## effect size relative to raw score but not difference score

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## effect size relative to raw score but not difference score

Hi, I would like to know is there any way to calculate effect size relative to raw score instead of difference score, in a paired-sample t-test.

I know the typical way to calculate Cohen's d for paired-sample t-test is to divide mean difference for difference score by standard deviation of difference score. So actually the effect is relative to difference score instead of raw score.

I found it seems to be able to calculate Cohen's d relative to raw score instead of difference score and would like to know the detail about how to do it. Does anyone know it?

from an online jamovi user-guide: https://www.learnstatswithjamovi.com/
on page 272:
"To the extent that you care about the practical consequences of your research, you often want to measure the effect size relative to the original variables, not the difference scores (e.g., the 1% improvement in Dr Chico’s class over time is pretty small when measured against the amount of between-student variation in grades), in which case you use the same versions of Cohen’s d that you would use for a Student or Welch test. It’s not so straightforward to do this in jamovi; essentially you have to change the structure of the data in the spreadsheet view so I won’t go into that here, but the Cohen’s d for this perspective is quite different: it is 0.22 which is quite small when assessed on the scale of the original variables."

Firstly, I don't quite understand "against the amount of between-student variation in grades"?

Secondly, I can't find the jamovi file mentioned in note 12: "If you are interested, you can look at how this was done in the chico2.omv file" (I would like to see how to "change the structure of the data")

Thanks a lot!
Nat

Posts: 5
Joined: Sat Mar 20, 2021 7:16 am

## Re: effect size relative to raw score but not difference sco

i'm not actually sure myself, but perhaps someone else will weigh in.

cheers

jonathon

jonathon

Posts: 1689
Joined: Fri Jan 27, 2017 10:04 am

## Re: effect size relative to raw score but not difference sco

Hi, @Nat.
In the text you are referring to (David Foxcroft, 2019) you have found the hint you need.
Use an Independent Samples T-Test.
To do this from jamovi, you need to switch the wide mode of your sheet data to a long mode, so you can apply an "Independent Samples T-Test".
This means that a single variable will have to report the data measured in the two different times, while a new variable (eg Time) will report the reference to the measurement time (eg: 1 and 2 or pre and post).
This change from wide to long will lead to a doubling of cases with their ID.
Take a look at the attached screenshot.
For the data referenced in the book, you missed this link: https://www.learnstatswithjamovi.com/#data

Cheers,
Maurizio
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MAgojam

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Location: Parma (Italy)