- The
**Partial correlational analysis**learning activity assignment is worth 50 points and will be graded using the designated rubric. Grading criteria include quality of content, appropriate citations, use of Standard English grammar, and overall organization and readability. - Create your assignment using a Microsoft Word application. The document should be saved in a .doc or .docx format.
- There is no required length but should be specific enough to address all requirements.
- The following sections should be included in the document (please copy and paste SPSS output in the Word document):
- Question #1
- Question #2
- Question #3
- Attached output files in .sav format

Use the provided data set sample and use SPSS to analyze the data. Use the SPSS Screenshot Guide as a reference when running the tests.

**Partial Correlation**

- Follow the procedures detailed in Chapter 12 of the
*SPSS Survival Manual*to calculate the partial correlation between optimism (toptim) and perceived stress (tpstress) while controlling for the effects of age. Compare the zero order correlations with the partial correlation coefficients to see if controlling for age had any effect. - Follow the same procedure while controlling for the effect of education.
- Interpret the results of the output.

**12**

**Partial correlation**

Partial correlation is similar to Pearson product-moment correlation (described in Chapter 11), except that it allows you to control for an additional variable. This is usually a variable that you suspect might be influencing your two variables of interest. By statistically removing the influence of this confounding variable, you can get a clearer and more accurate indication of the relationship between your two variables.

In the introduction to Part Four, the influence of contaminating or confounding variables was discussed (see the section on correlation versus causality). This occurs when the relationship between two variables (A and B) is influenced, at least to some extent, by a third variable (C). This can serve to artificially inflate the size of the correlation coefficient obtained. This relationship can be represented graphically as:

In this case, A and B may appear to be related, but in fact their apparent relationship is due to the influence of C. If you were to statistically control for the variable C then the correlation between A and B is likely to be reduced, resulting in a smaller correlation coefficient.

**DETAILS OF EXAMPLE**

To illustrate the use of partial correlation, I use the same example as described in Chapter 11 but extend the analysis further to control for an additional variable. This time I am interested in exploring the relationship between scores on the Perceived Control of Internal States Scale (PCOISS) and scores on the Perceived Stress Scale, while controlling for what is known as ‘socially desirable responding bias’. This variable refers to people’s tendency to present themselves in a positive, or socially desirable, way (also known as ‘faking good’) when completing questionnaires. This tendency is measured by the Marlowe-Crowne Social Desirability Scale (Crowne & Marlowe 1960). A short version of this scale (Strahan & Gerbasi 1972) was included in the questionnaire used to measure the other two variables.

If you would like to follow along with the example presented below, you should start IBM SPSS Statistics and open the file labelled **survey.sav**, which is included on the website accompanying this book.

**Example of research question:** After controlling for participants’ tendency to present themselves in a positive light on self-report scales, is there still a significant relationship between perceived control of internal states (PCOISS) and levels of perceived stress?

**What you need:**

two continuous variables that you wish to explore the relationship between (e.g. Total PCOISS, Total perceived stress)

one continuous variable that you wish to control for (e.g. total social desirability: tmarlow).

**What it does:** Partial correlation allows you to examine the relationship between two variables while statistically controlling for (getting rid of) the effect of another variable that you think might be contaminating or influencing the relationship.

**Assumptions:** For full details of the assumptions for correlation, see the introduction to Part Four.

Before you start the following procedure, choose** Edit** from the menu, select **Options**, and make sure there is a tick in the box **No scientific notation for small numbers in tables**.

**Procedure for partial correlation**

- From the menu at the top of the screen, click on
**Analyze**, then select**Correlate**, then**Partial**. - Click on the two continuous variables that you want to correlate (e.g. Total PCOISS: tpcoiss, Total perceived stress: tpstress). Click on the arrow to move these into the
**Variables**box. - Click on the variable that you wish to control for (e.g. Total social desirability: tmarlow) and move it into the
**Controlling for**box. - Click on
**Options**.

