Why does it make sense to work with null hypothesis about mean of population being equal to specific number?
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For example, let's assume that according to our old statistical research average wage of business analyst in US is 68125 dollars per month. Now we wonder if the average is still the same. So our null hypothesis is that the average is still equal to 68125 dollars, while the alternative hypothesis says that it's not equal to this number. We then can take samples and then ...
Wait a minute. Isn't it fool's agenda to try to support the alternative hypothesis when we can see from the start, that it has 100% probability to be true? Even more, if our samples will suggest that the null hypothesis holds, then most likely, such conclusion would be false.
Just think about this way. We can imagine the old average wage as number on number line. If we were to randomly to chose any number near this number on the number line, then what is the probability that we will pick our old average? Zero! There are infinitely many numbers near the old average on the number line. In other words, we have 0% probability that the current average wage will fluctuate to exactly the same value as our old average wage. Consequently it means that there is 100% probability that the alternative hypothesis is true. Yes, new average wage can be close to the old one (like just few dollars more or less), but it would be different nonetheless.
statistics hypothesis-testing
asked Nov 16 at 15:32
user161005
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For example, let's assume that according to our old statistical research average wage of business analyst in US is 68125 dollars per month. Now we wonder if the average is still the same. So our null hypothesis is that the average is still equal to 68125 dollars, while the alternative hypothesis says that it's not equal to this number. We then can take samples and then ...
Wait a minute. Isn't it fool's agenda to try to support the alternative hypothesis when we can see from the start, that it has 100% probability to be true? Even more, if our samples will suggest that the null hypothesis holds, then most likely, such conclusion would be false.
Just think about this way. We can imagine the old average wage as number on number line. If we were to randomly to chose any number near this number on the number line, then what is the probability that we will pick our old average? Zero! There are infinitely many numbers near the old average on the number line. In other words, we have 0% probability that the current average wage will fluctuate to exactly the same value as our old average wage. Consequently it means that there is 100% probability that the alternative hypothesis is true. Yes, new average wage can be close to the old one (like just few dollars more or less), but it would be different nonetheless.
statistics hypothesis-testing
asked Nov 16 at 15:32
user161005
18912
1
I would hope that your old statistical research did not propose such a precise figure for the average, without a discussion of uncertainty. In any case it would indeed be ridiculous to test whether that exact value was current. There are many more problems with standard hypothesis testing than this one.
– Ethan Bolker
Nov 16 at 15:35
The point is: you make some assumptions that are strong enough for to be able to compute or at least approximate probabilities of events, and then you compute the probability of a certain event that depends on the form of the alternative hypothesis and on the actual sample. For example, if your null hypothesis is that the mean has some value and your alternative hypothesis is that the mean exceeds that value, then the event whose probability you compute is the probability that the sample mean exceeds the sample mean you actually obtained.
– Ian
Nov 16 at 15:41
(Cont.) When that probability is small, it casts doubt on the null hypothesis...but more to the point, it also simultaneously casts doubt on other, similar null hypotheses, due to some kind of underlying continuity of the probability distribution with respect to the parameter.
– Ian
Nov 16 at 15:42
@EthanBolker "it would indeed be ridiculous to test whether that exact value was current." I don't know as you, but when I was watching lectures about hypothesis testing, there were examples of null hypothesis that the average is equal to specific number.
– user161005
Nov 16 at 15:42
1
The key point I was trying to make is that your null hypothesis has to be rigid enough to enable you to compute probabilities. This is a bit of a flaw in the design, but because you can define the result of the test as a function of the hypothesis itself, it can be worked around.
– Ian
Nov 16 at 15:51
|
show 8 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
For example, let's assume that according to our old statistical research average wage of business analyst in US is 68125 dollars per month. Now we wonder if the average is still the same. So our null hypothesis is that the average is still equal to 68125 dollars, while the alternative hypothesis says that it's not equal to this number. We then can take samples and then ...
Wait a minute. Isn't it fool's agenda to try to support the alternative hypothesis when we can see from the start, that it has 100% probability to be true? Even more, if our samples will suggest that the null hypothesis holds, then most likely, such conclusion would be false.
