Hello, this is Dr.. Grande welcome to my video when calculating the effect size after a man whitney you test in
Spss as
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[I] have here in the data Editor an Spss fictitious data. I'll be using for this example
I have an independent variable named treatment and has two levels psyChodynamic therapy and treatment as usual and
Then I have two
dependent variables
one is named depression and the other substance use and we can assume these scores come from a
psychometric instrument designed to capture these constructs
so we want to determine if there's a difference between
the psychodynamic group and the treatment as usual as
Measured on each of these dependent variables, and we'll assume this is going to be done with separate tests
So not a manova not including both dependent variables at the same time
but rather
like a t-test for
[the] depression dependent variable and a t-test for the substance use
however, what happens if we violate the assumptions for t-test in
That instance we would use a Mann-whitney [u] it's the non parametric
alternative to a t-Test
So with these variables in this example if I go to analyze
descriptive statistics and explore I
Move treatment over to the factor list it's an independent variable and depression and substance use over to the dependent list
under Plots
Uncheck stem-And-leaf check off histogram and check off normality plots with tests
click continue, so what I'm testing for here is to see if the
dependent variables are
Normally distributed for each level of the independent variable which would be an assumption
Of a t-test all right that's an assumption for t-test in this case
We're going to violate that assumption
After interpreting the results of Shapiro wilk so the output here
I'm moving down to the test or normality we have the [coma] [groff] smirnoff and Shapiro will kind of using Shapiro wilk here
and we can see in this table, the
null hypothesis for this test Rapira wilk [is] that the
Scores in the dependent variable were sampled from a normal distribution
So in order to assume that the data and dependent variable are normally distributed
We would need to fail to [reject] the null hypothesis
and that would mean we'd have a non statistically significant finding as we do here for treatment as usual and depression and
psyChodynamic substance use point 1 1 0 is above point 0 5 and point 0 5 7 is above [0.005]
So those are not statistically significant, and we would fail to reject the null hypothesis
So we would retain the null hypothesis and say that those scores were sampled from a normal distribution however
for psychodynamic
Depression and
treatment as usual
substance use
We have a statistically significant finding in both these cases
point 0 1 4 and point 0 4 2 [is]
Statistically significant so in this case we would reject the null hypothesis that the scores were sampled from the normal distribution
so in instance like this if we make the assumption that we have failed to
Meet the Normality assumption for [t-test]
We would conduct a Mann-whitney U and to do that. We'll go to
analyze
nonparametric tests legacy dialogues
to
independent samples and
under this two independent samples tests [dialogue]
notice the Mann-whitney U test is checked off by default and
Here we would have
treatment as the grouping variable
the
independent variable and
Depression and substance use so this is two separate tests
this is to
Mann-Whitney U tests this as I mentioned for this isn't combining these variables as we would in Manova
Now here for in this dialogue. We're going to need to
Define the groups so how do we know?
What values to use here for?
[group] [one] and group [two]
So I close out of this go back to the data editor up here. There's a
1k on the Ribbon you [can] see
psyChodynamic is coded as zero and
Treatment as usUal is coded as one
you could also go to the variable view and
See it under values 0 equals pSyChodynamic 1 equals
treatment as usual
so going back to
the
Mann-Whitney U
treatment in the grouping variable
Depression substance use in the test variable list now. We go to Define groups. We know the group 1 is 0
Group 2 is 1
Click continue, and then
[Click] ok
So of Interest here will be the results of Mann-Whitney u
specifically the [P] [value]
for depression and for substance use
And we can see that for depression. We fail to reject the null hypothesis. It's
0.36 1
So here we assume
there is no difference between the groups between
psychodynamic and treatment as usual as measured on a dependent variable depression for substance use however we have a
statistically significant result point 0 0 0 0 1 1
We would reject the null hypothesis and assume
there is a difference between the psychodynamic and treatment as usual levels of the independent variable treatment as measured on the
Substance use variable so from this point. How do we calculate the effect size?
We have [the] [P-value]
We know we have a non statistically significant finding for depression and a statistically significant finding for substance use
But we don't have the effect size
so moving over to excel I
have
built out this excel worksheet
So we can calculate the effect size and the effect size
I'm going to use here is R equals z divided by the Square [root] of N, and?
I'll also show you how to calculate R
Squared in two different ways so first I'm going to collect the values. I need for this table to the left
So for the depression variable I move back to the output
See that the z-Score is negative point nine one for
negative point nine One four
So I'll enter that in
To the Z-Score z squared will be equal
sign and then [the] z-Score
shift six for Carat and then two so z squared and we know from the
Example, it's 50. The sample size is 25 in each group. It's 50 and the square root of n [the] equal sign s
[qrt], and
then
selecting the
Sample size 50 it's 7.07 so moving back to the output we can see here under ranks
the
Total for Depression 50 and the total for substance use is 50 as well
So now to calculate the effect size [for] the depression variable. I'm moving over [here] to sell G for
We can see we have the equation r equals z divided by Square root of n. [so] this will be equal sign?
z
Divided by the Square root of n. Here in cell D5
that effect size is
negative
0.12 so what about the effect size for the substance use variable well? We'll just do the same thing except using the
z score
from the Mann-Whitney U results table for substance use and
The sample size from Substance use which of course is the same?
in this example going back to the output
the z-score for substance use
negative four point three nine four
I'm up here negative four point three nine four and I
Don't need to make any changes to the sample size. We have an effect size of negative
[0.62]
So this is to calculate R. This is the value of R. What about r-Squared well, you can just
[square] the value have here all right, so I do that [it's] equal sign
negative
0.62
shift six for the carrot, [too]
so point three eight or
We could use the equation z Squared divided by N
So it'd be equal sign
z squared from over Here d [three]
divided by the sample size
50
It's the same value
38.6%
so this is R squared it's also a two squared in this case and
It means that
Thirty-eight point six percent of the variance in the dependent variable in this case substance-use can be explained by the independent variable I
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