PMCC Hypothesis Testing - Question 8b (help)

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TheoP31
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Hi,

Just a little stuck with the first part of Q8b (posted below),

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"What would be the p-value?"

Okay, so I think that the p-value is still going to be 0.032. But I'm also curious as to whether it would be ±0.032 ? I'm pretty sure it isn't ± the p-value, since the p-value is specific to a set of data. So is this question just a trick question? The value stays the same, right? p=0.032 !

Thank you,
Theo
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mqb2766
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I suspect the original (part a) is a one sided test, so to go to a two sided test (part b), you'd double the p.
https://online.stat.psu.edu/stat501/lesson/1/1.9
Need to go over it properly in the morning though.
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TheoP31
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(Original post by mqb2766)
I suspect the original (part a) is a one sided test, so to go to a two sided test (part b), you'd double the p.
https://online.stat.psu.edu/stat501/lesson/1/1.9
Need to go over it properly in the morning though.
Yes, part (a) is one sided! Are you sure you double the p-value? I haven’t learnt that tbh.
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Hazzz01
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(Original post by TheoP31)
Yes, part (a) is one sided! Are you sure you double the p-value? I haven’t learnt that tbh.
For two-tailed tests, you're considering both ends of the tail so you'd need to double the areas: 2(0.032) = 0.064. Remember, p-value is the probability of getting the observed result or something more extreme so you need to add both the negative and the positive +-0.032 and bcos the areas are the same u can just double it.
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TheoP31
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(Original post by HS_1)
For two-tailed tests, you're considering both ends of the tail so you'd need to double the areas: 2(0.032) = 0.064.
Oh I didn’t think the p-value was an “area” in PMCC. Our teacher just told us it represents how correlated two things are.
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TheoP31
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(Original post by HS_1)
For two-tailed tests, you're considering both ends of the tail so you'd need to double the areas: 2(0.032) = 0.064. Remember, p-value is the probability of getting the observed result or something more extreme so you need to add both the negative and the positive +-0.032 and bcos the areas are the same u can just double it.
Ah okay, thank you! Kind of makes sense.
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Hazzz01
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(Original post by TheoP31)
Oh I didn’t think the p-value was an “area” in PMCC. Our teacher just told us it represents how correlated two things are.
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I don't know if there's a misunderstanding here but the pmcc r value represents the linear correlation between two variables where -1<r<1.
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mqb2766
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(Original post by TheoP31)
Oh I didn’t think the p-value was an “area” in PMCC. Our teacher just told us it represents how correlated two things are.
The p value takes into account both the correlation AND the number of data points. The latter is "ignored" if you just think of the strength of coorelation. 2 points are perfectly linearly correlated but the relationship has little significance. It's a hypothesis test, testing whether the correlation parameter is significantly non zero.
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TheoP31
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(Original post by HS_1)
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I don't know if there's a misunderstanding here but the pmcc r value represents the linear correlation between two variables where -1<r<1.
Ah okay, makes sense.
So is PMCC a probability or not?
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TheoP31
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(Original post by mqb2766)
The p value takes into account both the correlation AND the number of data points. The latter is "ignored" if you just think of the strength of coorelation. 2 points are perfectly linearly correlated but the relationship has little significance. It's a hypothesis test.
Okay, kind of makes sense. Thanks.
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Hazzz01
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(Original post by TheoP31)
Ah okay, makes sense.
So is PMCC a probability or not?
I mean, the pmcc is just a number between -1 and 1 and tells you how strong the correlation is between ''x'' and ''y''. I don't know if it'd be classed as a probability?
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TheoP31
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(Original post by HS_1)
I mean, the pmcc is just a number between -1 and 1 and tells you how strong the correlation is between ''x'' and ''y''. I don't know if it'd be classed as a probability?
Okay okay, thank you. It’s just that you sent a picture of a normal distribution before, when explaining PMCC.
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mqb2766
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(Original post by TheoP31)
Okay okay, thank you. It’s just that you sent a picture of a normal distribution before, when explaining PMCC.
The estimated correlation coefficient is a statistical quantity.
Its value is uncertain because it's based on limited data and as such has an associated pdf. We assume it's a normal pdf.
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(Original post by TheoP31)
Okay okay, thank you. It’s just that you sent a picture of a normal distribution before, when explaining PMCC.
also to edit my last post: pmcc r value can be negative so it obvs cannot be classified as a probability since probabilities are always positive. Also, sorry abt tht! tht was supposed to be for the two tailed test explanation so you can see on the diagram that the critical values are -1.96 and 1.96 and the areas are the same on each side.
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TheoP31
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(Original post by mqb2766)
The estimated correlation coefficient is a statistical quantity.
Its value is uncertain because it's based on limited data and as such has an associated pdf. We assume it's a normal pdf.
Ohh okay that makes sense, thanks!
But what do you mean by pdf? Distribution?
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TheoP31
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(Original post by HS_1)
also to edit my last post: pmcc r value can be negative so it obvs cannot be classified as a probability since probabilities are always positive. Also, sorry abt tht! tht was supposed to be for the two tailed test explanation so you can see on the diagram that the critical values are -1.96 and 1.96 and the areas are the same on each side.
Ohhh I get you! Okay thank you.
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mqb2766
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(Original post by TheoP31)
Ohh okay that makes sense, thanks!
But what do you mean by pdf? Distribution?
Yes probability distribution function (normal-bell) curve.

To think about it, imagine drawing another data set and estimating the correlation coefficient (again). You'd get a different, but similar, value. Doing this repeatedly would give the associated (normal) pdf, centred on the true correlation coefficient. You want to check that this distribution, which represents the estimation process, is significantly shifted away from zero. Or zero is in the tail(s) of the distribution.
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TheoP31
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(Original post by mqb2766)
Yes probability distribution function (normal-bell) curve.

To think about it, imagine drawing another data set and estimating the correlation coefficient (again). You'd get a different, but similar, value. Doing this repeatedly would give the associated (normal) pdf, centred on the true correlation coefficient. You want to check that this distribution, which represents the estimation process, is significantly shifted away from zero. Or zero is in the tail(s) of the distribution.
Ahhh, I’m not the best at statistics but that does make some sort of sense to me! Thank you!
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TheoP31
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Thank you to mqb2766 and to HS_1 for the help on this! It is much appreciated!
I would give you guys a load of “thumbs up” but apparently I can only do 1 every so often.
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Hazzz01
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(Original post by TheoP31)
Thank you to mqb2766 and to HS_1 for the help on this! It is much appreciated!
I would give you guys a load of “thumbs up” but apparently I can only do 1 every so often.
no worries! Also if u need help w applied maths check out: mathsgenie & Haberdashers' Adams Maths Dept (both are yt channels and are kinda more tailored towards Edexcel spec if ure doing tht? if not, it's still worth checking out.)
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