Just think about this way. We can imagine the old average wage as number on number line. If we were to randomly to chose any number near this number on the number line, then what is the probability that we will pick our old average? Zero! There are infinitely many numbers near the old average on the number line. In other words, we have 0% probability that the current average wage will fluctuate to exactly the same value as our old average wage. Consequently it means that there is 100% probability that the alternative hypothesis is true. Yes, new average wage can be close to the old one (like just few dollars more or less), but it would be different nonetheless.
statistics hypothesis-testing
asked Nov 16 at 15:32
user161005
18912
For example, let's assume that according to our old statistical research average wage of business analyst in US is 68125 dollars per month. Now we wonder if the average is still the same. So our null hypothesis is that the average is still equal to 68125 dollars, while the alternative hypothesis says that it's not equal to this number. We then can take samples and then ...
Wait a minute. Isn't it fool's agenda to try to support the alternative hypothesis when we can see from the start, that it has 100% probability to be true? Even more, if our samples will suggest that the null hypothesis holds, then most likely, such conclusion would be false.
Just think about this way. We can imagine the old average wage as number on number line. If we were to randomly to chose any number near this number on the number line, then what is the probability that we will pick our old average? Zero! There are infinitely many numbers near the old average on the number line. In other words, we have 0% probability that the current average wage will fluctuate to exactly the same value as our old average wage. Consequently it means that there is 100% probability that the alternative hypothesis is true. Yes, new average wage can be close to the old one (like just few dollars more or less), but it would be different nonetheless.
statistics hypothesis-testing
statistics hypothesis-testing
asked Nov 16 at 15:32
user161005
18912
asked Nov 16 at 15:32
user161005
18912
asked Nov 16 at 15:32
user161005
18912
asked Nov 16 at 15:32
user161005
18912
asked Nov 16 at 15:32
user161005
18912
18912
1
I would hope that your old statistical research did not propose such a precise figure for the average, without a discussion of uncertainty. In any case it would indeed be ridiculous to test whether that exact value was current. There are many more problems with standard hypothesis testing than this one.
– Ethan Bolker
Nov 16 at 15:35
The point is: you make some assumptions that are strong enough for to be able to compute or at least approximate probabilities of events, and then you compute the probability of a certain event that depends on the form of the alternative hypothesis and on the actual sample. For example, if your null hypothesis is that the mean has some value and your alternative hypothesis is that the mean exceeds that value, then the event whose probability you compute is the probability that the sample mean exceeds the sample mean you actually obtained.
– Ian
Nov 16 at 15:41
(Cont.) When that probability is small, it casts doubt on the null hypothesis...but more to the point, it also simultaneously casts doubt on other, similar null hypotheses, due to some kind of underlying continuity of the probability distribution with respect to the parameter.
– Ian
Nov 16 at 15:42
@EthanBolker "it would indeed be ridiculous to test whether that exact value was current." I don't know as you, but when I was watching lectures about hypothesis testing, there were examples of null hypothesis that the average is equal to specific number.
– user161005
Nov 16 at 15:42
1
The key point I was trying to make is that your null hypothesis has to be rigid enough to enable you to compute probabilities. This is a bit of a flaw in the design, but because you can define the result of the test as a function of the hypothesis itself, it can be worked around.
– Ian
Nov 16 at 15:51
|
show 8 more comments
1
I would hope that your old statistical research did not propose such a precise figure for the average, without a discussion of uncertainty. In any case it would indeed be ridiculous to test whether that exact value was current. There are many more problems with standard hypothesis testing than this one.
– Ethan Bolker
Nov 16 at 15:35
The point is: you make some assumptions that are strong enough for to be able to compute or at least approximate probabilities of events, and then you compute the probability of a certain event that depends on the form of the alternative hypothesis and on the actual sample. For example, if your null hypothesis is that the mean has some value and your alternative hypothesis is that the mean exceeds that value, then the event whose probability you compute is the probability that the sample mean exceeds the sample mean you actually obtained.
– Ian
Nov 16 at 15:41
(Cont.) When that probability is small, it casts doubt on the null hypothesis...but more to the point, it also simultaneously casts doubt on other, similar null hypotheses, due to some kind of underlying continuity of the probability distribution with respect to the parameter.
– Ian
Nov 16 at 15:42
@EthanBolker "it would indeed be ridiculous to test whether that exact value was current." I don't know as you, but when I was watching lectures about hypothesis testing, there were examples of null hypothesis that the average is equal to specific number.
– user161005
Nov 16 at 15:42
1
The key point I was trying to make is that your null hypothesis has to be rigid enough to enable you to compute probabilities. This is a bit of a flaw in the design, but because you can define the result of the test as a function of the hypothesis itself, it can be worked around.
