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Descriptive Statistical Analyses Reliability Analyses Review of Last Class

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Computing Scale Scores e.g., Global Life Satisfaction Recode Negatively worded items –How can you check you did it correctly? Compute a global life satisfaction score by taking the mean of all items –Can only do after reverse scoring –Why not take the sum of all items? Advantages vs. disadvantages –What types of things can/should you take sums of?

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Compute frequencies of variables to be recoded before and after recoding –The freq of people who are responding to specific categories of scale should shift appropriately based on the recoding Items that are negatively worded and positively worded should be positively correlated after recoding but negatively correlated before recoding Change the output view setting to show all commands you have run to see that you have only run the recode command once How to check if you recoded correctly?

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Correlations of un recoded items vs. recoded items What’s next…. Change the output view setting to show all commands you have run to see that you have only run the recode command once Students check sample output

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To change output view, Go to “edit”, click “options”, pick “viewer” tab, click on “Display commands in the log”

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Other issues When Computing Scale Scores Always compute reliabilities before computing scale scores. –Why? See output for specific satisfaction & stress Compute scale scores for each –Ensure you recode appropriate items –Drop items that have no variance and report in results –Decide on sum/mean based on meaning of scale

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Example syntax file has the commands for –Social relationship satisfaction –Social relationship stress –Notes about decisions made to drop specific items Students review output file generated & answer orally –What is the correlation between Social relationship satisfaction & social stress Social relationship satisfaction & life satisfaction stress life satisfaction & social stress Correct Syntax for previous slide

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Continuous –Interval –Ratio Discontinuous (Categorical) –Nominal –Ordinal Students provide examples from questionnaires completed in this course (e.g., 1 st day of class, student satisfaction survey etc.) Review of Types of Variables

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Types of Inferential Statistics Nature of Independent Variable ContinuousCategorical Nature of Dependent Variable ContinuousCorrelation/ Regression T-test /ANOVA Categorical

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Correlation Regression When both variables are continuous

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Assesses whether 2 variables are ‘linearly’ related to each other Varies from –1 to +1 to reflect the direction and the strength of the relation Associated with a significance level to determine its likelihood of occurring due to chance.05 likelihood of correlation occurring due to chance is regarded as significant; Anything more than.05 means it is not significant Significance Determined via t-test Review of Correlation

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Tom Cruise Vince Carter Calista Flockhart Julia Roberts r =.76; r 2 = 58%

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Better measure of the strength of a relation is the amount of explained variance (r 2 ) Ranges from 0 to 100 Difference between r=.3 & r=.4 is not the same as difference between r=.7 & r=.8 When comparing correlation charts for height & weight for women vs. men one can directly compare the amount of variance whereas one cannot directly compare size of correlations unless one does a transformation to the ‘r’s Review of Variance Explained

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For Male Celebrities: r =.27; r 2 = 7%

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For Female Celebrities: r =.78; r 2 =61 %

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Also known as multiple correlational analyses –Describes the relationship (R) between 3 or more variables (see example on next slide) Note: correlation (r) that only examines 2 variables –Uses the concepts of variance explained & significance levels as in r Significance determined differently –Uses (new) concept of regression coefficients ß & B What is a regression analyses?

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What is the combined relationship between the three variables housing satisfaction, leisure satisfaction and global life satisfaction Conducting a Regression Analyses

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Bec there was insufficient class participation, for this illustration, prof used part of the correlation matrix from Student Satisfaction & Performance article by Rode et al (handout article from which student satisfaction survey was created) directly into SPSS data window & then used syntax window –See raw data vs. correlational matrix –See syntax How example regression was done

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Raw data file for regression looks like this…

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A correlation matrix for regression looks like this…

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regression / matrix in (*) / var housesat lifesat leisure / dep lifesat / method enter housesat leisure. –Here the three variables are listed next to ‘var’ –The primary dependent variable is listed next to ‘dep’ –More on “method enter” later Syntax for simple regression with a matrix

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regression / var housesat lifesat leisure / dep lifesat / method enter housesat leisure. VS (note differences to below) regression / matrix in (*) / var housesat lifesat leisure / dep lifesat / method enter housesat leisure. Syntax for simple regression with raw data

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How to run a simple regression in menus?

