Welcome to our lesson
on Cohen's standards for small, medium
and large effect sizes.
Cohen's d, named for the United States statistician,
Jacob Cohen is a measure of the distance
between two means measured in standard deviations.
The calculated value is then compared
to Cohen's standards of small, medium
and large effect sizes shown in the table below.
And keep in mind these are just guidelines.
A small size of effect has a d value of approximately 0.2,
a medium size of effect has a d value approximately 0.5
and a large size of effect has a d value of 0.8 or more.
So again, keep in mind these are just guidelines
and the sign of Cohen's d tells the direction of the effect.
So for example if the d value is positive,
the distribution may be considered as a larger mean,
if the d value is negative,
the distribution being considered has a smaller mean.
And now take a look at the formulas.
Cohen's D is the measure of the difference
between two means divided by the pooled standard deviation.
So we have d equals the difference of x bar sub one
and x bar sub two divided by the pooled standard deviation.
And we have two formulas for the pool standard deviation,
one for unequal group sizes and one for equal group sizes.
Before we take a look at an example,
let's take a look at an animation.
Right now we have two distributions with the same mean
and we will see how changing the value of d
changes the distribution being considered.
So notice how as d increases the distribution may considered
has a larger mean which we see here
where the blue distribution is moving toward the right.
So here's a d value of 0.2 which is considered small,
we change d to 0.5,
this is considered a medium effect, notice how the mean
has changed from 70 to 75
and if we set d equal to 0.8,
we have what's considered a large effect
where in this case the mean has increased from 70 to 78.
Notice how when d is equal to one,
the distribution considered
has a mean one standard deviation larger
than the original distribution where you can see here,
the standard deviation or post inner deviation
is 10 since 80 minus 70 is equal to 10.
And notice how nd is negative
the distribution being considered has a smaller mean.
Let's take a look at an example.
We're asked to calculate Cohen's d
is the size of effects, small, medium
or large explain what the size of the effect of means
for this problem.
So here we ask them data from our previous problem
where we have one sample where the sample size is 11,
the sample mean is four
and the sample standard deviation is 1.5.
For the second sample, the sample size
is n the mean is 3.5
and the sample standard deviation is one.
We'll begin by determining the pooled standard deviation
for an unequal group sizes because we have a sample size
of 11 and the sample size of nine.
And I've already set this up on the next slide
where I've replaced n sub one and s sub one
with n sub a and s sub a
and n sub two and s sub two with n sub b and s sub b
which has already shown here and below,
taking the square to this quotient
gives us approximately 1.3017
which I've already calculated here.
Now that we have the pool of standard deviation,
we now find the difference of the means
and divide by the pooled standard deviation.
So letting x bar sub one equals x bar sub a
and x bar sub two equal x bars of b,
Cohen's d is equal to the quantity four minus 3.5 divided
by 1.3017 which is approximately 0.384.
Notice how this value
is between the small and medium effect
and since it doesn't reach the medium effect,
we will say the effect is small because 0.384
is between Cohen's value of 0.2 for a small effect size
and 0.5 for medium effect size.
The size of the differences of the means
is small indicating there
is not a significant difference between them.
I hope you found this helpful.