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In hypothesis you want to test some statement about the real world, e.g. the average length of all men is 1.75m. We would then formulate a hypothesis test like e.g. $H_0: \mu_L=1.75$ versus $H_1: \mu_L \ne 1.75$.

This is our statement and we want to test whether in the real world this is a fact. But frequentists state that in the real world this is either true or false. As in the real world $H_0$ is either true or false, this means that in the real world $P(H_0=TRUE)$ is either 0 or 1.

So in theory the result of our hypothesis test should be $H_0$ is true or false but as we only work on a sample we can not make such hard conclusions, therefore we try to use some statistical variant of a mathematical technique called 'proof by contradiction'. For detail see What follows if we fail to reject the null hypothesis?.

For a thread on p-values see Misunderstanding a P-value?

Baysians do something different; they express their belief or credibility they have in their conclusion of the test, so it is not realy the probability that $H_0$ is true, but more the degree of belief they have in their conclusion they make after the test about $H_0$. This is why it is called ''credibility''.

Taking your example, you test "$H_0:$ Vitamin D affects mood" versus "$H_1:$ Vitamin D doe not affect mood".

Based on a sample you compute some test-statistic and its probability of being exceeded when $H_0$ is true. If this value of the test statistic is very low (below our chosen significance level) then assuming that $H_0$ is true leads to something very improbable or it leads so to say to ''a statistical contradiction'' and

Frequentists will conclude that in such case $H_0$ leads to statistical non-sense. However, in the ''real world'' there is only one truth $H_0$ or $H_1$ !

Bayesians compute the probability that $H_0$ is true given the data. So there also, in the real world, $H_0$ is true or $H_1$ is true, but using data they can express their degree of belief (derived from the data) that $H_0$ is true.

They call this the ''credibility of the hypothesis'', but it does not say anything about the probability that $H_0$ is true (nor about the probability that $H_1$ is true)

They just express their belief in their ''conclusion of the test'' derived from ''available data''.

In hypothesis you want to test some statement about the real world, e.g. the average length of all men is 1.75m. We would then formulate a hypothesis test like e.g. $H_0: \mu_L=1.75$ versus $H_1: \mu_L \ne 1.75$.

This is our statement and we want to test whether in the real world this is a fact. But frequentists state that in the real world this is either true or false. As in the real world $H_0$ is either true or false, this means that in the real world $P(H_0=TRUE)$ is either 0 or 1.

So in theory the result of our hypothesis test should be $H_0$ is true or false but as we only work on a sample we can not make such hard conclusions, therefore we try to use some statistical variant of a mathematical technique called 'proof by contradiction'. For detail see What follows if we fail to reject the null hypothesis?.

For a thread on p-values see Misunderstanding a P-value?

Baysians do something different; they express their belief or credibility they have in their conclusion of the test, so it is not realy the probability that $H_0$ is true, but more the degree of belief they have in their conclusion they make after the test about $H_0$. This is why it is called ''credibility''.

In hypothesis you want to test some statement about the real world, e.g. the average length of all men is 1.75m. We would then formulate a hypothesis test like e.g. $H_0: \mu_L=1.75$ versus $H_1: \mu_L \ne 1.75$.

This is our statement and we want to test whether in the real world this is a fact. But frequentists state that in the real world this is either true or false. As in the real world $H_0$ is either true or false, this means that in the real world $P(H_0=TRUE)$ is either 0 or 1.

So in theory the result of our hypothesis test should be $H_0$ is true or false but as we only work on a sample we can not make such hard conclusions, therefore we try to use some statistical variant of a mathematical technique called 'proof by contradiction'. For detail see What follows if we fail to reject the null hypothesis?.

For a thread on p-values see Misunderstanding a P-value?

Baysians do something different; they express their belief or credibility they have in their conclusion of the test, so it is not realy the probability that $H_0$ is true, but more the degree of belief they have in their conclusion they make after the test about $H_0$. This is why it is called ''credibility''.

Taking your example, you test "$H_0:$ Vitamin D affects mood" versus "$H_1:$ Vitamin D doe not affect mood".

Based on a sample you compute some test-statistic and its probability of being exceeded when $H_0$ is true. If this value of the test statistic is very low (below our chosen significance level) then assuming that $H_0$ is true leads to something very improbable or it leads so to say to ''a statistical contradiction'' and

Frequentists will conclude that in such case $H_0$ leads to statistical non-sense. However, in the ''real world'' there is only one truth $H_0$ or $H_1$ !

Bayesians compute the probability that $H_0$ is true given the data. So there also, in the real world, $H_0$ is true or $H_1$ is true, but using data they can express their degree of belief (derived from the data) that $H_0$ is true.

They call this the ''credibility of the hypothesis'', but it does not say anything about the probability that $H_0$ is true (nor about the probability that $H_1$ is true)

They just express their belief in their ''conclusion of the test'' derived from ''available data''.

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user83346
user83346

In hypothesis you want to test some statement about the real world, e.g. the average length of all men is 1.75m. We would then formulate a hypothesis test like e.g. $H_0: \mu_L=1.75$ versus $H_1: \mu_L \ne 1.75$.

This is our statement and we want to test whether in the real world this is a fact. But frequentists state that in the real world this is either true or false. As in the real world $H_0$ is either true or false, this means that in the real world $P(H_0=TRUE)$ is either 0 or 1.

So in theory the result of our hypothesis test should be $H_0$ is true or false but as we only work on a sample we can not make such hard conclusions, therefore we try to use some statistical variant of a mathematical technique called 'proof by contradiction'. For detail see What follows if we fail to reject the null hypothesis?.

For a thread on p-values see Misunderstanding a P-value?

Baysians do something different; they express their belief or credibility they have in their conclusion of the test, so it is not realy the probability that $H_0$ is true, but more the degree of belief they have in their conclusion they make after the test about $H_0$. This is why it is called ''credibility''.