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SHAPE \* MERGEFORMAT   Z-TESTS  In order to run a Z-Test you must be provided with Population ( Population ( Equation:  EMBED Equation.3  Critical Z-Test values: 1-Tailed2-Tailed = .051.641.96/-1.96 = .012.332.58/-2.58 EXAMPLE:  SINGLE SAMPLE T-TEST  In order to run a Single Sample T-test you must: Be provided with Population ( Use the sample Standard Deviation to predict Population ( Equations:  EMBED Equation.3  df = N 1  EXAMPLE:  PAIRED SAMPLES T-TEST  Paired Samples T-Tests: Are also known as Dependent or Matched T-Tests Do not utilize population parameters, rather are a comparison of scores from a single sample measured across time Look for key words such as Test-retest; Pre-Post; Same individuals tested ( = 0 Equations:  EMBED Equation.3   EMBED Equation.3  df = N - 1 Confidence Intervals:  EMBED Equation.3  EXAMPLE:  INDEPENDENT SAMPLES T-TEST (Ns Equal) Independent Samples T-Tests: Are used to compare 2 Independent groups Have experimental groups / conditions May have unequal Ns Look for key words such as Experiment; Conditions; Random Assignment to one condition or another Equations:  EMBED Equation.3   EMBED Equation.3  N = n1 + n2 df = N - 2 Confidence Intervals:  EMBED Equation.3  EXAMPLE:  INDEPENDENT SAMPLES T-TEST (Ns Unequal) Equations:  EMBED Equation.3   EMBED Equation.3  df = N 2 Confidence Intervals:  EMBED Equation.3   EXAMPLE:  ANOVA  ANalysis Of VArience: Are virtually the same thing as an Independent T-Test except that there are more than 2 conditions Accounts for possible inflation of the ( level by dividing the ( level between all possible comparisons (i.e. 3 conditions = (/3 .: ( of 0.017 per comparison) Equations: SourceSums of Squares (SS)dfMean Square Error (MS)FBetween = EMBED Equation.3  k-1=  EMBED Equation.3 =  EMBED Equation.3 WithinSSTot - SSBtwnN-k =  EMBED Equation.3  OR  EMBED Equation.3  Total = EMBED Equation.3  N-1 Estimating the Magnitude of Experimental Effect: (eta) =  EMBED Equation.3  (omega) =  EMBED Equation.3   EXAMPLE:  CHI SQUARE Chi Square: Is used when you have ordinal data You are using the obtained data to make a prediction about what the relationship would have been if there were no difference between the groups Equations:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Likelihood Ratio:  EMBED Equation.3  EMBED Equation.3  Measures of Association: Used to test the strength of the relationship Phi: (2 by 2)  EMBED Equation.3  Cramrs Phi: (X by X)  EMBED Equation.3  Odds Ratio: (2 by 2)  EMBED Equation.3   EXAMPLE:  CORRELATION AND REGRESSION  Correlation: Does not imply causation Determine if two sets of continuous data co vary / can one predict the other? Regression: Is a way of predicting the score of the dependent (criterion) variable based on the level of the independent (predictor) variable Correlation Equation:  EMBED Equation.3  Regression Equations: Y= bX + a  EMBED Equation.3   EMBED Equation.3  Standard Error of the Estimate: SY 2 = Sy2(1-r2)  EMBED Equation.3  Confidence Limits on Y:  EMBED Equation.3   EMBED Equation.3  Note: for (t(/2), if your ( = 0.05, you would use the critical t value for ( = 0.025. Hypothesis Testing: Testing rTesting bTesting Independent bs EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 df = N - 2df = N - 2df = N - 4 EMBED Equation.3  EXAMPLE:  POWER  Power Calculations: What is the probability of correctly rejecting a false H0? Power is a function of: ( level H1 Sample size Test statistic used Where n is unknown, used the power table to estimate ( on a given ( level.  Power for 1 sample  Effect SizeNoncentrality parameterEstimating Required Sample Size EMBED Equation.3  EMBED Equation.3  EMBED Equation.3   Power for 2 samples (Ns Equal)  Effect SizeNoncentrality parameterEstimating Required Sample Size EMBED Equation.3  EMBED Equation.3  EMBED Equation.3   Power for 2 samples (Ns Unequal)  Effect Size *Where ( is pooledHarmonic NNoncentrality parameterEstimating Required Sample Size EMBED Equation.3   EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  Power when ( is known  Effect SizeNoncentrality parameterEstimating Required Sample Size EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EXAMPLE:     PAGE  PAGE 1 What type of data do I have? Continuous Data Only Categorical/Nominal data and Continuous data Do I know the population ( and (? Yes  Run a Z - Test No No Do I know the population (? Yes  Run a Single Sample T-test - Use Sample St. Dev. to predict ( Run Correlation and/or Regression analysis Do I have Independent Samples/Conditions? 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