# ABOUT Z TESTING, HYPOTHESIS TESTING AND α

#### joeb33050

##### Member
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.

#### Dason

If you plan on sticking around for a while why don't you tell us a little bit about yourself

#### joeb33050

##### Member
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.

#### fed2

##### Active Member
paratroops, professional basketball or as a Rhodes scholar
Any one of those is going to make a more readable book than t-tests. World needs another t-test book=not really.