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SE of a parameter test
How much we expect our parameter estimate to differ from the population estimate assuming the null hypothesis is true
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Tolerance
- Measure of redundancy between the x's
- Calculated as 1 minus the effect size of all other x's
- Low tolerance means hard to find effect
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t
Degree of deviation from beta zero when the null hypothesis is true
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P-value
- Comparison of critical t value to observed t value
- Significance
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Squared partial correlation
- Comparison of one of the model c's to model a in relation to the model c
- Use to calculate f-ratio
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Squared semi-partial correlation
- Comparison of one of the model c's to model a in relation to the model c with no variables
- Able to compare because they all have the same denominator
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Model c
A model that has all of the variables except for the variable if interest
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Computing partial correlations from accuracy
- Multiple r squared is a measure of accuracy
- Less ambiguous because only 1 value (instead of multiple sse's)
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Improved Default
- Add information: look at when the variable enters last AND first
- Descriptive language: use language that presents facts without bias
- Intellectually full: think about why it is that there is a difference between the separate tests and overall test
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All possible orders
Test for significance and effect size of variables in every possible combination to look for shifting patterns of significance
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Hierarchical regression
- Confirmatory analysis for which order you believe to be the model
- Each step needs to be significant in order to continue and add the next variable
- If any step is non-significant your hypothesis is wrong and you have to do exploratory analysis
- Each model acts as the model c for the next step
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Best possible subsets
Stupid and useless for psychology unless there is a practical application
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Default subsets inferences
- Always wrong because forget about model dependency
- As likely as chance to did the correct combination
- Problems: based on uniqueness, ignores PRE
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Stepwise regression
- Pulls out most highly correlated variable by partialling it out and then continues to find the next one
- No better than chance
- Problems: unique correlations, population dependent, ignores PRE
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All possible subsets regression
- Evaluates every possible combination and compares
- Considers PRE
- Problems: model dependent, not much better than chance
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Hierarchical regression subsets
- A priori sets
- Factorial ANOVA
- A priori control variables
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Factorial ANOVA
- Two or more levels of a favored creates a set
- The interaction between two variables creates another set of interaction variables
- Evaluate sets simultaneously when their enter last
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A priori sets
- Overall test: model A is all variables for all sets
- Separate tests: multiple regression of all sets except the set of interest
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Control set
- Control variables partialed out so that known variables (eg. gender) don't interfere with other relationships
- Overall test: model c includes set of control variables, model a includes other variables on top of model c
- Separate tests: look at every variable as it enters last (and first)
- Inferences: look at differences between model a and model c
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Multiple regression
- No a priori order
- No conceptual sets
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Simultaneous multiple regression mimic
- No a priori order
- Conceptual sets
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Hierarchical regression
- A priori order
- No conceptual sets
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Hierarchical regression with sets
- A priori order
- Conceptual sets
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Control sets
- A priori order
- Mix of sets and variables
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