T-stat

[mheithy]

Can someone explain to me the intuition behind the t-stat formula… r[sqrt(n-2)]/[sqrt(1-r²)]? I would like to know how its actually calculated and derived

[S2000magician]

I do so wish that candidates would stop talking about _ intuition _. You don’t want intuition (which is reaching a conclusion without understanding the reason why); you want understanding.

Here’s the understanding:

_r_√(n − 2) / √(1 − r²)

= r / [√(1 − r²) / √(n − 2)]

= (r − 0) / [√(1 − r²) / √(n − 2)]

= (r − 0) / √[(1 − r²) / (n − 2)]

This is how you see a normal t-statistic:

• r is the calculated value for the correlation
• 0 is the hypothesized value for the correlation
• 1 − r² is the variance for the calculated value
• n – 2 is the number of degrees of freedom
• √[(1 − r²) / (n − 2)] is the standard error

So the t-statistic is:

(calculated value − hypothesized value) / standard error

[mheithy]

thanks for the response, really cleared things up for me

[S2000magician]

You’re welcome.

[tickersu]

@S2000magician

I do so wish that candidates would stop talking about _ intuition _. You don’t want intuition (which is reaching a conclusion without understanding the reason why); you want understanding.

Here’s the understanding:

_r_√(n − 2) / √(1 − r²)

= r / [√(1 − r²) / √(n − 2)]

= (r − 0) / [√(1 − r²) / √(n − 2)]

= (r − 0) / √[(1 − r²) / (n − 2)]

This is how you see a normal t-statistic:

• r is the calculated value for the correlation
• 0 is the hypothesized value for the correlation
• 1 − r² is the variance for the calculated value
• n – 2 is the number of degrees of freedom
• √[(1 − r²) / (n − 2)] is the standard error

So the t-statistic is:

(calculated value − hypothesized value) / standard error

Glad to see you typing it in a more palatable way than I have been :P. This is one of the big reasons the prep companies, and the CFAI fail at their stats sections. They miss simple opportunities to explain ideas that could be far less complicated.