VIF) in regression analysis?
To test the assumption of multicollinearity
What is the difference between an interactive model and an additive model in moderated regression?
The interactive model assumes the effect of one predictor is dependent on the other predictor, while the additive model assumes the effects of the predictors are independent
What is the primary difference between conditional and unconditional effects in ANOVA or regression?
Unconditional effects represent the influence of one IV on the DV, without considering other IVs, while conditional effects represent the influence of one IV on the DV, considering other IVs.
What is the primary purpose of using a pick-a-point technique in moderated regression?
To produce a figure to describe the association between the predictor and outcome variable
What is the primary consequence of an unbalanced design in ANOVA?
Difficulty in isolating the independent effects of each IV
What is the primary issue in moderated regression?
Power, requiring a minimum of 150 participants
What is the primary purpose of Mauchly's test?
To determine if the data meets the assumption of sphericity
What is the primary purpose of using bootstrapping in mediated regression?
To determine the significance of the mediated pathway
What is the primary purpose of the KMO sampling technique in FA/PCA?
To determine the adequacy of the overall items in the solution
What is the primary difference between a mediated regression model and a hierarchical regression model?
The mediated regression model is used to identify the indirect effect of the predictor on the outcome variable, while the hierarchical regression model is used to identify the direct effect
What is the primary purpose of using moderated regression analysis?
To examine the influence of one predictor on the outcome variable conditional on the score of another predictor
What is the primary purpose of Bartlett's test of sphericity?
To determine if the factor solution is viable
What is the assumption of normality in regression analysis?
For any fixed value of the predictor variable, the outcome variable is normally distributed
What is the primary difference between a balanced and unbalanced design in ANOVA?
A balanced design has equal numbers of participants in each group, while an unbalanced design has unequal numbers
When is Mauchly's test not conducted in a study?
When the study has only two levels of the repeated factor
What is the primary assumption of ANOVA when the association between the covariate and the DV is the same for each group?
Homogeneity of regression
What is the primary assumption for using an ANCOVA?
The covariate is associated with the dependent variable and not the independent variable
What is the main difference between a bivariate correlation and a semi-partial correlation?
One is based on all variance in the independent variable and dependent variable, while the other shows how much unique variance is added to the explanation when other independent variables are controlled
What is the purpose of using a rotation in a factor matrix?
To produce more coherent factors which have different items loading on different factors
What is the primary purpose of assessing the reliability of factors in a principal components or factor analysis?
To determine if the factor is internally reliable
What is the purpose of Cook's Distance?
To measure the discrepancy between the actual score and the predicted score within the regression model
What is the primary purpose of using bootstrapping in mediated regression?
To generate a 95% confidence interval for the mediated effect
What is the main difference between a disordinal interaction and a ordinal interaction?
One is used when the effect of one independent variable differs at different levels of the second independent variable and the other is used when the effect of one independent variable does not differ at different levels of the second independent variable
What is the primary purpose of using an omnibus test in ANOVA?
To test for the overall experimental effect and determine if the difference lies somewhere
What is the primary purpose of using a covariate in an analysis?
To reduce error
What is the assumption of homogeneity of regression in ANCOVA?
The regression coefficients are the same across all groups
Study Notes
Standard Regression
- Predicts a dependent variable using two or more independent variables simultaneously.
- Best fitting line: the most appropriate line showing the relationship between dependent and independent variables.
Errors and Variance
- Error: the difference between the observed value and the true value (often unobserved).
- Total variance (SS total): difference between raw score and the mean score.
- SS regression: difference of predicted score from the mean (want to increase this).
- SS residual: the error - difference between raw score and predicted score (want to reduce this).
Coefficients and Correlation
- Regression coefficient (R2): represents the proportion of variance in the DV that is explained by the IV in the model (ranges from 0 to 1).
- Unstandardised coefficient: the slope of the regression line reflecting the change in the DV from one unit change in the IV, while holding all other variables constant.
- Standardised coefficient: the slope of the regression line in standard deviation units (generally -1 to +1), making it comparable with other standardised coefficients.
- Semi-partial correlation (sr2): correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
- Partial correlation: correlation between a predictor variable and outcome variable while removing the shared variance with other predictors.
Regression Assumptions
- Assumption of linearity: the relation between IV and the mean of DV is linear.
- Assumption of homoscedasticity: the variance of residual is the same for any of IV.
- Assumption of normality: for any fixed value of IV, DV is normally distributed.
Multicollinearity
- Multicollinearity: the association between predictors are independent.