In the Missing Values section, click on Exclude cases pairwise.

In the Statistics section, click on Zero order correlations.

- Click on
**Continue**and then**OK**(or on**Paste**to save to**Syntax Editor**).

The syntax from this procedure is:

PARTIAL CORR

/VARIABLES= tpcoiss tpstress BY tmarlow

/SIGNIFICANCE=TWOTAIL

/STATISTICS=CORR

/MISSING=ANALYSIS .

The output generated from this procedure is shown below.

Control Variables | tpcoiss Total PCOISS | tpstress Total perceived stress | tmarlow Total social desirability | ||

-none-^{a} |
tpcoiss Total PCOISS | Correlation | 1.000 | -.581 | .295 |

Significance (2-tailed) | . | .000 | .000 | ||

df | 0 | 424 | 425 | ||

tpstress Total perceived stress | Correlation | -.581 | 1.000 | -.228 | |

Significance (2-tailed) | .000 | . | .000 | ||

df | 424 | 0 | 426 | ||

tmarlow Total social desirability | Correlation | .295 | -.228 | 1.000 | |

Significance (2-tailed) | .000 | .000 | . | ||

df | 425 | 426 | 0 | ||

tmarlow Total social desirability | tpcoiss Total PCOISS | Correlation | 1.000 | -.552 | |

Significance (2-tailed) | . | .000 | |||

df | 0 | 423 | |||

tpstress Total perceived stress | Correlation | -.552 | 1.000 | ||

Significance (2-tailed) | .000 | . | |||

df | 423 | 0 |

- Cells contain zero-order (Pearson) correlations.

**INTERPRETATION OF OUTPUT FROM PARTIAL CORRELATION**

The output provides you with a table made up of two sections:

- In the top half of the table is the Pearson product-moment correlation matrix between your two variables of interest (e.g. perceived control and perceived stress),
*not*controlling for your other variable. In this case, the correlation is –.581. The word ‘none’ in the left-hand column indicates that no control variable is in operation. This is often referred to as the ‘zero-order correlation coefficient’. - The bottom half of the table repeats the same set of correlation analyses, but this time controlling for (removing) the effects of your control variable (e.g. social desirability). In this case, the new partial correlation is –.552. You should compare these two sets of correlation coefficients to see whether controlling for the additional variable had any impact on the relationship between your two variables of interest. In this example, there was only a small decrease in the strength of the correlation (from –.581 to –.552). This suggests that the observed relationship between perceived control and perceived stress is not due merely to the influence of socially desirable responding.

**PRESENTING THE RESULTS FROM PARTIAL CORRELATION**

Although IBM SPSS Statistics provides the correlation coefficients using three decimal places, they are usually reported in journal articles as two decimals (see APA *Publication Manual* for details).

The results of this analysis could be presented as:

Partial correlation was used to explore the relationship between perceived control of internal states (as measured by the PCOISS) and perceived stress (measured by the Perceived Stress Scale) while controlling for scores on the Marlowe-Crowne Social Desirability Scale. Preliminary assessments were performed to ensure no violation of the assumptions of normality and linearity. There was a strong, negative partial correlation between perceived control of internal states and perceived stress, controlling for social desirability, *r =* –.55, *n* = 425, *p* < .001, with high levels of perceived control being associated with lower levels of perceived stress. An inspection of the zero-order correlation coefficient (*r* = –.58) suggested that controlling for socially desirable responding had very little effect on the strength of the relationship between these two variables.

**ADDITIONAL EXERCISE**

**Health**

Data file: **sleep.sav**. See Appendix for details of the data file.

- Check the strength of the correlation between scores on the Sleepiness and Associated Sensations Scale (
*totSAS*) and the impact of sleep problems on overall wellbeing (*impact6*) while controlling for*age.*Compare the zero-order correlation (Pearson correlation) and the partial correlation coefficient. Does controlling for*age*make a difference?