Hello everyone,
My question is regarding interpretations of results of ‘association’
statistics when we have 2 categorical variables. In particular, are
interpretations affected by the ‘dimension’ of the contingency table i.e.
for a r x k table with r rows and k columns, does it make a difference to
our interpretation if r < k or r > k?
For example: suppose we have the following 2 x 4 table and we find that
the ‘association’ between the variables is significant.
blue brown green grey
Male F1 F2 F3 F4
female F5 F6 F7 F8
(F1…F10 are frequencies)
If we take ‘sex’ as the independent variable and ‘eye colour’ as the
dependent variable, could we view this association by plotting
F1/(F1+F2+F3+F4) vs F5/(F5+F6+F7+F8) and (separately) F2/(F1+F2+F3+F4) vs
F6/(F5+F6+F7+F8) etc….? as the null hypothesis is ‘that the proportion of
males with blue eyes is the same as the proportion of females with blue
eyes, that the proportion of males with brown eyes is the same as the
proportion of females with brown eyes, that the proportion of males with
green eyes is the same as the proportion of females with green eyes etc…..
Now if we had a 4 x 2 table:
Yes No
Yellow G1 G2
Blue G3 G4
Red G5 G6
Orange G7 G8
(G1….G8 are frequencies)
If we take ‘colour’ as the independent variable and ‘opinion’ as the
dependent variable, could we view the association by plotting G1/(G1+G2) vs
G3/(G3+G4) vs G5/(G5+G6) vs G7/(G7+G8), then (separately) G2/(G1+G2) vs
G4/(G3+G4) vs G6/(G5+G6) vs G8/(G7+G8)?…The null hypothesis would be that
‘the proportion of yellows who answer yes is the same as the proportion of
blues who answer yes is the same as the proportion of reds who answer yes is
the same as proportion of oranges who answer yes and that the proportion of
yellows who answer no is the same as the proportion of blues who answer no
is the same as the proportion of reds who answer no is the same as the
proportion of oranges who answer no.
Many thanks for your help on this,
Kim.
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