Multivariate Analyses
Terms
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Multiple Correlation
-definition- - Extends the bivariate Pearson correlation (r) to analytic circumstances involving 3+
- Multiple Correlation is also known as...
- Multiple R
- Mutliple Correlation allows us to...
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1) tell how much variation is ovserved w/in a selected criterion
2) And associated with the variation in socres noted within a given set of 2+ predictors - Multiple correlation has the capacity to help select what?
- Select the "best" set of predictors available
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Coefficient of Mutliple Correlation R
-definition- - A measure of correlation between 2+ predictor variables that have been optimally weighted to yield the highest possible correlation
- The value of multiple R is interpreted as...
- An indication of the strength/magnitude of the relationship
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Multiple R values signify
1) Close to 0
2) +1 or -1 -
1) Less consequential relationships
2) Strong, influential relationships -
Coefficient of Mulitple determination Râ‚‚
-definition- - Provides a measuire of explained variance
- Multiple Râ‚‚tells us...
- The proportion of variance in the criterion variable, expressed as %, that can be predicted, accounted for, and explained
- The R value can never exceed...
- 1.00
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Examples of R and Râ‚‚
1) R = 0.80
2) Râ‚‚ = 0.64 -
1) Strong correlation
2) Accounts for about 64% in variation - R and Râ‚‚ considered biased estimators, but what can be done to offset it?
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1) # of predictor variables should be kept small
2)Râ‚‚ should be adjusted downward -
Adjusted Râ‚‚
-definition- - When Râ‚‚ is adjusted downward to refelct the actual number of cases and predictor variables included in the analysis
- 4 Basic assumptions to meet BEFORE Mutliple correlation analysis
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1) Interval/Ratio are required
2)Relationships between the criterion variable and the predictors shoudl be reasonably linear
3) Data must be homoscedastic
4) Predictor variable should not correlate highly with another -
Homoscedasticity
-definition- - Equal scatter or consistent variance across a predictor variable
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Collinerity
-definition- - Predictor variables should not correlate highly with one another
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Multicollinearity
-definiton- - When 2+ predictors take up a good deal of the same explanatory space making findings inaccurate
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Mutliple Regression
-definiton- - Multivariate counterpart of the regression procedure involving a single predictor
- Multiple Regression allows us to predict the value of what?
- Predict the value of a criterion/dependent variable when we know the values of two or more predictor variables
- b Coefficient is also known as what?
- Slope or Partial Slope
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b Coefficient
-definition- - Computed for each predictor in the regression equation tells us how much of the criterion variable variation is accounted for by that predictor alone
- Beta weights is also known as...
- Beta coefficients or Partial regression Coefficients
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Beta coefficients
-definition- - Allows for the decription of the amount of variation in the criterion variable that's associated with each predictor variable
- Beta coefficients are determined by...
- Converting scores to their respective z-score
- 2 Critical Decisions when conducting a multiple regression analysis:
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1) Which predictor variables to include
2) Specifiying the order in which these items will be entered -
Hierarchial Inclusion Method
-definition- - Draw on their knowledge of the problem
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Stepwise Inclusion Method
-definition- -
Order in which th epredictor variables are entreed into the analysis is determined on statistical grounds.
Variable with highest correlate is entered 1st -
Dicotomous variable
-definition- - Offers only 2 response options
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Binary Variable
-definition- - Dichotomous variable in which 0 is used to signfiy none of something and 1 the presence of something
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Dummy Variable
-definition- - New stand-in variable that is mutually exclusive, a stnadardized unit, and 0 is meaningful
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Factor
-defintion- - Independent or predictor variable
- In describing ANOVAs you refer to...
- The number of factors involved
- The purpose of a 2way ANOVA is...
- To test the signficance of differences occuring among group means
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Main Effect
-definition- - When you focus on the impact of only 1 factor
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Interaction Effect
-defintition- - Focuses on the combined effect of the 2 independent variables
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Sum of Squares
-definition- - Tells us how much variation was observed in the depression scores obtained overall, the main effects, interaction, and residual error effect
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Grand Mean
-definition- - Overall group mean
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Error
-definition- - Variance associated with individual differences occuring among subjects within the 4 groups defined by these independent variables
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Degress of Freedom for Error
-definition- - Number of cases incolced minus the number of groups associated with the independent variables of factors
- E.G. of degrees of freedom for error
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2 x 2 Design with 40 Cases
DofF for E = 36
(40-4 = 36) -
Mean Square
-definition- - Dividing the sum of squares assoiated with each source by the degrees of freedom
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F-statistic
-definition- - Dividing the mean square derived for each main and interaction effect, by the mean sqaure associated with the error term