- Tolerance and variance inflation factor (VIF): both used to measure multicollinearity, tolerance is 0 (redundant) - 1 (independent), VIF is 10 redundant.
Regression Models
- Standard multiple regression: to predict a DV using two or more IV's, the IV's have equal importance to explanation.
- Hierarchical regression model: we determine what happens based on theory, entered based on theoretical importance or control.
- Statistical regression (stepwise): not based on theory, based on the size of the correlation.
- Mediated regression: mediated regression uses an indirect effect, where the IV influences the DV by a pathway through a second IV (mediator).
Mediated Regression
- Order of a mediated regression: the IV should precede the mediator in time, and the mediator should precede the DV.
- Parallel mediator model: two or more parallel mediator, that need each have an indirect pathway association.
- 4 steps of Baron and Kenny mediated regression: Path A, B, C, C' and a*b significant, Path C no longer required to be significant.
Bootstrapping and Moderated Regression
- Bootstrapping: used to test the significance of the mediated pathway, uses the 95% CI, sampling distribution, if contains 0 not statically significant.
- Moderating regression analysis: the influence of one IV on DV changes based on score on second IV (moderator).
- Unconditional: the predictors each add variance to the explanation of the DV, so each predictor is independent, so additive influence on the outcome.
- Moderated regression equation: y = b0 + b1X + b2M + b3(X*M)
Other Concepts
- Studentised residual: an outlier score, that is unusual on the IV.
- Discrepancy score: most unstable, unusual on IV and DV, use Cook's distance or gap measure to identify.
- Influential score: unusual on IV, can use Mahanobalis or Leverage to identify.
- Homogeneity of regression: the covariate must have the same effect at each level of moderator variable, so does not produce a conditional effect itself.
- ANOVA designs: between groups, repeated measures, and mixed.
- Main effect: the influence of IV without regard for other IV's in the analysis.
- Interaction: the influence of one IV on score of DV conditional on other IVs.
- Disordinal interaction: the effect of one IV, differing at level of second IV.
- Simple effects: specific set of cell means at different level of other IV's.
Correlation and Factor Analysis
- Bivariate correlation: describes linear relationships between two variables, with range of 0 to 1.
- Similarities between bivariate correlation and semi-partial correlation: both describe linear relationships between two variables, with range of 0 to 1.
- Factor analysis: used to produce more coherent factors which have different items loading on different factors.
- Eigenvalues: size of factor loadings for individual items change with rotation.
- Rotations: used to produce more coherent factors which have different items loading on different factors.
- Reliability: Cronbach alpha assesses internal consistency of items on each factor, so will determine if factor is internally reliable.
Covariates and ANCOVA
- Covariate: used when covariate is associated with DV & not IV, used to reduce error.
- Homogeneity of regression: assumption of ANCOVA, association between covariate & DV is same for each group, i.e., slopes are same.
- Conditional and unconditional effects: unconditional effects - influence of each IV independent of one another, conditional effects - influence of one IV on DV influenced by score on additional IV.
ANOVA and Other Concepts
- Omnibus test: test for an overall experimental effect, the difference lies somewhere.
- Mauchly's test: determines whether variances & covariance matrices across groups on repeated measures are same.
- KMO sampling technique: tells us about adequacy of overall items in solution, measures scores range from 0 to 1, closer to one better the solution.
- Bartlett's test of sphericity: is a factor/PCA solution viable, if significant shows there are groups of independent or semi-independent items, so FA can be conducted.
Standard Regression
- Predicts a dependent variable using two or more independent variables simultaneously.
- Best fitting line: the most appropriate line showing the relationship between dependent and independent variables.
Errors and Variance
- Error: the difference between the observed value and the true value (often unobserved).
- Total variance (SS total): difference between raw score and the mean score.
- SS regression: difference of predicted score from the mean (want to increase this).
- SS residual: the error - difference between raw score and predicted score (want to reduce this).
Coefficients and Correlation
- Regression coefficient (R2): represents the proportion of variance in the DV that is explained by the IV in the model (ranges from 0 to 1).
- Unstandardised coefficient: the slope of the regression line reflecting the change in the DV from one unit change in the IV, while holding all other variables constant.
- Standardised coefficient: the slope of the regression line in standard deviation units (generally -1 to +1), making it comparable with other standardised coefficients.
- Semi-partial correlation (sr2): correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
- Partial correlation: correlation between a predictor variable and outcome variable while removing the shared variance with other predictors.
