on
发帖数: 199 | 1 Type I / II errors depend on what is the null hypothesis... Let me use an
example. Suppose two manufacturers A and B produce similar ping-pong balls.
On average, balls by A have a higher average weight than by B. Now we have
100 balls, and we want test if these balls are from A or B (the truth is one
of them, say).
In this case, we can test Null Hypothesis the balls produced by A; or a Null
Hypothesis is Ball produced by B.
My question is: it seems we can flip a Null Hypothesis depending on what we
want to test... i.e. no certain way to say a Null Hypothesis has to be
something.. Is this correct?
Thanks. | F****n
发帖数: 3271 | 2 You didn't formulate your problem right. There's no hypothesis to test at
all.
.
one
Null
we
【在 on 的大作中提到】
: Type I / II errors depend on what is the null hypothesis... Let me use an
: example. Suppose two manufacturers A and B produce similar ping-pong balls.
: On average, balls by A have a higher average weight than by B. Now we have
: 100 balls, and we want test if these balls are from A or B (the truth is one
: of them, say).
: In this case, we can test Null Hypothesis the balls produced by A; or a Null
: Hypothesis is Ball produced by B.
: My question is: it seems we can flip a Null Hypothesis depending on what we
: want to test... i.e. no certain way to say a Null Hypothesis has to be
: something.. Is this correct?
| on
发帖数: 199 | 3 Let me simplify it further, and put some numbers:
Average weight of balls from A is 1. From B is 1.1 Their STDs are 0.1
Now we got a ball. Its weight is 1.05. We try to test if this ball is brand
A or B.
It seems me that we can test either of the following:
1) Null Hypothesis: the ball is from A.
or 2) Null Hypothesis: the ball is from B.
My question is: from a statistical view, there is nothing which would
dictate 1) or 2) should be Null Hypothesis. Either would be fine and can be
chosen depending on the actual objective.
【在 F****n 的大作中提到】
: You didn't formulate your problem right. There's no hypothesis to test at
: all.
:
: .
: one
: Null
: we
| F****n
发帖数: 3271 | 4 No, none of the two your said are Null Hypothesis.
And what you described is still not a hypothesis testing problem.
brand
be
【在 on 的大作中提到】
: Let me simplify it further, and put some numbers:
: Average weight of balls from A is 1. From B is 1.1 Their STDs are 0.1
: Now we got a ball. Its weight is 1.05. We try to test if this ball is brand
: A or B.
: It seems me that we can test either of the following:
: 1) Null Hypothesis: the ball is from A.
: or 2) Null Hypothesis: the ball is from B.
: My question is: from a statistical view, there is nothing which would
: dictate 1) or 2) should be Null Hypothesis. Either would be fine and can be
: chosen depending on the actual objective.
| on
发帖数: 199 | 5
This is embarrasing..
The implicit assumption is that balls from A and B follow a normal
distribution with different means for their weights. With all the numbers
give earlier, we couldn't reject Null 1 or 2 with any typical significance
values. Why can't it be a null hypothesis? could anyone reform the problem
and/or point me what exactly I missed?
thanks
【在 F****n 的大作中提到】
: No, none of the two your said are Null Hypothesis.
: And what you described is still not a hypothesis testing problem.
:
: brand
: be
| D******n
发帖数: 2836 | 6 it is up to you, no big difference.
brand
be
【在 on 的大作中提到】
: Let me simplify it further, and put some numbers:
: Average weight of balls from A is 1. From B is 1.1 Their STDs are 0.1
: Now we got a ball. Its weight is 1.05. We try to test if this ball is brand
: A or B.
: It seems me that we can test either of the following:
: 1) Null Hypothesis: the ball is from A.
: or 2) Null Hypothesis: the ball is from B.
: My question is: from a statistical view, there is nothing which would
: dictate 1) or 2) should be Null Hypothesis. Either would be fine and can be
: chosen depending on the actual objective.
| d******e
发帖数: 7844 | 7 it will make difference when you do hypothesis testing and specify
signifiance level.
【在 D******n 的大作中提到】
: it is up to you, no big difference.
:
: brand
: be
| F****n
发帖数: 3271 | 8 Hypothesis testing studies the relationship between samples and probability
distributions. Even sometimes you don't directly examine distribution
functions (e.g. test difference between sample means), they lurking behind (
assuming sample means following some distributions).
What you describe is about if one case belong to a category. It is a
classification problem, which has nothing to do with hypothesis testing.
You should read your intro stats textbook.
【在 on 的大作中提到】
:
: This is embarrasing..
: The implicit assumption is that balls from A and B follow a normal
: distribution with different means for their weights. With all the numbers
: give earlier, we couldn't reject Null 1 or 2 with any typical significance
: values. Why can't it be a null hypothesis? could anyone reform the problem
: and/or point me what exactly I missed?
: thanks
| F****n
发帖数: 3271 | 9 Since I have some time, let me give you some examples.
Let's say you have group A and B. Then for hypothesis testing, you need to
have a sample C, and you can test:
1. whether the distribution of C is normal;
2. whether the mean of C is different from A;
3. whether the mean of C is different from B;
4. whether the variance of C is different from A;
5. whether the variance of C is different from B.
probability
(
【在 F****n 的大作中提到】
: Hypothesis testing studies the relationship between samples and probability
: distributions. Even sometimes you don't directly examine distribution
: functions (e.g. test difference between sample means), they lurking behind (
: assuming sample means following some distributions).
: What you describe is about if one case belong to a category. It is a
: classification problem, which has nothing to do with hypothesis testing.
: You should read your intro stats textbook.
| on
发帖数: 199 | 10 Now I got more confused, since it seems some conflicting answers above :-)
Foxman, I guess your point is that data in my example is a classification
problem, since a ball is either from A or B; OK, let's forget about that one
.
