ABOUT Z TESTING, HYPOTHESIS TESTING AND α

#1
This is in the book after the Z testing chapter. Comments, criticism?
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.
 
#3
I assume that you want to know about me and stats; not about my experience in the paratroops, professional basketball or as a Rhodes scholar. Reading is important.

People should have a basic understanding of Statistics and Probability to understand the world; and teachers have done a woefully poor job teaching those subjects.

Understanding Statistics is about “clicks’, once the topic clicks in the student’s brain, she owns it-maybe for a long time. The multiplication table is not about clicks, it is about memory.

Subjects/topics/principles have basic, fundamental explanations that are easily understood, simple and memorable. I can explain the elements of E = MC2, radar, confirmation, and celestial navigation to anyone, in ten minutes; so that a click happens.

Ex: What is the Normal distribution?

Sample averages of n values, such as length or weight or age, from ANY distribution, form a distribution approaching a Normal distribution as n approaches infinity. Distributions of sample averages with n > 30 are close to Normal-closer as n increases.

My interest is in finding and describing these elements, surrounding each with coherent explanation, and making that available to all.
 

Dason

Ambassador to the humans
#5
Yeah I'm interested in your statistical background as well but I'm not sure what gave you the impression we wouldn't want to hear about that other stuff! Don't get me wrong - I definitely have some objections with your post (especially your description of the normal distribution) but I'd rather learn more about you in the meantime.