Correlation Between SAT and GWA

Workshop on Correlation:
Scholastic Admission Test (SAT) and Graded Weighted Average (GWA)
Seminar – Workshop 1
In these exercises, you will standardize the raw scores of the target group; determine the
correlation between their percentile ranks and GWA; and compare groups using the sex
variable in the correlation. The Scatterplot will also be use in the correlation output.
A. Opening the Spreadsheets Containing the Data.
1. Open the  WORKSHOP_DATA folder at the Desktop or with the use of the
Windows Explorer look for the  WORKSHOP_DATA folder in the Drive D: and
open it.
2. Double – click TARGET.XLS in the  WORKSHOP_DATA folder to open it.
3. Save the spreadsheet file with another name  File – Save – As “EXER05.XLS”.
The purpose of doing this is to reserve the original file. In case, you make mistakes in
the process, you can reopen the original file.
B. In this part, the Z–scores will be derived from the raw scores of the target group using
the mean (42.91) and standard deviation (12.264) of normative group composed of 961
examinees.
Z–Scores are a transformation of individual raw scores into a standard form, where
the transformation is based on knowledge about the standardization sample’s mean
and standard deviation.
The formula for computing Z–scores is the individual raw score (X) minus the mean of
the scores obtained by the standardization sample (M), divided by the standard
deviation of scores obtained by the standardization sample (sd). Z–scores have a mean
of 0 and a standard deviation of 1. (BROCK, 2012).
4. Currently, ‘EXER05.XLS is open. At the cell J2, type “ZCORES” and press
<ENTER>. Click the cell J3, type ‘=standardize(E3,42.91,12.264)’ and press
<ENTER>. The cell E3 is the location of the first raw score at column RSCORE. The
value 42.91 is the mean of the 961 examinees, and 12.264 is the Standard Deviation.
5. Click the cell J3 again and at the lower right corner of this cell, double – click the
small square to apply the same formula to the rest of the items.

C. Exporting the Data from EXERO5.XLS to IBM SPSS
6. Click File  Save As. The File – Save As Dialog Appears. In the ‘Save as Type’
section, select ‘Text (Tab delimited)’. Filename is still ‘EXER05’. Then click Save.
7. Click the Yes button.

8. Click File  Exit and then click No button.
9. Open IBM SPSS 16.0 or different version. If the opening window appears, just click
the Cancel button.
10.Click File  Read Text Data.

11. The Open Data dialog box appears. Go the  WORKSHOP_DATA folder and
look for ‘EXER05.TXT’ and then click the Open button.
12.The Text Import Wizard appears. Click Next in ‘Step 1 of 6’ window.
13.Click ‘Yes’ to answer the question “Are the variable names included at the top of
your file?. Then, click next.

14. Click Next on ‘Step 3 of 6’ to ‘Step 5 of 6’. Finally, click ‘Finish’ on ‘Step 6 of 6’.
15. Save your file as ‘EXER05.SAV.
NOTE: You can skip sections D to F and go directly to section G. Section G focuses
on the correlation between RSCORE and GWA.
D. In this part, you will compute the Percentile Ranks of the target group based on their
Z–scores.
16.Click TRANSFORM > COMPUTE. Type “PRCTLRANK” in the TARGET
VARIABLE box. Select “CDF & NONCENTRAL CDF” from the FUNCTION
GROUP box. Select “CDF.NORMAL” function from the FUNCTIONS AND
SPECIAL VARIABLES box. Click the up arrow , select “ZSCORES” from the
variable box and click the right arrow  to replace the first “?” inside the function
CDF.NORMAL(?,?,?). Type “0” for the second “?” represents the mean and type “1”
for the third “?” representing standard deviation. Click OK.
The resulting screen is shown.
CDF.NORMAL(ZSCORES,0,1)

17.In creating the column PRANK100, click TRANSFORM > COMPUTE VARIABLE.
Type “PRANK100” in the TARGET VARIABLE box. Select “PRCNTLRANK”
from the variables box and click the right arrow , to move it to NUMERIC
EXPRESSION box. Complete the numeric expression by type “* 100”. The purpose
of this expression is to convert the percentile ranks to the nearest ones. Then click OK.
PRCNTLRANK * 100

