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

-common currency of meta-analysis studies

-usually expressed as r

-ranges -1 to 1

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

-correlation does not infer causation

-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

Partial Correlations (path analysis)

Definition

Interpreting the Correlation Coefficient

(r high and low)

-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

Simple Linear Regression

Equation

-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

-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

->75%=very good

-50-75%=good

-25-49%=fair

-25% and less=poor or meanlingless

-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)

-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

-e_i = y_i - y

-y_i= actual value

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

-e represents errors called residuals

-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

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

-same goodness of fit scale

-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

-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

-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

Forward Selection

-computer puts the one with greatest relationship with y

-starts with nothing in the model

-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

-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

Nonparametric tests

Use when...

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

-when data are ordinal or ranked

-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

-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)

-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

-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

-SPSS refers to the standardized regression coefficients as beta

Chi-squared test

Assumptions

-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

Chi-squared

When valid?

-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

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

-look at equation

-test on different levels of two categorical variables

-estimating whether two categorical variables are independent or not