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Correlation Analysis
Correlation is a rather technical statistical concept - we're going to avoid most of the technical discussion here and just present some practical applications for using correlation to better understand survey results. This explanation is intended to help the layperson understand the basic concept of correlation without requiring a lot of technical knowledge.
Correlation is a statistic that measures the linear relationship between two variables (for our purposes, survey items). The values for correlations are known as correlation coefficients and are commonly represented by the letter "r". The range of possible values for r is from -1.0 to +1.0. Numbers less than zero respresent a negative relationship between variables and numbers greater than zero represent a positive relationship. You can think of the value of r almost like a percentage.
This screen shot (see below) of the output from our Correlation Engine shows how you might use correlation for an employee or customer satisfaction survey. You can select any Likert rating scale item (e.g. 5-point rating) from your survey and view all the statistically significant correlations with that item.
When you use the correlation engine, you will see the following at the bottom of the page:
Correlations (r) significant at p < 0.05. This is a customary indication of the likelihood that the observed correlations are a result of chance. For our purposes, we have set this probability (p) threshold to be no more than 0.05 or 5%. There is less than a 5% likelihood that the correlations listed here are a result of chance.
Whenever you view correlations, it is important to look for this p-level. You don't need to understand more about it than is explained here. Just know that "p < 0.05" is the most common standard threshold for statistical significance.
"n" indicates the total number of respondents. This is important for statistical significance because when you have a large n, a smaller correlation can still be statistically significant. Conversely, with a small n, you need a much larger correlation for statistical significance. If you are looking at two sets of correlations that have very different numbers of respondents, you can NOT compare the correlation coefficients from each list to one another. You need to look at each list independently and draw conclusions only within each list.
In the example above, the correlations are pretty close to one another in value. Notice in the example below how there are bigger gaps between the correlations. When you see a couple of items at the top with much higher coefficients (r) than the others and then a big drop in r for the following items, focus your attention much more on those top items. If you have several items that are close to one another, you should still start at the top of the list, but give more equal weight to the items that follow the top items. There is often a natural cut-off point somewhere in the list where you will see a big drop in r - use this as a logical point to limit your analysis.
In this second example, there is a big gap after the first item, so we might conclude that the number one factor that determines whether people are satisfied with their supervisor is competence. We would also want to look at the second and third items since these are still strong correlations and provide useful additional information. In fact, we would probably want to consider all the items down to the next big drop in r where it goes from 0.57 to 0.50. At this point, we have about as many items as we can deal with - the remaining items are still of interest, but should not be focused on too closely.
The most common way that correlation is used in most surveys is to find out what matters most to people by correlating survey items with some measure of overall satisfaction. As you've seen in the examples above, this is a technique that you can safely use without worrying about all the technical stuff. We filter out all the noise and just show you those correlations that are statistically significant. You just start at the top of the list to see what matters most. (Remember to also look at the bottom of the list - high negative correlations, while less common, are just as important as high positive correlations. A negative correlation indicates an inverse relationship between items.)
For more details on using correlations to measure satisfaction, click here.
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