Hypothesis: The effect of gender on helping family members is stronger in urban areas than in rural areas. In more detail: we expect that both in rural and in urban areas women are more likely to help family members than men but the difference between men and women is bigger in urban areas.
RECODE gndr (1=0)(2=1) INTO gndr_dummy.
VARIABLE LABELS gndr_dummy ‘Gender dummy’.
VALUE LABELS gndr_dummy 0’Male’ 1’Female’.
fre gndr gndr_dummy.
RECODE domicil (1 2=1)(3 thru 5=2) into domicil_dummy.
VARIABLE LABELS domicil_dummy ‘Big city or outskirts vs not big city’.
VALUE LABELS domicil_dummy 1’Big city or outskirts’ 2’Not big city’.
fre domicil domicil_dummy.
RECODE hlpfmly (1=0)(2=1) into hlpfmly_dummy.
VARIABLE LABELS hlpfmly_dummy ‘Looking after’.
VALUE LABELS hlpfmly_dummy 0’yes’ 1’no’.
fre hlpfmly hlpfmly_dummy.
CROSSTABS hlpfmly_dummy BY gndr_dummy BY domicil_dummy /CELLS=COLUMN /STATISTICS=CHISQ LAMBDA RISK.
Epsilon (big city):5,6-7,6=-2 percentage point
Epsilon (not big city): 6,9-10,9=-4 percentage point.
Note: you have to see the absolute value of the epsilons to determine the effect size.
In urban areas, the proportion of those who look after family members
is 2 percentage points lower among men than among women. So, in urban areas the effect size of gender on helping family members is -2 percentage points.
In rural areas, the proportion of those who look after family members is 4 percentage points lower among men than among women. So, the effect of gender on looking after family members in rural areas is -4 percentage points.
The difference of epsilons:
So, here you have to subtract the two epsilons
4-2=2 percentage point
The difference between men and women is 2 percentage points
higher in small cities than in big cities.
The second-order odds ratio:
(comparing big cities to not big cities):
It shows: How many times is the effect of the independent variable
larger/smaller by different values of the new variable (small/big city)?
The second-order odds ratio: 0,719/0,602=1,194
In big cities the effect of gender on helping family members and others
is 1,194 times as high as in small cities.
-> see: big cities is in the numerator,
so we compare big cities to small cities in the interpretation.
In cases where the odds ratios in the categories of the third variable are lower than 1 it is difficult to interpret the second-order odds ratio. In this example 0,719 shows a smaller effect size than 0,602. So, the ratio of the two numbers show a number which is higher than 1 but here we cannot interpret this as the effect is bigger in the category in the numerator.
When both the odds-ratios are below 1 then we have to interpret the second-order odds ratio saying that the effect of gender on helping family members is 1,194 times as high in small cities as in big cities. So, we are interpreting not for the nominator, but the denominator.
Conclusion: Among those who live in a big city the effect of gender on helping is not significant. Among those who live in a small city the effect of gender is significant. So, there is an interaction effect because the effect of gender is different in the two categories of the two variables. It does not matter how different it is. If it is different then we say that there is an interaction effect.
The results refute our hypothesis stating that “we expect that both in rural and in urban areas women are more likely to help family members than men but the difference between men and women is bigger in urban areas”. How do we know this? We get to this conclusion after examining the epsilon and the p-values. So, in big cities there is no significant difference (p=0,395 >0,05). This means that we don’t have evidence that a higher proportion of women help their family members. In contrast to this, in the small cities there is a significant difference (p=0,015 < 0,05). It means that a significantly lower (or higher) proportion of men or women help their family members. Men or women? The epsilon shows us in which category is this difference higher or lower -> In rural areas, the proportion of those who look after family members is 4 percentage points lower among men than among women.
Thus, this is an example of the 1st type of interaction effect: In one sub-table there is a significant effect and in the other sub-table there is no effect.