# Teaching notes - The Alpha Trap

`modules/personality-individual-differences/tools/12-alpha-trap/`

**What it teaches.** Cronbach's alpha rises with the number of items
and with how strongly they correlate, and neither is a property of the
construct being measured. Repeated items add reliable variance without
adding breadth, so alpha can keep climbing while the scale narrows and
its relationship with a relevant outcome actually gets worse.

**Before students start.** None needed. Decide whether the room
predicts individually on the page or as a show of hands; the page has
a skip button for the second option.

**What students do.**
1. Predict how many of the five content areas the final scale will
   cover, and what it will correlate with a relevant outcome.
2. Press "add another way of asking it" five times, reading alpha and
   effective content areas each time, and the outcome correlation from
   the fifth press onward.
3. Drop the repeated items and compare the two scales side by side.
4. Diagnose three fictional published scales, then predict and check
   what happens when the repaired scale has its repeats added back.

**What to look for.** Alpha climbs from .684 to .852 over the five
additions, while the outcome correlation peaks after the first
addition at .581 and falls to .536 by the fifth. "Content areas
covered" stays at five out of five the whole time, which is why the
readout also tracks effective content areas, a figure that drops from
5.00 to 2.50 over the same five presses.

**Debrief.** A reviewer writes "the reliability of this scale is
excellent, alpha equals .93." What has that established, and what has
it not? When is a low alpha the more informative result?

**Common misconception / caution.** Students often conclude that a
high alpha means the items measure one thing. Alpha is not a
dimensionality test: this particular scale ends up both unidimensional
and narrow, which is its own separate failure. No sampling error is
modelled anywhere in the tool, so none of these figures carry a
confidence interval, and a very high alpha in a short scale is a
warning about redundancy rather than a mark of quality.

**Use in class / timing.** A tight demonstration runs 8 to 10 minutes.
With both challenges and the debrief, allow 30 to 35 minutes.