# PMCC Hypothesis Testing - Question 8b (help)

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Hi,

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

"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

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

"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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#2

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.

https://online.stat.psu.edu/stat501/lesson/1/1.9

Need to go over it properly in the morning though.

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(Original post by

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.

**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.

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#4

(Original post by

Yes, part (a) is one sided! Are you sure you double the p-value? I haven’t learnt that tbh.

**TheoP31**)Yes, part (a) is one sided! Are you sure you double the p-value? I haven’t learnt that tbh.

Last edited by Hazzz01; 3 months ago

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(Original post by

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.

**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.

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(Original post by

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.

**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.

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#7

(Original post by

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.

**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.

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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#8

**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.

Last edited by mqb2766; 3 months ago

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(Original post by

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.

**HS_1**)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.

So is PMCC a probability or not?

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(Original post by

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.

**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.

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#11

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(Original post by

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?

**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?

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#13

(Original post by

Okay okay, thank you. It’s just that you sent a picture of a normal distribution before, when explaining PMCC.

**TheoP31**)Okay okay, thank you. It’s just that you sent a picture of a normal distribution before, when explaining PMCC.

**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.

Last edited by mqb2766; 3 months ago

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#14

**TheoP31**)

Okay okay, thank you. It’s just that you sent a picture of a normal distribution before, when explaining PMCC.

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(Original post by

The

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.

**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.

But what do you mean by pdf? Distribution?

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(Original post by

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.

**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.

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#17

(Original post by

Ohh okay that makes sense, thanks!

But what do you mean by pdf? Distribution?

**TheoP31**)Ohh okay that makes sense, thanks!

But what do you mean by pdf? Distribution?

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.

Last edited by mqb2766; 3 months ago

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(Original post by

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.

**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.

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#20

(Original post by

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.

**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.

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