Joshua conducted an independent samples t-test and found t(20) = 10.25, p < .05. he then calculated his effect size and obtained a value of d = 0.05. what should joshua say in the reports on his results?

On this case since the p value is less than 0.05 then the results are significant. So then Joshua can say that the t-test conducted is significant. And on this case makes sense report the effect size.

Step-by-step explanation:

Effect size is defined as a "quantitative measure of the magnitude of the experimenter effect". If we have a high value for the effect size then we can conclude that we have a stronger relationship between two variables.

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

The independent t-test, is an statistical test in order to determine if we have statistically significant difference between the means of two unrelated groups.

We can check for example the following hypothesis:

Null hypothesis:

Alternative hypothesis:

The statistic for this test is given by:

(1)

The value obtained after apply the formula (1) was 10.25.

And the degreed of freedom are calculated from:

On this case since the p value is less than 0.05 then the results are significant. So then Joshua can say that the t-test conducted is significant. And on this case makes sense report the effect size.

Usually when the Cohen effect size value d=0.2 or lower we can consider this as a 'small' effect size, and that's our case.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!