E. In this part, you will be creating another column similar to stanine but have five scales
only. The table below will be used.
FIVE
SCALES
VERBAL
DESCRIPTION
RANGES OF
PERCENTILE
RANKS
PERCENTAGES
STANINE
SCALE
5 Superior (4%) 96 and above 4% 9
89 – 95 7% 8
4
Above Average
(19%) 77 – 88 12% 7
60 – 76 17% 6
40 – 59 20% 5
3 Average (54%)
23 – 39 17% 4
11 – 22 12% 3
2
Below Average
(19%) 4 – 10 7% 2
1 Low (4%) Below 4 4% 1
18.In the menu, click TRANSFORM > XY RECODE INTO DIFFERENT
VARIABLES. Select PRANK100 from the variable box at the left and move it into
the INPUT VARIABLE  OUTPUT VARIABLE box by clicking the right arrow .
Type “FSCALE” into the NAME box and LABEL box at the OUTPUT VARIABLE
section. Then click the CHANGE button.

Then click the OLD AND NEW VALUES button.
Perform the following steps in entering the different ranges of percentile ranks for
each scale:
Type 0 in the RANGE box and 3.9 in the THROUGH box. Type 1 in the
VALUE under the NEW VALUE section and then click the ADD button in the
OLD  NEW section.
Type 4 in the RANGE box and 22.4 in the THROUGH box. Type 2 in the
Type 22.5 in the RANGE box and 76.4 in the THROUGH box. Type 3 in the
Type 76.5 in the RANGE box and 95.4 in the THROUGH box. Type 4 in the
Type 95.5 in the RANGE box and 100 in the THROUGH box. Type 5 in the
The resulting screen is shown.
Click the CONTINUE button. Then OK. The column FSCALE is added.

F. In this part, you will be creating the histogram of the column FSCALE.
19.At the menu, click GRAPHS > LEGACY DIALOGS > HISTOGRAM. Select
FSCALE from the variables box, click the right arrow. Click  DISPLAY NORMAL
CURVE. Click OK.
The resulting histogram is shown.
Next, save your file.
G. Correlation Between RSCORES and GWA using Pearson Product Moment
Correlation (PPMC).
Correlation refers to any of a broad class of statistical relationships involving between
two random variables or two sets of data (Correlation and Dependence, 2012). One
way to express correlation is by the use of Pearson Product Moment Correlation
coefficient.
The Pearson Product – Moment Correlation Coefficient (r), or correlation coefficient
for short is a measure of the degree of linear relationship between two variables,
usually labeled X and Y. The correlation coefficient may take on any value between
plus and minus one. (Stockburger, 1996)

20. At the ANALYZE menu, click CORRELATE > BIVARIATE. Select RSCORE and
GRADE and move to the VARIABLES box using the right–arrow . By default,
PEARSON, TWO–TAILED, and  FLAG SIGNIFICANT CORRELATIONS
are already selected.
Click OPTIONS button, check MEANS AND STANDARD DEVIATIONS. Then
click CONTINUE.
Next, click OK.

21. Save the viewer file as ‘EXER0501”. These are the information you can see in the
output.
The correlation coefficient between
RSCORE and GRADE is 0.260, which
is a weak correlation..
The p–value is found in the row of Sig
(2–tailed). The p–value is 0.009 which
is lesser than the alpha value of 0.05,
and marginal to 0.01.
This means that there is a significant
relationship between SEX and
RSCORE.
H. In this part, you will be using the Scatterplot graph.
22.At the GRAPHS menu, click LEGACY DIALOGS > SCATTER/DOT…. and then
select SIMPLE SCATTER and click the DEFINE button.

