# 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.