Regression Assumptions
- Assumption of linearity: the relation between IV and the mean of DV is linear.
- Assumption of homoscedasticity: the variance of residual is the same for any of IV.
- Assumption of normality: for any fixed value of IV, DV is normally distributed.
Multicollinearity
- Multicollinearity: the association between predictors are independent.
- Tolerance and variance inflation factor (VIF): both used to measure multicollinearity, tolerance is 0 (redundant) - 1 (independent), VIF is 10 redundant.
Regression Models
- Standard multiple regression: to predict a DV using two or more IV's, the IV's have equal importance to explanation.
- Hierarchical regression model: we determine what happens based on theory, entered based on theoretical importance or control.
- Statistical regression (stepwise): not based on theory, based on the size of the correlation.
- Mediated regression: mediated regression uses an indirect effect, where the IV influences the DV by a pathway through a second IV (mediator).
Mediated Regression
- Order of a mediated regression: the IV should precede the mediator in time, and the mediator should precede the DV.
- Parallel mediator model: two or more parallel mediator, that need each have an indirect pathway association.
- 4 steps of Baron and Kenny mediated regression: Path A, B, C, C' and a*b significant, Path C no longer required to be significant.
Bootstrapping and Moderated Regression
- Bootstrapping: used to test the significance of the mediated pathway, uses the 95% CI, sampling distribution, if contains 0 not statically significant.
- Moderating regression analysis: the influence of one IV on DV changes based on score on second IV (moderator).
- Unconditional: the predictors each add variance to the explanation of the DV, so each predictor is independent, so additive influence on the outcome.
- Moderated regression equation: y = b0 + b1X + b2M + b3(X*M)
Other Concepts
- Studentised residual: an outlier score, that is unusual on the IV.
- Discrepancy score: most unstable, unusual on IV and DV, use Cook's distance or gap measure to identify.
- Influential score: unusual on IV, can use Mahanobalis or Leverage to identify.
- Homogeneity of regression: the covariate must have the same effect at each level of moderator variable, so does not produce a conditional effect itself.
- ANOVA designs: between groups, repeated measures, and mixed.
- Main effect: the influence of IV without regard for other IV's in the analysis.
- Interaction: the influence of one IV on score of DV conditional on other IVs.
- Disordinal interaction: the effect of one IV, differing at level of second IV.
- Simple effects: specific set of cell means at different level of other IV's.
Correlation and Factor Analysis
- Bivariate correlation: describes linear relationships between two variables, with range of 0 to 1.
- Similarities between bivariate correlation and semi-partial correlation: both describe linear relationships between two variables, with range of 0 to 1.
- Factor analysis: used to produce more coherent factors which have different items loading on different factors.
- Eigenvalues: size of factor loadings for individual items change with rotation.
- Rotations: used to produce more coherent factors which have different items loading on different factors.
- Reliability: Cronbach alpha assesses internal consistency of items on each factor, so will determine if factor is internally reliable.
Covariates and ANCOVA
- Covariate: used when covariate is associated with DV & not IV, used to reduce error.
- Homogeneity of regression: assumption of ANCOVA, association between covariate & DV is same for each group, i.e., slopes are same.
- Conditional and unconditional effects: unconditional effects - influence of each IV independent of one another, conditional effects - influence of one IV on DV influenced by score on additional IV.
ANOVA and Other Concepts
- Omnibus test: test for an overall experimental effect, the difference lies somewhere.
- Mauchly's test: determines whether variances & covariance matrices across groups on repeated measures are same.
- KMO sampling technique: tells us about adequacy of overall items in solution, measures scores range from 0 to 1, closer to one better the solution.
- Bartlett's test of sphericity: is a factor/PCA solution viable, if significant shows there are groups of independent or semi-independent items, so FA can be conducted.
Standard Regression
- Predicts a dependent variable using two or more independent variables simultaneously.
- Best fitting line: the most appropriate line showing the relationship between dependent and independent variables.
Errors and Variance
- Error: the difference between the observed value and the true value (often unobserved).
- Total variance (SS total): difference between raw score and the mean score.
- SS regression: difference of predicted score from the mean (want to increase this).
- SS residual: the error - difference between raw score and predicted score (want to reduce this).
Coefficients and Correlation
- Regression coefficient (R2): represents the proportion of variance in the DV that is explained by the IV in the model (ranges from 0 to 1).
- Unstandardised coefficient: the slope of the regression line reflecting the change in the DV from one unit change in the IV, while holding all other variables constant.
