Last week, Abby opened the door to one of my favorite topics — statistics. When used properly, statistics can add a layer of justification to our assessment results by further explaining the numbers in our datasets. I thought I’d take some time in my next few posts to further explain statistics and its (potential) use in our assessments.
Descriptive vs Inferential Statistics
The vast majority of assessment results rely on descriptive statistics. Descriptive statistics merely describe what’s going on in a given dataset. Mean, median, mode, maximum, minimum, and standard deviation, are all descriptive statistics.
Mean – also known as the “average” this term is used to tell people they are dreadfully un-special! Mathematically, it’s the sum of the values divided by the number of values. That is, if I tell 3 friends a set of 10 puns and those three friends laugh at 4,5, and 6 of the puns, the mean is 5 (4+5+6 divided by 3). This may be the most used descriptive statistic!
Median – I have a pet peeve. One of our summer orientation presenters likes to say “only half of you can be above average!” This tears me up inside because it’s not true. If we have 4 students, 3 of them have a “B” grade (3.0) and one has a “D” grade (1.0), then the average is a 2.5. All three “B” students are above average and that one “D” student is making everyone else look good. This is why the median was invented. The median is the place where half of the people are above you and half are below you. To find the median, rank all of the values from lowest to highest (1,3,3,3) and take the middle value. In cases where you have an even number of values, average the two closest to the middle. For this dataset (1,3,3,3) the median is 3 (the average of 3 and 3). Since modern grade distributions look less like a bell and more like a wave — with everyone squished in the mid-3 range and a tail of students performing poorly — the median can be a great way for students to compare themselves to their peers academically.
Mode – this statistic is almost useless. It tells you which value occurs the most. It’s not mode’s fault, we just don’t often care which value shows up the most. I’m sorry Mode, it’s not you, its me. But it’s really you.
Maximum – this is the highest value in a dataset. When I’m at the gym, I often ask the maximum amount of weight a given bar can handle. Because if I’m doing bench presses, I don’t want to break the bar.
Minimum – conversely, this is the lowest value in a set of data.
Standard Deviation – this value tells you how much your data varies. It’s useful for larger datasets (i.e., more than just a handful of numbers) because it can tell you how one value compares to the dataset. Standard Deviation is in some ways a gateway into inferential statistics, which I’ll explain in my next post.
This post explains the more useful descriptive statistics. You may be thinking — but Mark, my survey only covers %25 of my students (and I can’t chase down the rest), does this mean I can only make conclusions about that %25 of students? Is there a way I can, using this information, make conclusions about my entire group (%100)? The answer, an annoying aspect of statistics, is sort of. I’ll dive into this further in my next post!