In practice, we often have a typical null hypothesis; for example, to test a
treatment is effective, the null is not effective; to test if a person is
ill based on a blood test, the null is that the person is healthy, etc.
My question is: From a pure statistical theory point of view, is it possible
to switch Null and Alternative hypothesis? In other words, as far as stat
theory goes, it won't dictate which one should be Null, and which should be
Alternative.. Is that right?
So I tried hard to come up with an example which makes a null hypothesis
less obvious... guess it's not a good one.
again thanks for the discussion.
probability
(
【在 F****n 的大作中提到】
: Hypothesis testing studies the relationship between samples and probability
: distributions. Even sometimes you don't directly examine distribution
: functions (e.g. test difference between sample means), they lurking behind (
: assuming sample means following some distributions).
: What you describe is about if one case belong to a category. It is a
: classification problem, which has nothing to do with hypothesis testing.
: You should read your intro stats textbook.
| | | j*******y
发帖数: 58 | 11 of course you can switch your null hypothesis with alternative, but won't
make any difference in the testing result.
For example if you test \mu<5 vs. \mu>5, and your test statistic is 2, then
the p value is the right hand side of the standard normal distribution which
is <0.05.
Then you switch you hypothesis to \mu>5 vs \mu<5, then your test statistic
is still 2, but your p value is the left hand side of the normal
distribution which is >0.05.
so no matter what hypothesis you choose, you won't make a difference in the
testing result.
you guys really should go back to school to take elementary stat courses.
one
a
possible
be
【在 on 的大作中提到】
: Now I got more confused, since it seems some conflicting answers above :-)
: Foxman, I guess your point is that data in my example is a classification
: problem, since a ball is either from A or B; OK, let's forget about that one
: .
: In practice, we often have a typical null hypothesis; for example, to test a
: treatment is effective, the null is not effective; to test if a person is
: ill based on a blood test, the null is that the person is healthy, etc.
: My question is: From a pure statistical theory point of view, is it possible
: to switch Null and Alternative hypothesis? In other words, as far as stat
: theory goes, it won't dictate which one should be Null, and which should be
| x**********0
发帖数: 163 | 12 I have seen a similar one in a textbook.
There are two identically appearing bowls of jelly beans. Bowl 1 contains 60
red and 40 black jelly beans, and bowl 2 contains 40 red and 60 black jelly
beans. Therefore, the proportion of red jelly beans, p, for the two bowls
are
Bowl 1: p = 0.6
Bowl 2: p = 0.4.
One of the bowls is sitting on the table, but you do not know which one it
is.
You suspect that it is bowl 2, but you are not sure.
To test your hypothesis that bowl 2 is on the table, you sample 5 jelly
beans.
Thus the null hypothesis is H0: p = 0.4.
the alternative hypothesis is H1: p = 0.6
In such a case, you can flip the null hypothesis and the alternative
hypothesis, and basically no difference.
but in another cases, the null hypothesis represents the status quo, which
means if you reject the null hypothesis, you need to make a change and this
will create the difference. | M*P
发帖数: 6456 | 13 还是有区别的。因为你总有一个背景问题。比如疾病的几率是很小的。在这种情况下，
控制alpha才有意义。
【在 on 的大作中提到】
: Now I got more confused, since it seems some conflicting answers above :-)
: Foxman, I guess your point is that data in my example is a classification
: problem, since a ball is either from A or B; OK, let's forget about that one
: .
: In practice, we often have a typical null hypothesis; for example, to test a
: treatment is effective, the null is not effective; to test if a person is
: ill based on a blood test, the null is that the person is healthy, etc.
: My question is: From a pure statistical theory point of view, is it possible
: to switch Null and Alternative hypothesis? In other words, as far as stat
: theory goes, it won't dictate which one should be Null, and which should be
| on
发帖数: 199 | 14 小东西,
thanks a lot for your example. It seems confirming my own example is a
reasonable one anyway :-)
If at least in some cases, one can flip null / alternative hypothesis, then
type I and type II errors would flip too correspondingly. That was actually
what I really wanted to get confirmation..
60
jelly
【在 x**********0 的大作中提到】
: I have seen a similar one in a textbook.
: There are two identically appearing bowls of jelly beans. Bowl 1 contains 60
: red and 40 black jelly beans, and bowl 2 contains 40 red and 60 black jelly
: beans. Therefore, the proportion of red jelly beans, p, for the two bowls
: are
: Bowl 1: p = 0.6
: Bowl 2: p = 0.4.
: One of the bowls is sitting on the table, but you do not know which one it
: is.
: You suspect that it is bowl 2, but you are not sure.
| g***l
发帖数: 22 | 15 The choice of Null and alternative depends on your point of interest. You
always want a low probability (usually 0.05) to make a type I error (reject
the NULL when it is true.)
In your case, if you don't want to misclassify a "A" ball as a "B" ball,
then the hypothesis will be:
H0: Brand is A
Ha: Brand is B
as the prob. of type I error (misclassify a "A" ball as a "B" ball) is
usually controlled at 0.05 or etc.
and vice versa.
Of course it might not be a very good example as it implies a classification
rule that favor brand "A", but still could explain the relationship between
Type I and II error when you filp H0 and Ha. Yes, they will interchange. | B******Q
发帖数: 58 | 16 En, this makes sense.
probability
(
【在 F****n 的大作中提到】
: Hypothesis testing studies the relationship between samples and probability
: distributions. Even sometimes you don't directly examine distribution
: functions (e.g. test difference between sample means), they lurking behind (
: assuming sample means following some distributions).
: What you describe is about if one case belong to a category. It is a
: classification problem, which has nothing to do with hypothesis testing.
: You should read your intro stats textbook.
|
|
