common pattern and shape with real life example very good
http://www.mathbootcamps.com/common-shapes-of-distributions/
hypothesis testing
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http://www.mathbootcamps.com/using-nfl-understand-hypothesis-testing/
he sentence that should catch the eye of any statistics student is the phrase “the ruling on the field stands”. The ref’s are very careful not to say “the ruling on the field was correct” – instead, they elect to say something that implies “we didn’t see enough evidence to overturn the call”. These are two very different things! It is sort of like a court of law. We don’t find people innocent; instead, we find them “not guilty”. In other words, we didn’t see any evidence to change our minds from the assumption that they were innocent.
@Null hypothesis usually the opposite we want to prove. Then we try to gather evidence against so that automatically our claim becomes true.
here is the tricky part. We can never PROVE the null hypothesis is true because we base all of our calculations on assuming it is true. We can only state whether there is evidence against it. Of course, in our football example , the referees probably could actually prove that the original call was correct, but reviewed plays are often a bit borderline (and I’m sure no one wants to say “that other ref was wrong”) so they choose to simply state that there is evidence against the null hypothesis. That is, that there is enough video evidence to make them change their minds about the call. This is the same as saying “we reject the null hypothesis”.
The competing hypothesis is the alternative (H_{a}). We can almost think of this as the hypothesis that “something interesting is happening”. In other words, whatever we want to prove – whether it be that sales are increased by talking to customers or that a certain medicine reduces the number of headaches – will be the alternative hypothesis. When we reject (H_{0}), we are saying there is evidence towards the alternative hypothesis. We are saying that the sample is unique enough under the null hypothesis to make us question it altogether.
When the refs overturn a call, they are saying “we reject (H_{0}), there is evidence towards the alternative hypothesis”. That is, “we have enough evidence to make us question the original call”. In this case, the video was enough to make them seriously question the null hypothesis (that the call was correct).
@However it is NOT to say that alternative is correct, just to say that considerable evidence against null, so alternative likely to be correct, but it is the word likely,not proved.
a small p-value makes you reject the null hypothesis.
http://www.mathbootcamps.com/what-is-a-p-value/
The p-value is actually the probability of getting a sample like ours, or more extreme than ours IF the null hypothesis is true. So, we assume the null hypothesis is true and then determine how “strange” our sample really is. If it is not that strange (a large p-value) then we don’t change our mind about the null hypothesis. As the p-value gets smaller, we start wondering if the null really is true and well maybe we should change our minds (and reject the null hypothesis).
>>>
http://www.mathbootcamps.com/common-shapes-of-distributions/
hypothesis testing
>>
http://www.mathbootcamps.com/using-nfl-understand-hypothesis-testing/
he sentence that should catch the eye of any statistics student is the phrase “the ruling on the field stands”. The ref’s are very careful not to say “the ruling on the field was correct” – instead, they elect to say something that implies “we didn’t see enough evidence to overturn the call”. These are two very different things! It is sort of like a court of law. We don’t find people innocent; instead, we find them “not guilty”. In other words, we didn’t see any evidence to change our minds from the assumption that they were innocent.
@Null hypothesis usually the opposite we want to prove. Then we try to gather evidence against so that automatically our claim becomes true.
here is the tricky part. We can never PROVE the null hypothesis is true because we base all of our calculations on assuming it is true. We can only state whether there is evidence against it. Of course, in our football example , the referees probably could actually prove that the original call was correct, but reviewed plays are often a bit borderline (and I’m sure no one wants to say “that other ref was wrong”) so they choose to simply state that there is evidence against the null hypothesis. That is, that there is enough video evidence to make them change their minds about the call. This is the same as saying “we reject the null hypothesis”.
The competing hypothesis is the alternative (H_{a}). We can almost think of this as the hypothesis that “something interesting is happening”. In other words, whatever we want to prove – whether it be that sales are increased by talking to customers or that a certain medicine reduces the number of headaches – will be the alternative hypothesis. When we reject (H_{0}), we are saying there is evidence towards the alternative hypothesis. We are saying that the sample is unique enough under the null hypothesis to make us question it altogether.
When the refs overturn a call, they are saying “we reject (H_{0}), there is evidence towards the alternative hypothesis”. That is, “we have enough evidence to make us question the original call”. In this case, the video was enough to make them seriously question the null hypothesis (that the call was correct).
@However it is NOT to say that alternative is correct, just to say that considerable evidence against null, so alternative likely to be correct, but it is the word likely,not proved.
a small p-value makes you reject the null hypothesis.
http://www.mathbootcamps.com/what-is-a-p-value/
The p-value is actually the probability of getting a sample like ours, or more extreme than ours IF the null hypothesis is true. So, we assume the null hypothesis is true and then determine how “strange” our sample really is. If it is not that strange (a large p-value) then we don’t change our mind about the null hypothesis. As the p-value gets smaller, we start wondering if the null really is true and well maybe we should change our minds (and reject the null hypothesis).
>>>
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