The DEFINE SIMPLE SCATTER PLOT dialog.
Move the RSCORE variable to X–AXIS, and GRADE variable to Y–AXIS and then
click OK.
The resulting graph is shown.
To add a FIT LINE through the scattered dots, double–click on
the graph to display the CHART EDITOR. At the CHART
EDITOR click the ADD FIT LINE AT TOTAL icon.
By the time you click the ADD FIT LINE AT TOTAL icon, its
PROPERTIES dialog will appear. Simply click the CLOSE
button of the PROPERTIES dialog, then click FILE > CLOSE
the CHART EDITOR to close.
The resulting graph is shown.

The Line of Best Fit or Fit Line is inclined
upward to the right.
Finally, save your file.
I. In this part, you will perform the Subgroup Correlations by Sex
23.You need to get SPSS to calculate the correlation between RSCORE and GWA
separately for males represented as 1 and females represented as 2. The easiest way
to do this is to split our data file by sex.
In the main menu, select DATA > SPLIT FILE. Select ORGANIZE OUTPUT BY
GROUPS and GROUPS BASED ON SEX. This means that any analyses you specify will
be run separately for males and females. Then, click Ok.
Notice that the order of the data files has been changed. It is now sorted by SEX,
with males at the top of the file.

Now, select ANALYZE > CORRELATION > BIVARIATE. The same variables
and options you selected last time are still in the dialog box.
Click OPTIONS button, check MEANS AND STANDARD DEVIATIONS.
Then click CONTINUE. Then, click OK.
Take a moment to check to see for you. The output follow broken down by males
(1) and females (2).
Display results for Males:

Display results for Females:
J. Scatterplots of Data by Subgroups
In this part, you will create a more complicated scatterplot that illustrates the pattern
of correlation for males and females on one graph.
24.First, you need to turn off SPLIT FILE. Select DATA > SPLIT FILE from the main
menu. Then select ANALYZE ALL CASES, do not compare groups and click OK.
Now, you can proceed.
The SPLIT FILE is turn off.

25.Select GRAPHS > LEGACY > SCATTER. Then, select SIMPLE and click DEFINE.
Select GRADE as the Y Axis and
RSCORE as the X Axis. Then,
select SEX for SET MARKERS
BY. This means SPSS will
distinguish the males dots from the
female dots on the graph. Then,
click OK.
To distinguish clearly the dots from the males and females, you will edit the graph.
Double click the graph to activate the CHART EDITOR.

Then double click on one of the female (2) dots. SPSS will highlight all the female
dots. Then click the MARKER menu.
Select the CIRCLE under MARKER TYPE and chose a Fill color. Then click
APPLY. Then CLOSE. You can do the same procedure for the male (1) dots by
double clicking on the male dot as a start. Choose a different color for the male.
26. You would like to alter our graph to include the line of best fit for the male and
female groups. Under ELEMENTS, select FIT LINE at SUBGROUPS. Then
select LINEAR and click APPLY and CLOSE. Lastly, in the CHART EDITOR,
click FILE > CLOSE.

The resulting graph follows.
Finally, save your files.
References:
Brock, S. E. Descriptive Statistics and Psychological Testing. California State
University, Sacramento. Retrieved April 05, 2012.
Correlation. In http://www.uvm.edu. Retrieved August 21, 2012, from
http://www.uvm.edu/~dhowell/fundamentals7/SPSSManual/SPSSLongerManual
/SPSSChapter5.pdf
Correlation and Dependence (2012, March 16). In http://www.wikipedia.org.
Retrieved August 21, 2012, from http://www.wikipedia/correlation_and_
dependence.html
Cohen, R. J., & Swerdlik, M. E. (2005). Psychological Testing and Assessment:
An Introduction to Tests and Measurement. (6th
Edition.) McGraw–Hill.
Stockburger, D. W. (1996). Introductory Statistics: Concepts, Models, and
Applications. Atomic Dog Publishing. Missouri State University
Zucker, S. (2003, December). Fundamentals of Standardized Testing. Retrieved
April 06, 2012 from http://www.hemweb.com.

Contents of TARGET.XLS:

Correlation Between SAT and GWA

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