Hello everyone
I would be grateful for any comments on the following.
Say we have 2 categorical variables and we use the appropriate statistic to
get an indication of the association them (by observing exact p values). I
would like to know if the following is the best way to display this
information pictorially:
Say if we have the following scenario
Yes No
Male 250 250
Female 5 10
1.From the above table, for this sample, 50% of males answer yes and 50%
answer no; 33% of females answer yes and 66% of females answer no.
2.Alternatively 98% of those answering yes are male and 2% of those
answering yes and female; 96% of those answering no are male and 4% of those
answering no are female.
Using 2. (above) we could not say that this indicates that more ‘yes’ votes
come from males: there are merely more males in the sample! Therefore we
could not plot say a histogram with bars corresponding to 98% for male and
2% for female as this would give a false picture of the male and female
comparison.
Wouldn’t it be best to view this by plotting the proportion of males who
answer ‘yes’ (50%) and the proportion of females which answer ‘yes’ (33%)
and compare the height of the bars? This is what a chi square test does
according to Siegal and Castellan.
Am I correct in thinking that we should always employ this tactic when
trying to demonstrate the relationship between two cross-tabulated
categorical variables? I.e. in the following table
C D
A F1 F2
B F3 F4
We should look to see if the proportion of individuals with variable A which
are in category C is the same as the the proportion of individuals with
variable B which are in category C; and the proportion of individuals with
variable A which are in category D is the same as the the proportion of
individuals with variable B which are in category D.
Many thanks for your help,
Kim.
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