ABOUT Z TESTING, HYPOTHESIS TESTING AND α

If a client asked me to find out if the gizmos his factory made on the night shift were longer than the day shift gizmos. I would explain that nobody could give him a “yes/no” answer; but that I could give him an “

*adjective*likely” answer. (Adjectives include “not very” and “highly”.

I would take random samples of n, day and night gizmos, measure the lengths, and calculate x̄ D, x̄ N, s D and s N.

I would estimate s, calculate (x̄ D -, x̄ N) / (s / √ n), look up P (Z ≤ Z test), and using all the information gathered, select an adjective and, write a short declarative sentence-the answer-to the client.

I would not write a Hypothesis; I do not need one. The hypothesis signals left, right or two tail tests; I do a “no-tail” test.

I would not select or use an α. α is not selected based on the “importance” of the test if it ever was. n can and should be selected based on that importance, s N and s D, and x̄ D and x̄ N.

The larger the absolute value of (s N – s D), the larger n should be. At some large absolute value of (s N – s D) I would decline to continue the test.

The larger the absolute value of (x̄ N – x̄ D), the larger n should be.

The greater the importance of the test, the larger n should be.

If n must be < some number, for any reason, I would decline to continue the test.

Without α and a hypothesis, there is no “Accept/Reject”. There is just adjective selection.

Without α, there is no “confidence level or interval”, no “significance”. There are no TYPE I or II errors. All children of α.

The p value? Why bother?

n and P (Z ≤ Z test) are the nut. The rest are the trunk, branches, roots, and leaves.