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Thread: Formula for Cohen's d effect size

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    Exclamation Formula for Cohen's d effect size




    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

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    Quote Originally Posted by valkyerie11 View Post
    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}}.

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

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    Quote Originally Posted by valkyerie11 View Post
    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.

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    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

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    Quote Originally Posted by valkyerie11 View Post
    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.

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

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    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

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    Quote Originally Posted by valkyerie11 View Post
    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.

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    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?

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    Quote Originally Posted by valkyerie11 View Post
    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.

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    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!

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    Quote Originally Posted by valkyerie11 View Post
    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.

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