**Learning Goal: **I’m working on a statistics question and need a sample draft to help me learn.

## Prepare

Please make sure you read chapter 7 and review the before attempting this assignment. You can also watch the video below related to calculating correlations ( it is not the question you will be analyzing). Please note that I interpreted the output for you below, all you have to do is compare you output to my interpretations. These interpretations will help you with your final group research paper.

## Purpose

Please use the **SPSS data** set to complete this assignment. The purpose of this assignment is to teach you how to use SPSS to calculate a correlation. This assignment is broken down into three parts. Part 1 will teach you how to graph a correlation. Part II will teach you how to run a correlation analysis in SPSS.

### Details of Example

To demonstrate the use of correlation, I will explore the interrelationships among some of the variables included in the data file. The survey was designed to explore the factors that affect respondents psychological adjustment and wellbeing (see the Appendix for a full description of the study). In this example, I am interested in assessing the correlation between respondents feelings of control and their level of perceived stress. Details of the two variables I will be using are provided below.

**Example of research question:** Is there a relationship between the amount of control people have over their internal states and their levels of perceived stress? Do people with high levels of perceived control experience lower levels of perceived stress?

**What you need: Two variables:** both continuous, or one continuous and the other dichotomous (two values).**What it does:** Correlation describes the relationship between two continuous variables, in terms of both the strength of the relationship and the direction.

## Procedure

- From the menu at the top of the screen, click on
**Analyze**, then select**Correlate**, then**Bivariate**. - Select your two variables and move them into the box marked
**Variables**(e.g. Total perceived stress: tpstress, Total PCOISS: tpcoiss). If you wish you can list a whole range of variables here, not just two. In the resulting matrix, the correlation between all possible pairs of variables will be listed. This can be quite large if you list more than just a few variables. - In the
**Correlation Coefficients**section, the**Pearson**box is the default option. - Click on the
**Options**button. For**Missing Values**, click on the**Exclude cases pairwise box**. Under Options, you can also obtain means and standard deviations if you wish. - Click on
**Continue**and then on**OK**(or on Paste to save to**Syntax Editor**).

**Export your Output file to PDF format, saving the file as Correlation Last Name Output.pdf.**

## How to Read the SPSS Output

**Step 1: Checking the information about the sample**

The first thing to look at in the table labelled Correlations is the N (number of cases). Is this correct? If there are a lot of missing data, you need to find out why. Did you forget to tick the Exclude cases pairwise box in the missing data option? Using listwise deletion (the other option), any case with missing data on any of the variables will be removed from the analysis. This can sometimes severely restrict your N. In the above example we have 426 cases that had scores on both of the scales used in this analysis. If a case was missing information on either of these variables, it would have been excluded from the analysis

**Step 2: Determining the direction of the relationship**

The second thing to consider is the direction of the relationship between the variables. Is there a negative sign in front of the correlation coefficient value? This would suggest a negative (inverse) correlation between the two variables (i.e. high scores on one are associated with low scores on the other). The interpretation of this depends on the way the variables are scored. Always check with your questionnaire, and remember to take into account that for many scales some items are negatively worded and therefore are reversed before scoring. What do high values really mean? This is one of the major areas of confusion for students, so make sure you get this clear in your mind before you interpret the correlation output.

In the example given here, the Pearson correlation coefficient (.58) and Spearman rho value (.56) are negative, indicating a negative correlation between perceived control and stress. The more control people feel they have, the less stress they experience.

**Step 3: Determining the strength of the relationship**

The third thing to consider in the output is the size of the value of the correlation coefficient. This can range from 1 to 1. This value will indicate the strength of the relationship between your two variables. A correlation of 0 indicates no relationship at all, a correlation of 1 indicates a perfect positive correlation, and a value of 1 indicates a perfect negative correlation.

**Step 4: Calculating the coefficient of determination**

To get an idea of how much variance your two variables share, you can also calculate what is referred to as the coefficient of determination. Sounds impressive, but all you need to do is square your r value (multiply it by itself). To convert this to percentage of variance, just multiply by 100 (shift the decimal place two columns to the right).

In our example the Pearson correlation is .581, which, when squared, indicates 33.76 per cent shared variance. Perceived control helps to explain nearly 34 per cent of the variance in respondents scores on the Perceived Stress Scale. This is quite a respectable amount of variance explained when compared with a lot of the research conducted in the social sciences.

**Step 5: Assessing the significance level**

The next thing to consider is the significance level (listed as Sig. 2 tailed). This is a frequently misinterpreted area, so care should be exercised here. The level of statistical significance does not indicate how strongly the two variables are associated (this is given by r or rho), but instead it indicates how much confidence we should have in the results obtained. The significance of r or rho is strongly influenced by the size of the sample. In a small sample (e.g. n=30), you may have moderate correlations that do not reach statistical significance at the traditional p<.05 level. In large samples (N=100+), however, very small correlations (e.g. r=.2) may reach statistical significance. While you need to report statistical significance, you should focus on the strength of the relationship and the amount of shared variance (see Step 4).

## Presenting the Results

The relationship between perceived control of internal states (as measured by the PCOISS) and perceived stress (as measured by the Perceived Stress Scale) was investigated using Pearson product-moment correlation coefficient. Preliminary analyses were performed to ensure no violation of the assumptions of normality, linearity and homoscedasticity. There was a strong, negative correlation between the two variables, r = .58, n = 426, p <

.001, with high levels of perceived control associated with lower levels of perceived stress.