- Standardised coefficient: the slope of the regression line in standard deviation units (generally -1 to +1), making it comparable with other standardised coefficients.
- Semi-partial correlation (sr2): correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
- Partial correlation: correlation between a predictor variable and outcome variable while removing the shared variance with other predictors.
Regression Assumptions
- Assumption of linearity: the relation between IV and the mean of DV is linear.
- Assumption of homoscedasticity: the variance of residual is the same for any of IV.
- Assumption of normality: for any fixed value of IV, DV is normally distributed.
Multicollinearity
- Multicollinearity: the association between predictors are independent.
- Tolerance and variance inflation factor (VIF): both used to measure multicollinearity, tolerance is 0 (redundant) - 1 (independent), VIF is 10 redundant.
Regression Models
- Standard multiple regression: to predict a DV using two or more IV's, the IV's have equal importance to explanation.
- Hierarchical regression model: we determine what happens based on theory, entered based on theoretical importance or control.
- Statistical regression (stepwise): not based on theory, based on the size of the correlation.
- Mediated regression: mediated regression uses an indirect effect, where the IV influences the DV by a pathway through a second IV (mediator).
Mediated Regression
- Order of a mediated regression: the IV should precede the mediator in time, and the mediator should precede the DV.
- Parallel mediator model: two or more parallel mediator, that need each have an indirect pathway association.
- 4 steps of Baron and Kenny mediated regression: Path A, B, C, C' and a*b significant, Path C no longer required to be significant.
Bootstrapping and Moderated Regression
- Bootstrapping: used to test the significance of the mediated pathway, uses the 95% CI, sampling distribution, if contains 0 not statically significant.
- Moderating regression analysis: the influence of one IV on DV changes based on score on second IV (moderator).
- Unconditional: the predictors each add variance to the explanation of the DV, so each predictor is independent, so additive influence on the outcome.
- Moderated regression equation: y = b0 + b1X + b2M + b3(X*M)
Other Concepts
- Studentised residual: an outlier score, that is unusual on the IV.
- Discrepancy score: most unstable, unusual on IV and DV, use Cook's distance or gap measure to identify.
- Influential score: unusual on IV, can use Mahanobalis or Leverage to identify.
- Homogeneity of regression: the covariate must have the same effect at each level of moderator variable, so does not produce a conditional effect itself.
- ANOVA designs: between groups, repeated measures, and mixed.
- Main effect: the influence of IV without regard for other IV's in the analysis.
- Interaction: the influence of one IV on score of DV conditional on other IVs.
- Disordinal interaction: the effect of one IV, differing at level of second IV.
- Simple effects: specific set of cell means at different level of other IV's.
Correlation and Factor Analysis
- Bivariate correlation: describes linear relationships between two variables, with range of 0 to 1.
- Similarities between bivariate correlation and semi-partial correlation: both describe linear relationships between two variables, with range of 0 to 1.
- Factor analysis: used to produce more coherent factors which have different items loading on different factors.
- Eigenvalues: size of factor loadings for individual items change with rotation.
- Rotations: used to produce more coherent factors which have different items loading on different factors.
- Reliability: Cronbach alpha assesses internal consistency of items on each factor, so will determine if factor is internally reliable.
Covariates and ANCOVA
- Covariate: used when covariate is associated with DV & not IV, used to reduce error.
- Homogeneity of regression: assumption of ANCOVA, association between covariate & DV is same for each group, i.e., slopes are same.
- Conditional and unconditional effects: unconditional effects - influence of each IV independent of one another, conditional effects - influence of one IV on DV influenced by score on additional IV.
ANOVA and Other Concepts
- Omnibus test: test for an overall experimental effect, the difference lies somewhere.
- Mauchly's test: determines whether variances & covariance matrices across groups on repeated measures are same.
- KMO sampling technique: tells us about adequacy of overall items in solution, measures scores range from 0 to 1, closer to one better the solution.
- Bartlett's test of sphericity: is a factor/PCA solution viable, if significant shows there are groups of independent or semi-independent items, so FA can be conducted.
Standard Regression
- Predicts a dependent variable using two or more independent variables simultaneously.
- Best fitting line: the most appropriate line showing the relationship between dependent and independent variables.
Errors and Variance
- Error: the difference between the observed value and the true value (often unobserved).
- Total variance (SS total): difference between raw score and the mean score.
- SS regression: difference of predicted score from the mean (want to increase this).
- SS residual: the error - difference between raw score and predicted score (want to reduce this).
