Dependece of Type I error on Type II error
$begingroup$
In hypothesis testing we have two errors Type I ($alpha$) and Type II ($beta $) errors. Also note the if we know $S_R$ (rejection region) (and hence $S_A = S - S_R$ (acceptance region) ), then we have uniquely defined the test. For obtaining the most powerful test we fixes $alpha$ and then choose to minimize $beta$. My confusion is if we fix $alpha$ then aren't we specifying $S_R$ and hence specifing the test and therefore $beta$.
Also is it necessary that the region $S_R$ is a connected region?
statistical-inference
asked Dec 13 '18 at 23:06
henceprovedhenceproved
1628
$endgroup$
add a comment |
$begingroup$
In hypothesis testing we have two errors Type I ($alpha$) and Type II ($beta $) errors. Also note the if we know $S_R$ (rejection region) (and hence $S_A = S - S_R$ (acceptance region) ), then we have uniquely defined the test. For obtaining the most powerful test we fixes $alpha$ and then choose to minimize $beta$. My confusion is if we fix $alpha$ then aren't we specifying $S_R$ and hence specifing the test and therefore $beta$.
Also is it necessary that the region $S_R$ is a connected region?
statistical-inference
asked Dec 13 '18 at 23:06
henceprovedhenceproved
1628
$endgroup$
$begingroup$
assume sample size is fix
$endgroup$
– henceproved
Dec 13 '18 at 23:11
add a comment |
$begingroup$
In hypothesis testing we have two errors Type I ($alpha$) and Type II ($beta $) errors. Also note the if we know $S_R$ (rejection region) (and hence $S_A = S - S_R$ (acceptance region) ), then we have uniquely defined the test. For obtaining the most powerful test we fixes $alpha$ and then choose to minimize $beta$. My confusion is if we fix $alpha$ then aren't we specifying $S_R$ and hence specifing the test and therefore $beta$.
Also is it necessary that the region $S_R$ is a connected region?
statistical-inference
asked Dec 13 '18 at 23:06
henceprovedhenceproved
1628
$endgroup$
In hypothesis testing we have two errors Type I ($alpha$) and Type II ($beta $) errors. Also note the if we know $S_R$ (rejection region) (and hence $S_A = S - S_R$ (acceptance region) ), then we have uniquely defined the test. For obtaining the most powerful test we fixes $alpha$ and then choose to minimize $beta$. My confusion is if we fix $alpha$ then aren't we specifying $S_R$ and hence specifing the test and therefore $beta$.
Also is it necessary that the region $S_R$ is a connected region?
statistical-inference
statistical-inference
asked Dec 13 '18 at 23:06
henceprovedhenceproved
1628
asked Dec 13 '18 at 23:06
henceprovedhenceproved
1628
asked Dec 13 '18 at 23:06
henceprovedhenceproved
1628
asked Dec 13 '18 at 23:06
henceprovedhenceproved
1628
asked Dec 13 '18 at 23:06
henceprovedhenceproved
1628
1628
$begingroup$
assume sample size is fix
$endgroup$
– henceproved
Dec 13 '18 at 23:11
add a comment |
$begingroup$
assume sample size is fix
$endgroup$
– henceproved
Dec 13 '18 at 23:11
$begingroup$
assume sample size is fix
$endgroup$
– henceproved
Dec 13 '18 at 23:11
$begingroup$
assume sample size is fix
$endgroup$
– henceproved
Dec 13 '18 at 23:11
add a comment |
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$begingroup$
assume sample size is fix
$endgroup$
– henceproved
Dec 13 '18 at 23:11