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Parametric
 depend on population characteristics
 more sensative and versatile

ZTest
Ttest
Independent tTest
 Ztest: need mean and SD, and Pop scores must be normally distributed
 TTest: need mean and Pop scores normally distributed
 Independent tTest: need equal Pop variances

Nonparametric
distributionfree tests (ChiSquare)

ChiSquare uses
frequencies

2Way ChiSquare
2 categorical variables to determine if variables are independent/related

Assumptions of ChiSquare
 Groups are mutually exclusive
 Tallies obtained independently

Repeated Measures ANOVA
same individuals measured across time or in more than 2 conditions

Advantages of Repeated Measures ANOVA
 Reduces unsystematic variability and gives greater power to detect differences
 Fewer participants required
 Sphericityscores likely to be related

Sphericity
equality of variance between treatment levels

Mauchly's Test
 tests sphericity
 If significant (below .05), then sphericity isn't met

Multiple Regression
 predict outcome based on >1 IV (multivariable)
 Outcome = model + error

The Model
best fitting straight line used to estimate outcome variable

Total Sum of Squares
 E(oe)^{2}^{ }
 how good mean is as a model

Residual Sum of Squares
difference between observed and regression line

Model Sum of Squares
 difference between outcome and regression line
 shows reduction in inaccuracy


Residual
 Predicted Outcome  Sample Data Outcome
 have to standardize
 >5% = model is poor representation of data

Cook's Distance
 Influences of a case on the model
 >1 = cause for concern

Leverage (Hat Values)
 0 (no influence) to 1 (complete influence)
 Influence of observed over predicted

Mahalanobis Distance
Measures distance of cases from the mean of predictor

Multiple Regression Assumptions
 Nonzero variance
 Absence of Multicollinearity
 Homoscedascicity
 Independent and Normally Distributed Errors
 Independence
 Linearity

MANOVA
 Multivariate: many DVs
 Omnibus test statistic

Alphas: Nominal, Actual, Familywise, Experimentwise
 Nominal alpha researcher desires
 Actual alpha obtained (type I error)
 Familywise type I error within a test
 Experimentwise all tests used within a study

MANOVA Assumptions
 Independence
 Random Sampling
 Multivariate Normality
 Homogeneity of Covariance Matrices

Following a Significant MANOVA
 Multiple ANOVAs (for each DV)
 Reverse variables to predict which group people belong to

Factorial ANOVA
Second IV that's been systematically manipulated by assigning people to different conditions

Factorial ANOVA: 3 Things
 Main Effect for X
 Main Effect for Y
 Interaction Between X and Y

Factorial ANOVA: "way" means:
number of IV

Multivariable vs. Multivariate
 Multivariable 2+ IV
 Multivariate 2+ DV

Path Analysis
X causes Y and Y causes Z

One Sample tTest
sample compared to population

Independent Measures tTest
means compared between 2 groups

Repeated Measures tTest
means compared between 2 conditions with 1 group


Orthogonality
zero correlation between variables

Experimental
 Researcher controls IV
 Random assignment

Multiple Regression: Nonzero Variance
 Predictors should have some variation in value
 They cannot and should not have variances of 0 (otherwise, there is nothing to measure)

Multiple Regression: Absence of Collinearity
 There should be NO perfect linear relationship between two or more predictors
 AND no two predictors should be too highly correlated

Multiple Regression: Homoscedasticity
 At each level of the predictor variable, the variance of the residual terms should be constant
 If variances are different Heteroscedastic

Multiple Regression: Independent Errors
 For 2 observations, residual terms should be uncorrelated (independent)
 Values range between 0 and 4. Values of 2 means residuals are uncorrelated

Multiple Regression: Normally Distributed Errors
 Residuals in the model are random, normally distributed variables with a mean of 0
 (DOES NOT mean predictors should be normally distributed)

Multiple Regression: Linearity
 The mean values of the outcome variable for each increment of the predictor lie along a straight line
 AKA the relationship is linear!

MANOVA: Multivariate Normality
DVs and any combination of DVs must be normally distributed

MANOVA: Homogeneity of Covariance Matrices
 Variances for all DVs must be equal across the experimental groups
 AND
 The covariance for all unique pairs of DVs should be equal

