One of the most worrisome parts about Big Data in schools is the unethical targeting of teachers based on single data points — often misused. It’s therefore imperative that specialists, well-versed in statistics, are present for data based conversations. Here’s a great example:

**NWEA MAP “Achievement Status and Growth Summary Report”**

No doubt my least favorite data report generated for administrators is the *Achievement Status and Growth Summary Report*. It contains this little gem:

Feels a little judgy, doesn’t it? It makes people ask questions like, “Why aren’t all students meeting their projections? Why only 42%?”

But this is misguided. We would expect teachers to have approximately 50% of their students exceed the projection, and 50% fall short. In a normally distributed population, the mean is at the center of the distribution like so:

We can see that approximately half of our distribution is to the right of the vertical mean-line and half is to the left. But bringing in the emotion of thinking about “students meeting their potential” makes us think that *all* should be hitting their projections.

**If we have to compare…**

A better way to compare – but I don’t recommend doing this sort of comparison- would be to run hypothesis tests. We could then see if we should consider this difference due to normal chance, or to a specific *treatment*.

We will set µ=6 and σ=6.55, since this is given to us by NWEA as the mean and standard deviation of growth. We design our test as follows:

H_{0 }: x̄ = µ

H_{A }: x̄ ≠ µ

test type: t-test

α = 0.05

For exploratory purposes, lets look at a normal distribution with µ=6 and σ=6.55 compared with our sample mean:

At this point, I’m pretty confident that the sample mean is well within our 95% t confidence interval. If it wasn’t, I would expect to see that red line out in the *tails* of the distribution. We can continue with R’s t.test function:

We end with p=0.095 so we fail to reject the null hypothesis at the α = 0.05 significance level.

See? Stats to the rescue!

But truthfully, I wouldn’t recommend running a bunch of t-tests on teacher results. That could quickly turn into a *witch hunt* and leave teachers feeling like we’re *looking* for a problem.

*Disclaimer: The data and graphics used on this site are simulated re-creations intended to protect the privacy of the original data sources.*