Coefficients and Correlation
- Regression coefficient (R2): represents the proportion of variance in the DV that is explained by the IV in the model (ranges from 0 to 1).
- Unstandardised coefficient: the slope of the regression line reflecting the change in the DV from one unit change in the IV, while holding all other variables constant.
- Standardised coefficient: the slope of the regression line in standard deviation units (generally -1 to +1), making it comparable with other standardised coefficients.
- Semi-partial correlation (sr2): correlation between the predictor and outcome variable with variance shared between other predictors controlled in the predictor variable only.
- Partial correlation: correlation between a predictor variable and outcome variable while removing the shared variance with other predictors.
Regression Assumptions
- Assumption of linearity: the relation between IV and the mean of DV is linear.
- Assumption of homoscedasticity: the variance of residual is the same for any of IV.
- Assumption of normality: for any fixed value of IV, DV is normally distributed.
Multicollinearity
- Multicollinearity: the association between predictors are independent.
- Tolerance and variance inflation factor (VIF): both used to measure multicollinearity, tolerance is 0 (redundant) - 1 (independent), VIF is 10 redundant.
Regression Models
- Standard multiple regression: to predict a DV using two or more IV's, the IV's have equal importance to explanation.
- Hierarchical regression model: we determine what happens based on theory, entered based on theoretical importance or control.
- Statistical regression (stepwise): not based on theory, based on the size of the correlation.
- Mediated regression: mediated regression uses an indirect effect, where the IV influences the DV by a pathway through a second IV (mediator).
Mediated Regression
- Order of a mediated regression: the IV should precede the mediator in time, and the mediator should precede the DV.
- Parallel mediator model: two or more parallel mediator, that need each have an indirect pathway association.
- 4 steps of Baron and Kenny mediated regression: Path A, B, C, C' and a*b significant, Path C no longer required to be significant.
Bootstrapping and Moderated Regression
- Bootstrapping: used to test the significance of the mediated pathway, uses the 95% CI, sampling distribution, if contains 0 not statically significant.
- Moderating regression analysis: the influence of one IV on DV changes based on score on second IV (moderator).
- Unconditional: the predictors each add variance to the explanation of the DV, so each predictor is independent, so additive influence on the outcome.
- Moderated regression equation: y = b0 + b1X + b2M + b3(X*M)
Other Concepts
- Studentised residual: an outlier score, that is unusual on the IV.
- Discrepancy score: most unstable, unusual on IV and DV, use Cook's distance or gap measure to identify.
- Influential score: unusual on IV, can use Mahanobalis or Leverage to identify.
- Homogeneity of regression: the covariate must have the same effect at each level of moderator variable, so does not produce a conditional effect itself.
- ANOVA designs: between groups, repeated measures, and mixed.
- Main effect: the influence of IV without regard for other IV's in the analysis.
- Interaction: the influence of one IV on score of DV conditional on other IVs.
- Disordinal interaction: the effect of one IV, differing at level of second IV.
- Simple effects: specific set of cell means at different level of other IV's.
Correlation and Factor Analysis
- Bivariate correlation: describes linear relationships between two variables, with range of 0 to 1.
- Similarities between bivariate correlation and semi-partial correlation: both describe linear relationships between two variables, with range of 0 to 1.
- Factor analysis: used to produce more coherent factors which have different items loading on different factors.
- Eigenvalues: size of factor loadings for individual items change with rotation.
- Rotations: used to produce more coherent factors which have different items loading on different factors.
- Reliability: Cronbach alpha assesses internal consistency of items on each factor, so will determine if factor is internally reliable.
Covariates and ANCOVA
- Covariate: used when covariate is associated with DV & not IV, used to reduce error.
- Homogeneity of regression: assumption of ANCOVA, association between covariate & DV is same for each group, i.e., slopes are same.
- Conditional and unconditional effects: unconditional effects - influence of each IV independent of one another, conditional effects - influence of one IV on DV influenced by score on additional IV.
ANOVA and Other Concepts
- Omnibus test: test for an overall experimental effect, the difference lies somewhere.
- Mauchly's test: determines whether variances & covariance matrices across groups on repeated measures are same.
- KMO sampling technique: tells us about adequacy of overall items in solution, measures scores range from 0 to 1, closer to one better the solution.
- Bartlett's test of sphericity: is a factor/PCA solution viable, if significant shows there are groups of independent or semi-independent items, so FA can be conducted.
Test your understanding of standard regression, error, and unique variance in statistics and data analysis.
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