Pearson r Correlations and Regressions with SPSS

First, read or prepare SPSS system files, tell SPSS to perform the required statistics, and save the results on a result file on your a: drive.

After preparing your data file,

Descriptive Statistics

  1. Click "Analyze"
  2. Click "Descriptive Statistics"
  3. Click "Frequencies"
  4. Select the appropriate variables
  5. Select don't display frequency tables (to save paper)
  6. Click "Statistics" and select the appropriate descriptive statistics
  7. Click "Charts" if a histogram with superimposed normal curve is needed
  8. Click "Ok"

Scatterplot

  1. Click "Graphs"
  2. Click "Scatter"
  3. Select "Simple"
  4. Click "Define" and select appropriate variables for X and Y axes (Y=dependent variable)
  5. Add labels to the graph if desired
  6. Click "Ok"

Pearson r Statistics

  1. Click "Analyze"
  2. Click "Correlate"
  3. Click "Bivariate"
  4. Select only the appropriate variables
  5. Select Pearson r (not Spearman rho)
  6. Select the appropriate test of significance (one-tailed versus two-tailed)
  7. Click "Ok"

Spearman-Brown Prophecy Formula

Hand-calculate and use the following equation with split-half reliability

 rtt=2roe/(1+roe)

 where "roe" is the correlation coefficient from the two halves ("oe" means "odd-even"), and where "rtt" is the adjusted correlation coefficient for the whole test ("tt" means "total test").

Simple Linear Regression Statistics

  1. Click "Analyze"
  2. Click "Regression"
  3. Click "Linear"
  4. Select the appropriate dependent and independent variables
  5. Click "Ok"

Regression Formula

Hand calculate particular results using the following formula

Yest=a + bX

where "Yest" equals the estimated value on dependent variable, "a" equals the intercept (supplied by SPSS),  "b" equals the slope (supplied by SPSS), and "X" equals the given value on the independent variable.

After applying the formula, state "Yest" in terms of a range defined by the standard error of the estimate.

Examples 

Refer to the following example of a typical SPSS output file (excluding the graphic scatterplots, etc.).

The following are the descriptive statistics for the relevant variables:

Number of valid observations (listwise) =        30.00

Variable  ONE

Mean            40.167                  Std Dev         24.532
Kurtosis         -.903                  S.E. Kurt         .833
Skewness          .193                  S.E. Skew         .427
Range           87.000                  Minimum           1.00
Maximum          88.00

Valid observations -       30         Missing observations -        0

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Variable  TWO

Mean          1316.033                  Std Dev        399.647
Kurtosis          .750                  S.E. Kurt         .833
Skewness         -.526                  S.E. Skew         .427
Range         1626.000                  Minimum         340.00
Maximum        1966.00

Valid observations -       30         Missing observations -        0
  

The following is the beginning of the Pearson r report, beginning with some simple descriptives:

9 Nov 94 SPSS for MS WINDOWS Release 6.0
This software is functional through June 30, 1995.
 

Variable     Cases           Mean          Std Dev

EIGHT           40      1521.9750         430.7801
TWO             40        47.0000          28.5890
 

The following shows Pearson r correlation coefficients between the two selected variables based on a two-tailed test:

                      - -  Correlation Coefficients  - -

EIGHT  TWO

EIGHT   1.0000      -.3039
             (   40)     (   40)
             P= .        P= .057

TWO           -.3039      1.0000
             (   40)     (   40)
             P= .057     P= .
 

(Coefficient / (Cases) / 2-tailed Significance)

" . " is printed if a coefficient cannot be computed
 

Now come regression statistics:

           * * * *   M U L T I P L E   R E G R E S S I O N   * * * *

Listwise Deletion of Missing Data

Equation Number 1    Dependent Variable..   SCHMARN

Block Number  1.  Method:  Enter      MONTHS

Variable(s) Entered on Step Number
   1..    ONE
 

Multiple R           .81747   (same as a Pearson r correlation)
R Square             .66826   (as indicated, R squared)
Adjusted R Square    .65641
Standard Error    234.25839   (standard error of the estimate)

Analysis of Variance
                    DF      Sum of Squares      Mean Square
Regression           1       3095259.17088    3095259.17088
Residual            28       1536555.79579      54876.99271

F =      56.40359       Signif F =  .0000

------------------ Variables in the Equation ------------------

Variable              B        SE B       Beta         T  Sig T

ONE           13.317535    1.773252    .817472     7.510  .0000
(Constant)   781.112360   83.080219                9.402  .0000

Under "B" above, the figure 13.317 is the slope, and the figure 781.112 is the intercept.