– Ian
Nov 16 at 15:51
1
1
I would hope that your old statistical research did not propose such a precise figure for the average, without a discussion of uncertainty. In any case it would indeed be ridiculous to test whether that exact value was current. There are many more problems with standard hypothesis testing than this one.
– Ethan Bolker
Nov 16 at 15:35
I would hope that your old statistical research did not propose such a precise figure for the average, without a discussion of uncertainty. In any case it would indeed be ridiculous to test whether that exact value was current. There are many more problems with standard hypothesis testing than this one.
– Ethan Bolker
Nov 16 at 15:35
The point is: you make some assumptions that are strong enough for to be able to compute or at least approximate probabilities of events, and then you compute the probability of a certain event that depends on the form of the alternative hypothesis and on the actual sample. For example, if your null hypothesis is that the mean has some value and your alternative hypothesis is that the mean exceeds that value, then the event whose probability you compute is the probability that the sample mean exceeds the sample mean you actually obtained.
– Ian
Nov 16 at 15:41
The point is: you make some assumptions that are strong enough for to be able to compute or at least approximate probabilities of events, and then you compute the probability of a certain event that depends on the form of the alternative hypothesis and on the actual sample. For example, if your null hypothesis is that the mean has some value and your alternative hypothesis is that the mean exceeds that value, then the event whose probability you compute is the probability that the sample mean exceeds the sample mean you actually obtained.
– Ian
Nov 16 at 15:41
(Cont.) When that probability is small, it casts doubt on the null hypothesis...but more to the point, it also simultaneously casts doubt on other, similar null hypotheses, due to some kind of underlying continuity of the probability distribution with respect to the parameter.
– Ian
Nov 16 at 15:42
(Cont.) When that probability is small, it casts doubt on the null hypothesis...but more to the point, it also simultaneously casts doubt on other, similar null hypotheses, due to some kind of underlying continuity of the probability distribution with respect to the parameter.
– Ian
Nov 16 at 15:42
@EthanBolker "it would indeed be ridiculous to test whether that exact value was current." I don't know as you, but when I was watching lectures about hypothesis testing, there were examples of null hypothesis that the average is equal to specific number.
– user161005
Nov 16 at 15:42
@EthanBolker "it would indeed be ridiculous to test whether that exact value was current." I don't know as you, but when I was watching lectures about hypothesis testing, there were examples of null hypothesis that the average is equal to specific number.
– user161005
Nov 16 at 15:42
1
1
The key point I was trying to make is that your null hypothesis has to be rigid enough to enable you to compute probabilities. This is a bit of a flaw in the design, but because you can define the result of the test as a function of the hypothesis itself, it can be worked around.
– Ian
Nov 16 at 15:51
The key point I was trying to make is that your null hypothesis has to be rigid enough to enable you to compute probabilities. This is a bit of a flaw in the design, but because you can define the result of the test as a function of the hypothesis itself, it can be worked around.
– Ian
Nov 16 at 15:51
|
show 8 more comments
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I would hope that your old statistical research did not propose such a precise figure for the average, without a discussion of uncertainty. In any case it would indeed be ridiculous to test whether that exact value was current. There are many more problems with standard hypothesis testing than this one.
– Ethan Bolker
Nov 16 at 15:35
The point is: you make some assumptions that are strong enough for to be able to compute or at least approximate probabilities of events, and then you compute the probability of a certain event that depends on the form of the alternative hypothesis and on the actual sample. For example, if your null hypothesis is that the mean has some value and your alternative hypothesis is that the mean exceeds that value, then the event whose probability you compute is the probability that the sample mean exceeds the sample mean you actually obtained.
– Ian
Nov 16 at 15:41
(Cont.) When that probability is small, it casts doubt on the null hypothesis...but more to the point, it also simultaneously casts doubt on other, similar null hypotheses, due to some kind of underlying continuity of the probability distribution with respect to the parameter.
– Ian
Nov 16 at 15:42
@EthanBolker "it would indeed be ridiculous to test whether that exact value was current." I don't know as you, but when I was watching lectures about hypothesis testing, there were examples of null hypothesis that the average is equal to specific number.
– user161005
Nov 16 at 15:42
1
The key point I was trying to make is that your null hypothesis has to be rigid enough to enable you to compute probabilities. This is a bit of a flaw in the design, but because you can define the result of the test as a function of the hypothesis itself, it can be worked around.
– Ian
Nov 16 at 15:51