Hypothesis Testing by Hand: The Significance of a Correlation Coefficient - Part 1
Вставка
- Опубліковано 9 лют 2025
- This short video details the steps to be followed in order to undertake a Hypothesis Test for the significance of a Correlation Coefficient. In particular, we test the significance of a Pearson Correlation Coefficient, with that said; the test is similar to that for a Spearman Correlation Coefficient. Small error: Df should be n - 2 and not n -1.
Hi Guys, just be a little careful, as correctly pointed out by Venkiah and Onkoka, below; the degrees of freedom should have been (n-2), and not (n-1). Thanks guys.
Sir i have a question ..
That
If null hypothesis is accepted than is there a correlation between 2 variables?
Please urgently reply me ..i have a need of your support
Sir i am waiting for your kindness
in computing test statistics... is it also ok to use 1 - r squared as a denominator?
Kindly if I want to know in a scenario where by your given a question but you have to know which side is Y and which side is X
You're really great at what you do. I've watched a few of your videos now and noticed that your explanations are some of the best. You also use the proper symbols which is comforting as a confused stats student. Thanks for making these helpful videos! 😎
Hi jaa-snickers,
Thank you for those kind words it is really appreciated.
Regards.
Jonathan
listening to you saying correlation coefficient makes me chuckle! better than me though with my thick lisp. Great video!
Why do we use df=n-2 in linear correlation unlike in normal hypothesis testing? Is it because we are dealing with two variables?
Thank you very much mister for this very informative and wonderful guide. I would just like to ask if this does work for spearman rank correlation too?
Hi Henry. The same test statistic is used for Spearman rank correlations. Just substitute your Spearman correlation in place of the Pearson correlation. Regards. Jonathan
the r in the problem i am doing is a negative number. What do I do?
Hello sir, significance of multiple correlation coefficient is tested by which test?
Rpa=0.8 ( portfolio size ) Ria=0.3 ( age ) given Rpi=0.7 ( income level ) , n=63 . How could we test that on a 0.05 level? Where R = pearson correletion coefficient , thanks
Very nicely explained. But I have some doubt here. You are dealing with 2 variables, then how can you have (n-1) degrees of freedom. Isn't it supposed to be (n-2) DF.
Very good video indeed, but I think the df is (n-2) as you have rightly observed. Thanks
Hi Venkiah, Hi Onkoka. That's correct the degrees of freedom should have been calculated as (n -2) and not (n-1). A rush of blood to the head I'd say. Thanks again guys. Jonathan.
How do you take p=o and not egaul to zero rather the greater then equal to and less than ....I mean how do you get that you need to take it p = 0
Hi Khadija. We are testing to see if there is evidence of a correlation in the population. As such the null position is to assume that there is no correlation, rho = 0 (population correlation = 0).
@@MathsAndStats thnkyou so much
Really helpful 😍😍, thank you sir
Thanks
Hi Jonathan, thanks for the video. Just wondering, as in your example, you rejected the Null. But if my critical value is bigger than my t value does it reject the Alternative then instead? I'm not quite sure how to phrase it.
Hi Dylan. No is the quick answer. Frist thing, we can only ever reject the null in favour of the alternative. When we fail to reject the null that doesn't mean that we accept it. Don't forget we have assumed that the null is true t the start of our experiment, just because we have not found evidence to suggest that it's false doesn't make it true.
So to phrase it depends on your accepted reporting style, maybe something like this (I'm assuming a test of correlation, and a sample size of n = 57, therefore my degrees of freedom are n - 2 = 57 -2 = 55):
A Pearson Product Moment Correlation was undertaken to ascertain the strength of the association between attendance at lectures and exam performance. A strong association was observed at the 5% level of significance (r(55)= .78, p =.02).
I hope this helps.
hi, i want to ask if the question like "test the hypothesis H0:p=0", how can i know this test is two tailed or one tail?
It is all dependent on the H1. If we believe that the absolute value of the correlation is more than 0, then it can only be a one sided tail, but if our H1 states that p is not equal to 0, it means that our p is either less than zero or more than 0, meaning that it's a two tailed test. Hope this helps.
in the critical value graph with the bell curve, why did you have to divide ALPHA by 2?
I don't know if you still need this considering you madd this comment three years ago😂but it's because it's a two tail test, so the significance level needs(alpha) needs to be divided by two
Hi can you help me with statistics?
Hi Shallon. Have you got specific questions? Regards. Jonathan.
Thank you
Why is it p=0 and not r=0? I'm so confused.
Hi Anxiety San.
The reason is that we are using sample statistics to infer something about the population parameter. Let me explain:
First, a hypothesis is always a statement about a population parameter.
Second, we use different symbols for population parameters compared to sample statistics. (UA-cam doesn't allow math symbols so I'll spell them).
Consider the mean: mu for population, x_bar for sample
Consider the variance: sigma_squared for population, s_squared for sample
Consider the correlation: rho for population, r for sample
So in his video we are testing a correlation coefficient. In particular, the population coefficient rho (which we don't know). We take a sample and calculate the sample correlation r. We use that in the test statistic.
I really hope this helps. Kindest regards. Jonathan.
Is your critical value 5% or 2.5%?
Hi John. The test that we undertook was a two-tailed test, as I just wanted to show that the correlation coefficient was different to zero so either r < 0 or r > 0. And so I did a two-tailed test, with a two-tailed test your chosen significance level is split into both tails; in this case, 0.025 is placed in both tails. Just keep an eye on the degrees of freedom, they should be n - 2, I think I picked n - 1.
I got r to be 0.032 even after repeating twice...how did you get 0.94
Hi Arielle, I have sanity checked the calculation and all seems to be good. I also sanity checked in Excel and got a correlation coefficient of 0.93592614, which agrees with my result in the video.
I would suggest that you compare your calculations step-by-step with those within the table and also from the formula. a small mistake in the calculations can result in a massive difference in the correlation coefficient.
I hope this helps, and please let me know if you find your error.
Regards.
Jonathan
@@MathsAndStats sorry, my bad. I have seen where I missed it. I have repeated now and gotten 0.94. Thanks 🤗
Why rho is 0?
Hi 니헤야,
Rho does not have to be zero, with that said in this case we are testing to see if what we observed provides evidence to suggest that Rho is not zero. Remember that Rho is the true population correlation, and no true correlation between the two variables would mean that the population correlation is zero. So, in this case we are testing to see if our evidence, observations from the population (sample), suggests that the true population correlation is different to zero.
Does this help?
Jonathan
This started out so simple then it became complicated☹️
HI!! WHAT'S "P"/
Hi Daniella, Do you mean rho? If so it is the true population correlation coefficient that we are trying to infer. If you mean the p = 0.025 listed in the tables, this is to calculate the critical value that has 0.025 of the area under the curve to its right.
That answer possibly didn't cover your question, if you can give me a bit more information and maybe the minute within the video where I mention it. I cannot see 'P' listed anywhere in the video.
I look forward to your reply. Kindest Regards.
Jonathan