OK, so lets get back to Excel and talk correlations. What’s a correlation? Why is it important in data driven decision making? First, lets set the foundation. When I say correlation, think relationship. How are 2 seemingly different variables related? What is the correlation (relationship) between variable A and variable B? The statistical sign for correlation is 'r', which I'll continue to use in the descriptions.
Let’s set the stage. In Mr. Smith’s classroom, lets say he has been watching students at recess. Some of them run around, are very energetic, playing for the entire recess. At the same time, Mr. Smith has noticed what he thinks might be a ‘drop’ in academic performance of some students in the afternoon sessions. Mr. Smith is wondering if there is any correlation (relationship) between students who are very active at recess and his perceived drop in academic performance in the afternoon?
Yes, it’s a very simplified example, but still it provides a nice context for us to work from and discuss correlations.
A correlation shows relationship, stated in terms between -1.0 and 1.0. Not too much of a range is it? Not really. Still, a perfect relationship is stated a 1.0, meaning there is a direct relationship between 2 variables, such as amount of activity during recess and a drop in performance in afternoon academic sessions. So if true, we'd say the correlation (r) between active recess and afternoon performance is r=1.0, or a positive correlation of 1.0. If there was no relationship between active recess and afternoon performance, what do you think we'd state? It seems a bit misleading, but we'd say r=0. There is no relationship with the correlation calculation is 0. If there were an opposite relationship, or a negative correlation, we'd state it as r= -1.0. Generally speaking, we usually don't see perfect positive or negative correlations, they generally fall someplace in between. Review this site for more information: http://www.socialresearchmethods.net/kb/statcorr.php
Here's a video overview. Although it attempts to apply correlation to psychology, it still is a nice, short overview of what a positive correlation looks like:
What type of data do we need to make a correlation? It's important to know that the only data you can use for a correlation study is Interval Data, or data that has an absolute zero that has meaning. For example, age. When defining your age, 0 is the starting point. Unlike with temperature, where 0 is another number on the scale. You can have a negative temperature, but you can not have negative age.
The stronger your correlation (r value) is to either -1.0 (negative correlation) or 1.0 (positive correlation) the stronger the relationship, in either direction. No correlation (or relationship) would be right in the middle, or 0. Lets say we investigate Mr. Smith's class, collecting data about time running at recess (there is an absolute zero) and their classroom performance after lunch (again the data has an absolute zero). We use Excel to calculate the correlation, and come up with an r=-.9. We would say there is a negative correlation of -.9 between active recess participation and afternoon academic performance.
One of the most important things to remember with measuring correlations is that the relationship, or lack of relationship, doesn't mean there is a cause and effect. Because there is a positive correlation between two variables that doesn't mean that you can definitively state that one causes they other, only that they are related. You need to investigate more on the cause - effect relationship. In our example of Mr. Smith's class, if there were a positive correlation of r= -.9, we can say there is a relationship between active participation at recess and a drop in afternoon performance. What we can't say is that students running around during recess leads to their lower performance, only that there is one. It might be attributed to other factors. Maybe the students are overly sweaty or feel they smell, therefore preoccupied with these thoughts and can't focus on work. More investigation is required once the relationship has been established. Here's a site that will discuss that a bit more: http://www.nvcc.edu/home/healthier/methods/correlation.htm.
What example of two variables of data that you can collect(with an absolute zero) to determine a correlation with your Action Research project or benchmark assignment?
Good news is that Excel will calculate the correlation coefficient for you. You can look up the statistical measures and do it yourself, available here, but after you do, I think you'll agree it's much easier to have an application do it for you instead of by hand!
Lets look at how Excel can calculate the correlation coefficient for us and the discuss what it might mean.
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Excel Assignment |
For this project we are going to determine if there are any relationships (correlations) between the Science Scale Score and the rest of the individual science tests. Think about why might you want to look at this type of relationships within one particular content area?
- Review the screencast on how to calculate the correlation coefficient using Excel.
- Using the 4th grade data set from previous Excel projects, calculate the correlations between:
- Science Scale score and Science Inquiry.
- Science Scale score and Life Science.
- Science Scale score and Physical Science.
- Science Scale score and Earth/Space Science.
- What do each of the correlations mean?
- Which correlation was the strongest? Were you suprised by that? Why or why not?
- Can you determine if there is a correlation between gender and Life Science? Why or why not?
- Post your answers to the bottom of this assignment area in the threaded discussion. Be sure to talk about the relationship between each of the scores and what they might mean.
- Also address, What other correlations might you want to look for? Why?
- For example, if you calculated the correlation coefficient for Global perspectives and Government. Would you expect a correlation? What kind? Why?
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