Finding a critical value for a left-tailed test will have a familiar feel to it if you are used to looking up areas in a z-table (which should have been covered by this point in any elementary statistics class). Even if you haven’t used a z-table before, this article walks you through the process.
Sample question: find the critical value in the z-table for α=.012 (left-tailed test).
Step 1: Draw a diagram, like the one above. Shade in the area in the left tail (because you’re looking for a critical value for a left-tailed test).
This area represents alpha, α — the “alpha level.”
Step 2:Subtract alpha (α) from 0.5.
Step 3: Find the result from step 2 in the center part of the z-table.
Step 4:Add a negative sign to Step 3 (left-tail critical values are always negative).
Like the explanation? Check out our statistics how-to book, with a how-to for every elementary statistics problem type.