Hypothesis Testing by Hand: The Significance of a Correlation Coefficient - Part 2

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. Note: the degrees of freedom calculation should have been n-2 and not n-1. Either way, the process is the same.

[@czarinamaen.ricarte2883]

THANK YOU! You saved me from failing my performance task.

[@melonsapphire]

Very detailed, i used to get confused with the calculation before, but not anymore. Thank you so much!

[@MathsAndStats]

No problem MelonSapphire. Please share. Thanks. Jonathan.

[@Elmate_delp]

U did what my materials didn’t. You are the best i got it 100% on the first take.

[@RexEPerez]

i think the df should be n-2

[@MathsAndStats]

Hi RexEPerez. That's correct it should be n - 2. I shall put a note highlighting that. Thanks Jonathan.

[@tanimzaman9233]

Thanx for your in details explanation....

[@patvb3243]

Really great explanation, exactly what I was looking for, Thanks!

[@MathsAndStats]

Just watch the degrees of freedom calculation, I think I did n-1 and it should be n-2 🙂

[@mehmetkazanc5855]

Very Helpful. I finally understand the main story.

[@edgarpedrobalderramagastel1389]

Thank you. Now I understand.

[@cherrylime3540]

thank you so much!

[@huichen6461]

such a wonderful and beautiful lecture. Thank you.

[@ismailabdirahmanmohamoud7048]

thank you so much

[@nchimunyamuloongo4436]

The video was very helpful

[@dinglemingle2546]

your channel is a Gem, do you have a video about the correlation Z-test?

[@mehnaaz4481]

This is very good explanation

[@sampath9044]

Thank you ... That was soo helpful

[@sukhisstylebysukhikaur5657]

It was helpful.
Thankyou sir

[@kushaln5399]

Thanks

[@banushasathi3526]

Thank you so much sir

[@sidraanjum2624]

sooooo helpful

[@nadiahusna5266]

this is really help me for my learning process 👍

[@onyameabasa]

Very helpful

[@emmamelanson3556]

THANK U DUDE

[@hotsincejanuary]

I wish you were my statistics instructor at school

[@PaulNyameteasemusic]

What if you have a negative correlation? How do you calculate the t test for that correlation

[@rakanfadhel9622]

thank you

[@angelarosealbis1728]

what does rho
what does rho=0 in null hypothesis mean in Layman's term

[@MathsAndStats]

Hi Angela, remember that you are trying to infer about a population from a sample. The true population correlation coefficient is rho and the sample correlation coefficient is r. Also, the hypothesis is always a statement about the population parameter. If there was no correlation between both datasets in the population then rho would be zero, indicating no correlation. We then use the sample correlation r as evidence for the value of rho. I hope this helps. Jonathan.

[@angelarosealbis1728]

Maths And Stats I see. Thank you so much! Your video really helped in my exam a while ago. God bless

[@yuenjessie]

i don't understand the(1-r^2), what does it represent ? the not-correlated part?

[@MathsAndStats]

Hi Jessie,
Recall that r^2 represents the amount of variance in the dependent variable that we can understand, hence 1 - r^2 must represent the amount of variance that we do not understand. The rationale for this interpretation comes from a sum of squares ratio - which I have not covered in this video.
Regards
Jonathan

[@yuenjessie]

Thank you for your reply! :-D

[@AbrahamT312Plus]

Can we apply this formula when sample size is more than 200

[@jaykenarn6223]

so if the problem is not about the population then how to write the hypothesis?
Is it still Ho: p= 0 and Ha: p ≠ 0?

[@MathsAndStats]

Hi Jayke. First, hypothesis testing only works when your data has been randomly selected from a larger group. The selected data is called a sample and the bigger group the population. The hypothesis test allows you to infer something about the population by considering only the sample. Maybe provide a little bit more context and I will try respond. Regards. Jonathan.

[@jaykenarn6223]

@@MathsAndStats Hello. Thank you for answering. I just wanted to know when to use μ or p when writing a hypothesis. They kind of confuse of me. And I don't know the right terms to use in order to search the answer in the internet (I have been browsing for a while without getting the answer I am looking for)

[@MathsAndStats]

@@jaykenarn6223 First Greek letters are used for population concepts and English (Latin) symbols for sample characteristics. With that in mind, the hypothesis (null and alternative) is always a statement about a population characteristic and so always includes Greek letters. See the following for a list of symbols and their meanings: www.chegg.com/homework-help/definitions/population-parameter-31 Scroll to the table halfway down. Regards. Jonathan.

[@jaykenarn6223]

@@MathsAndStats I think I understand now sir. Thank you very much.

[@jaykenarn6223]

@@MathsAndStats Thank you very much.

[@metoffice5035]

IT MUST BE n- 2

[@MathsAndStats]

Hi, That's correct and I have updated my comment above to reflect this. Thanks for the comment.

[@joelosuta4573]

i thought it was n-2 df?
just asking.

[@MathsAndStats]

Hi Joel, Yes, that correct. The degrees of freedom should have been n - 2. Good observation. Regards. Jonathan

[@joelosuta4573]

@@MathsAndStats thanks too

[@melg7022]

I was wondering..why did you divide the alpha?

[@nicolleinterior8949]

How to know the rho regards with the sample size right after I get my r?

[@imactuallyleft-handed6168]

Hello, sir will we still use the t distribution table if the sample is over thirty? Or can we use the z-table?

[@joelosuta4573]

use z-distribution

[@khadijajamil4136]

But 0.025 is one tail? There is no 0.025 in One tail

[@Hiwot_Beyene]

ain't the degree of freedom = n-2????

[@jitendranath4058]

DF taken n-1 is wrong it is n-2

[@angelarosealbis1728]

thank you so much