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Under analyze, Choose regression & Linear

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Click on appropriate var to be your dependent Click on predictor var to be independent

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What is correlation? What is regression? –An example analysis Syntax/menu to use for regression analyses Data file/correlation to use Reviewing the output to learn about regression concepts –Similarity to and differences from correlation What we did so far…what’s next

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Examine results of simple regression analysis to learn about common concepts in correlation & regression

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r 2 vs R 2 r 2 =.22 2 R 2 =.43 2 Housing sat Life sat Housing sat Life sat Leisure sat r 2 =.43 2 Leisure sat Life sat

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R is significant at F=77.89 p<.0001 or p=.000 –Note significance of correlations is determined by t-test Variance explained (R 2 )=.19 –Same as variance explained in correlations Significance test for R vs. r & Variance explained

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Regression Coefficients Standardized Unstandardized Examine the output of simple regression example to learn new concepts in regression

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Similar to r –Vary from -1 to 1 and indicate strength & direction of relations –Their significance determined by t-test Different from r –Estimate the relationship between 2 variable (e.g., life sat & leisure) after taking the relationship between 1 st and 3 rd variable into account (e.g., life sat & ) housing) Similarities & differences between r and ß

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Similarities & differences between ß & B –Vary on the scale of the variable rather than between -1 to +1 (i.e., as in ß) –Used predominantly in economics –Can be used (along with its standard error) to calculate how much change in predictor (e.g., housing satisfaction) is needed to obtain a specific amount of change in dependent (e.g., life satisfaction) Another additional concept in regression: Unstandardized regression coefficient (B)

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How is correlation similar and different from regression –R vs. r –Variance explained is the common concept –Coefficients Standardized= ß vs. r Unstandardized= B vs. r What we learned so far

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Which type of satisfaction best predicts life satisfaction? –Stepwise (hierarchical) regression analyses Conducting a More Sophisticated Regressional Analyses

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What happens if house satisfaction is entered into the equation first? regression / matrix in (*) / var housesat lifesat leisure / dep lifesat / method enter housesat /method enter leisure. What happens if leisure satisfaction is entered into the equation first? regression / matrix in (*) / var housesat lifesat leisure / dep lifesat / method enter leisure /method enter housesat. Syntax for stepwise/hierarchical regression

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How to run a stepwise/hierarchical regression in menus?

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Under analyze, Choose regression & Linear

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Click on appropriate var to be your dependent Click on first predictor to be independent

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When you click on “next” button, you should come here...

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Choose your next dependent to be entered in the ‘next’ step

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Modifications to hierarchical analyses You can enter multiple dependent variables in same block or in separate blocks using the previous and next buttons

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Interpreting the output from stepwise regression When variable is entered first RR2R2 Total R when adding the other variable Total R 2 by adding the other variable Leisure satisfaction.430.185.434.189 Housing Satisfaction.220.048.434.189

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Test the explanation for a finding via a mediator analysis –Why might a particular type of satisfaction (e.g., housing) affect your performance? Implies a corr b/w housing sat & perf –Because that makes you less satisfied with your life which, in turn, affects your performance Implies that corr b/w housing sat & perf is due to the corr between housing sat and life sat and between life sat & perf Using regression as a preliminary test of an explanation

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Conditions to be met before running a mediator analyses Life sat Performance Life sat Housing sat Performance Housing sat r 2 =.14 2 r 2 =.10 2 r 2 =.22 2

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Results of Mediator Regressional Analyses Stepßt-valuep-valueTotal R 2 1Housing Satisfaction.102.6.009.01 2Housing Satisfaction.071.9.06.03 Life Satisfaction.123.17.002

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Types of Inferential Statistics Nature of Independent Variable ContinuousCategorical Nature of Dependent Variable ContinuousCorrelation/ Regression T-test /ANOVA Categorical

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Using t-test to test the hypothesis whether the women in the sample are older than men?

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1 st Step= “Analyze”, 2 nd Step=“Compare means” 3 rd Step=“Independent samples t-test”

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Move “age” to test-variable window & move “gender” to “grouping variable” window

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Click on Define Groups,

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In “Define Groups” menu, type ‘m’ in Group 1, ‘f’ in Group 2

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Info to extract from the output window… After defining groups, click continue, then click OK to get the output window

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When Independent Variable is Categorical & Dependent Variable is Continuous T-testANOVA One Independent VariableMore than one independent Variable Independent Variable has only 2 values Independent variable has more than 2 values Paired t-test if values from the two groups are from the same people Repeated measures ANOVA if values from the groups are from same people

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Correlation Regression T-test What you learned today

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Types of Inferential Statistics Nature of Independent Variable ContinuousCategorical Nature of Dependent Variable ContinuousCorrelation/ Regression T-test /ANOVA CategoricalChi-square, Spearman Rank, Kappa, Phi

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When both variables are continuous: –r (Pearson product-moment) When both variables are nominal (categorical) –Two categories for each variable: Phi –Multiple categories for each variable: Kappa When both variables are ordinal: Spearman rank Appendix: Types of Correlations

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Copyright © 2010 Pearson Education, Inc. 17-1 Chapter Seventeen Correlation and Regression.

Copyright © 2010 Pearson Education, Inc. 17-1 Chapter Seventeen Correlation and Regression.

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