odds ratio: calculation unclear

[stats2019]

Hi,

I am looking at the hypothesis, that there is a difference between gender and group membership to "hxTypAchiever".
It looks like this:


The problem (for me) is, that I assumed, that the probability to belong to the hxAchiever group for male people is .552 of that for female.
I come to this interpretation, because male is the group shown left (before) female in the contingency table.That makes me assume odds ratio displays male-to-female-relation.
I used Field[1], section 19.8.4 to calculate the odds ratio by hand (Excel):

The first (top) calculation shows male-to-female relation, the second (bottom) female-to-male.
As you can see, the odds ratio calculated by jamovi is actually the one of female-to-male.

How does the user know, which way is calculated without recalculating by hand? I would think, this is knowledge needed for meaningful interpretation and should maybe be shown somewhere.


[1] Field, A. (2018). Discovering statistics using IBM SPSS statistics (5. Aufl.). Los Angeles: SAGE.

Olaf

[jonathon]

oh yup, seems like a footnote is in order ... you can create an issue on gh

with thanks

jonathon

[stats2019]

Hi,

done: https://github.com/jamovi/jamovi/issues/882

Olaf

[MAgojam]

Hi Olaf.
Sorry if I recall things that are already in your knowledge.

In Jamovi, as in other software, for a 2x2 table, the Odds ratio is calculated with the rule:
OR = (a / b) / (c / d) = (a * d) / (c * b)
In your data you find an OR = 0.552, this is because in the 4 cells of the table you have the observations given by these combinations:
(a) hxTypAchiever (0 = no) and Sex (0 = male)
(b) hxTypAchiever (0 = no) and Sex (1 = female)
(c) hxTypAchiever (1 = yes) and Sex (0 = male)
(d) hxTypAchiever (1 = yes) and Sex (1 = femmia)

An OR value greater than 1 is more readable than one lower than 1 as in the data and to read it in terms of males towards females you should do the reciprocal and read it in the hxAchiever group (yes).
In jamovi just go to DATA -> Setup -> DATA VARIABLE -> hxTypAchiever, select the line in Levels with (1 = yes) and with the arrow (up or down) move it to the first line of the list.
See the screenshot.

ScreenShot.PNG (90.97 KiB) Viewed 5247 times

You will get an Odds ratio = 1.81.
That is to say that in this sample the males have a 1.81 probability of belonging to the yes hxTypAchiever group of the females.
If you don't change the positions in Levels for hxTypAchiever, you can do it for Sex, taking the females to the first level and you will have the same OR = 1.81.
That is to say that in this sample the females have a 1.81 probability of belonging to the no hxTypAchiever group of males.

Cheers,
Maurizio