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Stats Final Review
Dr. Spray's Final-FI
33
Mathematics
Graduate
12/13/2010

Additional Mathematics Flashcards

 


 

Cards

Term
What is effect size?
Definition

-term used to measure the magnitude of a treatment or relationship effeect

-common currency of meta-analysis studies

Term
What is a correlation?
Definition

-usually expressed as r

-ranges -1 to 1

Term
What is the correlation coefficient?
Definition

-expresses quantitatively the magnitude  and direction of a relationship between two variables

-correlation does not infer causation

 

Term
Properties of r
Definition

-value of r does not depend on the unit of measurement for either variable, nor does it depend on which variable is label x or y

-the value of r must be between -1 and 1

-a positive value of r indicates a positive linear relationship between the variables; therefore, as x increases so does y

-Pearson's r should only be used when data are normally or somewhat normally distributed are near normal-not heavily skewed or kurtosis

Term

Partial Correlations (path analysis)

Definition

Definition
-a correlation coefficient between two variables while holding another variable constant
Term

Interpreting the Correlation Coefficient

(r high and low)

Definition

-r ranging from about .20 to .40 may be regarded as indicating a low degree of correlation

-r ranging from about .40 to .60 may be regarded as indicating a moderate degree of correlation

-r ranging from about .80 to 1.00 may be regarded as indicating high correlation

-p > .05 then not significant different than 0

-p < .05 then significantly different than 0

Term

Simple Linear Regression

Equation

Definition

-equation: y=a + bx
-a is the intercept, wherever it crosses the y axis

-b is the slope of the line, slope indicates how much y increases for every unit that x increases

 

Term
R2 (coefficient of determination or correlation coefficient squared)
Definition

-used to determine how well a regression line or model fits the data

-represents the proportion of variability in y that can be explained by the variability in x

 

Term
R2 goodness of fit %'s
Definition

->75%=very good

-50-75%=good

-25-49%=fair

-25% and less=poor or meanlingless

Term
Purpose of regression analysis
Definition

-develop an equation for prediction purposes, able to predict the value of the DV for any individual in the population based on the IV(s)

-explain the relationship between the DV and IV(s)

Term
Assumptions of regression analysis
Definition

-the IVs are fixed

-IVs are measured w/o error

-the relationship between the IV(s) and the DV is assumed to be linear

-the distribution of all variables should be roughly normal

-the DV should be measured on an interval or ratio scale

-errors are not correlated with either the DV or IV(s)

-the variance of the residuals across all values of the IV(s) is consistant

-errors are normally distributed

Term
Multiple regression equation-
Definition

-ei = yi - y

-yi= actual value

-y=predicted or expected value (space between line and dot)

-e represents errors called residuals

Term
multiple correlation (R)
Definition

-similar to the R in simple regression and is comparable to the Pearson correlation coefficient

-measures the correlation between the actual value of the DV and the predicted value of the DV

Term
Coefficient of determination (adjusted R2)
Definition

-interpreted as the % of variation in the DV that can be explained by the combo of IVs

-same goodness of fit scale

Term
Multicollinearity
Definition
-two or more IVs are moderately high to highly correlated, meaning they contribute basically the same info to the model
Term
Problems with multicollinearity-
Definition

-restricts the size of the correlation coefficient R

-makes it difficult to determine the importance of individual predictors

-tends to inflate the standard errors of the Betas so that the resulting prediction equation is not very precise

Term
How to determine multicollinearity
Definition

-examine the correlations among the IVs that you have measured

-run diagnostic stats that assess collinearity: tolerance=a measure of collinearity, varies from 0 to 1, small values indicate collinearity, and good rule of thumb is a value of .2 or less; variance of inflation factor=another measure of collinearity, don't want too large

Term
Model Selection
Definition

-want to select IVs that give us an efficient regression equation w/o including everything under the sun

-have at least 15 participants for every one predictor

-forward, backward, and stepwise

Term

Forward Selection

 

Definition

-computer puts the one with greatest relationship with y

-starts with nothing in the model

Term
Backward Selection
Definition

-starts with all predictors in the model

-shoots out the ones that aren't significant

-run both backward and forward and you will get the same result usually

Term
Stepwise Selection
Definition

-a variation of forward selection, yet it's a better method (with caution)

-enters predictors, then looks at subsets and could spit out the predictors that are significant

Term

Nonparametric tests

Use when...

Definition

-when a continuous DV doesn't meet the assumptions required in a parametric test

-when data are ordinal or ranked

Term
Spearman Rho correlation
Definition

-other verison of the Pearson correlation coefficient

-used to calculate correlation coefficients when one or both of the continuous variables is either ordinal or there are extreme values in your data

Term
Wilcoxon Signed-Ranks test
Definition

-alternative to the paired t-test

-use when your DV is nonparametric and you are using one measure on two diff occasions (ex. pre/post tests)

Term
Mann-Whitney U test
Definition

-used in place of independent t-test or one-way ANOVA

-use when DV is nonparametric and the group variable (IV) has only TWO levels

Term
Kruskal Wallis H test
Definition
-use in place of one-way ANOVA when you DV is nonparametric and the group variable (IV) has THREE OR MORE levels
Term
Logistic Regression
Definition

-like linear regression except the DV (y) is nominal

-relationship between the DV (y) and an IV (x) is expressed by the odds ratio

-odds ratio is a measure of association

-P/1-P=odds event occured

-code 1 to the adverse event to make it easier to explain

Term
What is dummy coding?
Definition
-where you assign a 0 or a 1 to a variable with two levels
Term
What are the standardized regression coefficients?
Definition

-SPSS refers to the standardized regression coefficients as beta

 

Term

Chi-squared test

Assumptions

Definition

-data should be a representative sample (randomly drawn if possible)

-data must be categorical (nominal data)

-the individual observations must be independent of each other

Term

Chi-squared

When valid?

Definition

-when a cell (# of the frequency of observations in that category) in a 2 row and 2 column analysis contains at LEAST 5 observations

-Fisher's exact test may replace the chi-squared test when the above requirements are not met

Term
Chi-squared goodness-of-fit test
Definition

-a chi-squared test on different levels of a single categorical variable

-look at equation

Term
Chi-squared test of independence
Definition

-test on different levels of two categorical variables

-estimating whether two categorical variables are independent or not

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