t test Type II error %
- Thread starter joeb33050
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The method seems to work, finding beta error in t land is simple.
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.
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.
Hi Joe,
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,
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,
Hi Joe,
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
.
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
.
I didn't explain clearly. My analysis is based on two t distributions with v1 = v2 and mu1 not equal to mu 2. I think of an x axis with a center at zero; and two identical t distributions, free to slide, sitting on the x axis. I can position each anywhere on the x axis. When they are exactly congruent = Ho. The x axis is graduated in inches or pounds or IQ or ????????
No non-central t distribution involved or required. t describes samples of x1-x2 taken from 1 = one distribution.
Does that help?
No non-central t distribution involved or required. t describes samples of x1-x2 taken from 1 = one distribution.
Does that help?
Hi Joe,
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
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
If you know the populations means: mu1 not equal to mu 2, you don't need to run a test
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:
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:
Well, obh, I have failed to explain. You and I are talking about different things in different languages. I surrender. Back to the subject:
“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.
“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.
