• Descriptive Statistical Analyses

• Reliability Analyses

Review of Last Class

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?

• 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?

• 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

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

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

• 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

• Continuous– Interval– Ratio

• Discontinuous (Categorical)– Nominal– Ordinal

• Students provide examples from questionnaires completed in this course (e.g., 1st day of class, student satisfaction survey etc.)

Review of Types of Variables

Types of Inferential Statistics

Nature of Independent Variable

Continuous Categorical

Nature of Dependent Variable

Continuous Correlation/Regression

T-test/ANOVA

Categorical

• Correlation

• Regression

When both variables are continuous

• 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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Height (cm)

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Tom Cruise

Vince Carter

Calista Flockhart

Julia Roberts

r = .76; r2 = 58%

• Better measure of the strength of a relation is the amount of explained variance (r2)

• 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; r2 = 7%

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For Female Celebrities: r = .78; r2 =61 %

• 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?

• What is the combined relationship between the three variables housing satisfaction, leisure satisfaction and global life satisfaction

Conducting a Regression Analyses

• 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

Raw data file for regression looks like this…

A correlation matrix for regression looks like this…

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

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

How to run a simple regression in menus?

Under analyze, Choose regression & Linear

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

• 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

Examine results of simple regression analysis to learn about

common concepts in correlation & regression

r2 vs R2

r2=.222

R2=.432Housing sat

Life sat

Housing sat

Life sat

Leisure sat

r2=.432

Leisure sat

Life sat

• R is significant at F=77.89 p<.0001 or p=.000– Note significance of correlations is determined by

t-test

• Variance explained (R2 )=.19– Same as variance explained in correlations

Significance test for R vs. r & Variance explained

• Regression Coefficients• Standardized• Unstandardized

Examine the output of simple regression example to learn new concepts in regression

• 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 1st and 3rd variable into account (e.g., life sat & ) housing)

Similarities & differences between r and ß

• 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)

• 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

• Which type of satisfaction best predicts life satisfaction?– Stepwise (hierarchical) regression analyses

Conducting a More Sophisticated Regressional Analyses

•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

How to run a stepwise/hierarchical regression in menus?

Under analyze, Choose regression & Linear

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

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

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

Modifications to hierarchical analyses

• You can enter multiple dependent variables in same block or in separate blocks using the previous and next buttons

Interpreting the output from stepwise regression

When variable is entered first

R R2 Total R when adding the other variable

Total R2 by adding the other variable

Leisure satisfaction .430 .185 .434 .189

Housing Satisfaction .220 .048 .434 .189

• 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

Conditions to be met before running a mediator analyses

Life sat

Performance

Life sat

Housing sat

PerformanceHousing sat

r2=.142

r2=.102

r2=.222

Results of Mediator Regressional Analyses

Step ß t-value p-value Total R2

1 Housing Satisfaction

.10 2.6 .009.01

2 Housing Satisfaction

.07 1.9 .06.03

Life Satisfaction

.12 3.17 .002

Types of Inferential Statistics

Nature of Independent Variable

Continuous Categorical

Nature of Dependent Variable

Continuous Correlation/Regression

T-test/ANOVA

Categorical

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

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

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

Click on Define Groups,

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

• Info to extract from the output window…

After defining groups, click continue, then click OK to get the output window

Group Statistics

9 29.22 6.399 2.133

21 27.90 6.722 1.467

1=genderm

f

2=ageN Mean Std. Deviation

Std. ErrorMean

Independent Samples Test

.499 28 .622 1.317 -4.095 6.729t df Sig. (2-tailed)

MeanDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

When Independent Variable is Categorical & Dependent Variable is Continuous

T-test ANOVA

One Independent Variable More 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

• Correlation

• Regression

• T-test

What you learned today

Types of Inferential Statistics

Nature of Independent Variable

Continuous Categorical

Nature of Dependent Variable

Continuous Correlation/Regression

T-test/ANOVA

Categorical Chi-square,

Spearman Rank,

Kappa,

Phi

• 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