- Thread starter joeb33050
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Convert alpha to x units, inches etc

Form the beta distribution in x units with x alpha.

Convert the beta x unit distribution to t units.

Solve for t </= t alpha beta.

Would someone look at the explanation? I'll email it.

Thanks;

joe b.

what t-test are you trying to calculate?

You should write what is the H0 distribution, whats is the critical value, what is the H1 distribution

You are doing the left tail. (one tail not two tails)

I prefer to calculate only the priori test power, in this case, you calculates the other avg(x) based on the "change" that you want the test to identify:

change=avg(x1)-avg(x2)

In the z-test the H1 also has the normal distribution, but in the t-test the H1 has the non-central t distribution,

H1 is the alternative hypothesis.

non-central t is a different distribution, similar to t but not symmetrical with a lower peak.

https://en.wikipedia.org/wiki/Noncentral_t-distribution

https://www.statskingdom.com/doc_test_power.html

.

No non-central t distribution involved or required. t describes samples of x1-x2 taken from 1 = one distribution.

Does that help?

You show me calculations instead of defining what you test.

If both populations distriibute normally (or similar),

and you estimate the mean and standard deviations, (that why using t distribution)

and your hypotheses are as following:

H0: mu1 = mu2

H1: mu1! = mu2 (or for one tail mu1 > mu2)

Then you need to use non-central t distribution for the H1

So I assume you know the averages, and try to understand if based on the samples you may conclude for the populations...

If you know the population standard deviation σ, you should use the z test.

If you don't know the population standard deviation you should estimate S and use a t-test.

In this case, the null assumption distributes non-central t.

You can look at the following video:

“Power” is the probability of rejecting Ho: µ 1 = µ 2 when Ho: is false.

The β error is the probability of accepting Ho when Ho is false.

Thus, power = 1 – β error.

In the example above, power = 1 - .2820 = .7180, 71.8%.

The non-central t distribution can be ignored.

I am beginning to suspect that the mathematical edifice constructed about t testing, β error and power was built on the premise that β error in t testing cannot be easily calculated; and that that premise is incorrect.