Although data is meant to be objective, there are some best practices we should discuss in order to avoid being featured on this Wikipedia page. This lesson will discuss the limits of generalizing and predicting given a data set.
Take a look at the following data set and figure out who the weakest student in the class is:
Did you say Esteban Stephens? Well, this was a trick question! We have no idea if Esteban is the weakest student in the class. We only have one data point with which to make a decision. Maybe Esteban hadn’t gotten any sleep the night before, or maybe his mind was still on the playground bullies from an hour ago. We don’t know, but we can take one thing away from this example:
Rule #1: Don’t jump to conclusions without plenty of evidence.
It would be more accurate, not to mention fair, if we included a wider body of work from Esteban before we make a conclusion. There is no hard-and-fast rule for how many data-points you need, and this will change depending on the course and grade-level you teach. Just use your professional judgment and remember:
Rule #2: The more data you use, the more accurate your analysis will be.
As time passes, we record more grades from class and add the data to our spreadsheet. Now that we have more data points, we can gauge each student more effectively. It appears as if Mark Alford is truly struggling and is in need of intense intervention. Each test score is lower than the last, so we might be tempted to say that without extra help, he will earn below a 34 on the next test.
This process is called “extrapolation.” We extrapolate when we don’t have data in the future and make an educated guess on what future data points will be. It’s basically fancy-speak for “prediction.” We must be careful when we extrapolate because we honestly don’t know. It’s important to have an idea of what will happen in the future, but we must be sure to limit extrapolation to the very near future and use it sparingly. For example, predicting the next test score would be appropriate for intervention purposes. Predicting the final average for a student who just completed the first three weeks of school would not be appropriate.
Take a look at this different example class data. While analyzing, try and answer these three questions:
- Who requires help in gaining competency? Interventions should be data-driven, so try and find the greatest areas of need.
- Are there trends in the data? Certain students may be improving or continuing to struggle.
- Do you see any big drops or increases? Not all assessments were created equal, so be on the lookout for a large, student-wide fall or rise in the data to determine if that old test from 2005 needs to be tweaked.
- Extrapolation is tempting but dangerous! Be careful when predicting the future. Tweet
- The more data, the better! Tweet
- Only interpret info if you have enough data points to justify an interpretation! Tweet
Graphing data makes interpretation much easier. Copy and paste the data from the example above into your own spreadsheet and make a graph of it. Did you see anything different that you didn’t notice the first time?