Question

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?

Answer 1

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.

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:
`\mu_(1) \leq \mu_(2)`

Alternative hypothesis:
`\mu_(1) > \mu_(2)`

The statistic for this test is given by:

`t=\frac{\bar X_(1)-\bar X_(2)}{\sqrt{(s^2_(1))/(n_(1))+(s^2_(2))/(n_(2))}}` (1)

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

And the degreed of freedom are calculated from:

`df=n_1 +n_2 -2 =20`

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.