Formula for Cohen's d effect size

valkyerie11

New Member
Help!! I am struggling to figure out the effect size formula ( the spooled part) to get the effect size calculation. I have two groups (55 and 33) both with a SD of 12. I am particularly not understanding the s 2 over 1 part.

i have the main formula: u1-u2/Spooled, but the spooled formula is quite confusing.

(I am a PhD Psych major and this is an adv. stats. class)

I appreciate any help, I am completely stuck until I can get this effect size calculated!

Val

Dragan

Super Moderator
Help!! I am struggling to figure out the effect size formula ( the spooled part) to get the effect size calculation. I have two groups (55 and 33) both with a SD of 12. I am particularly not understanding the s 2 over 1 part.

i have the main formula: u1-u2/Spooled, but the spooled formula is quite confusing.

(I am a PhD Psych major and this is an adv. stats. class)

I appreciate any help, I am completely stuck until I can get this effect size calculated!

Val
Can't you just use this formula (and plug in):

$$d=\frac{\bar{x}_{1}-\bar{x}_{2}}{s}$$

where

$$s=\sqrt{\frac{\left ( n_{1}-1 \right )s_{1}^{2}+\left ( n_{2}-1 \right )s_{2}^{2}}{n_{1}+n_{2}-2}}$$.

valkyerie11

New Member
Thanks for your reply, but isn't the "s" what I have to calculate to finish the 1st formula?

Dragan

Super Moderator
Thanks for your reply, but isn't the "s" what I have to calculate to finish the 1st formula?

Yes, you calculate the "s" using the second formula by using the two different samples sizes (55 and 33) and the variances 12^2 = 144 for both groups.

Once you have "s" from the second formula you plug it into the first formula and solve for Cohen's d.

valkyerie11

New Member
ok, so the sample variances are 144?

I get .0308 if I am on the right track?

u1(54.29)-u2(49.79)=4.5

Dragan

Super Moderator
ok, so the sample variances are 144?

I get .0308 if I am on the right track?

u1(54.29)-u2(49.79)=4.5

I am getting d = 0.379, where s = 11.8629.

valkyerie11

New Member
The professor wanted us to use a s=12 for both, but it looks like I am still way off?

valkyerie11

New Member
Here is my work: 54(144) + 32(144); 7776+4752=12528

divided by 54+32=86

12528/86=145.67

4.5/145.67= .0308

Dragan

Super Moderator
Here is my work: 54(144) + 32(144); 7776+4752=12528

divided by 54+32=86

12528/86=145.67

4.5/145.67= .0308

No, (1) Check 32*144, (2) you divide by 55+33 = 88 (not 86), and (3) you forgot to take the square root.

Look carefully at the formula.

valkyerie11

New Member
yes, i saw I missed the SQ step. But we take N-1(55-1 and 33-1) for both groups which puts us at 86 instead of 88, right?

Dragan

Super Moderator
yes, i saw I missed the SQ step. But we take N-1(55-1 and 33-1) for both groups which puts us at 86 instead of 88, right?
No, again, scroll up and look at the formula. In the denominator it is n1 + n2 which is 88 --- not 86.

valkyerie11

New Member
I see. It looks like the formula in my textbook and yours are different there. But I know how to get there now. I can't thank you enough for your time and patience-you have been a Godsend!

Dragan

Super Moderator
I see. It looks like the formula in my textbook and yours are different there. But I know how to get there now. I can't thank you enough for your time and patience-you have been a Godsend!

It appears that some authors use the N - 2 instead of N in the denominator where n1 + n2 = N. Either way, the effect sizes will be close for large N sizes, however.