Ugrás a tartalomhoz

## SOCIAL STATISTICS

Renáta Németh, Dávid Simon

ELTE

Controlling the relationship

## Controlling the relationship

### An apparent relationship

Cf.: smoking and seeing a doctor. Before looking at gender differences we hypothesised that smoking is the independent variable which affects the frequency of seeing a doctor: smokers tend to see their doctor less frequently as they feel uncomfortable because of their unhealthy habit. However, it turned out both variables strongly correlate with gender and this caused the apparently strong relationship between them.

Another example of using a control variable:

1. Apparently, at fire stations staffed by more fire fighters there is higher damage at the fires where they are alerted to. The more staff the less effective work?

 Extent of damage Staff at station Small Great Small 70% 30% Great 30% 70% Total 100% 100%

2. If we use the control variable ’graveness of fire’, we find that both small and big fires caused smaller damage if there were more firefighters at the scene. Let’s see the data broken up by the categories of the control variable:

SMALL FIRES: The relationship within the given category of the control variable point the other way and it’s weaker: 100%-88%=12%

 Damage caused by fire cases attended by a given station Number of staff Small Great Small 88% 100% Great 12% 0% Total 100% 100%

GREAT FIRES: The partial relationship has been reversed and it has weakened: 12%-0%=12%

 Damage caused by fire cases attended by a given station Number of staff Small Great Small 0% 12% Great 100% 88% Total 100% 100%

So the model of the relationship:

### The ’intermediary’ relationship

The following table is supposed to demonstrate how being religious immediately determines attitudes to abortion:

(GSS 1988-1991)

 Are you por-abortion? Religion Catholic Protestant Yes 34% 45% No 66% 55% Total 100% 100%

According to another hypothesis what religion affects immediately is one’s ideas concerning ideal family size and these ideas are what shape attitudes to abortion. So ideal family size is a control variable that acts as an intermediary standing in between religion and abortion attitudes.

Using this control variable proves this hypothesis as shown by the 3 tables below. (Note: in order to prove the effect of the intermediary variable, one has to analyse all the 3 tables and prove the existence of all the three relationships in bold.)

• (proving that religion family size) Religion correlates with preferred family size :

 Preferred family size Religion Catholic Protestant Large 52% 27% Small 48% 73% Total 100% 100%
• Preferred family size correlates with abortion attitudes (proving that family size abortion attitude):

 Are you pro-abortion Preferred family size Large small Yes 25% 50% No 75% 50% Total 100% 100%

3: Within the given category of the intermediary variable there is no correlation between religion and abortion attitudes (or there’s hardly any) (proving that there’s no immediate religion abortion attitude).

 Preferred family size Are you pro-abortion? Religion Catholic Protestant SMALL Yes 46% 52% No 54% 48% Total 100% 100% Are you pro-abortion? Religion Catholic Protestant Large Yes 24% 28% No 76% 72% Total 100% 100%

Note: Analysing this last table is especially important as this one proves that religion only affects abortion attitudes through the intermediary variable.

The causal relationship:

Final conclusion: Catholics are less pro-abortion than Protestants because they prefer larger families.

### Modifying the effect

Another way of using a control variable is when it is only the strength of the relationship between the independent and the dependent variable in the model that changes in accordance with a third, modifying variable.

(e.g. Országos Lakossági Egészségfelmérés 2000.) Health status surveys prove the case very well. The following are fictitious data.

3. There are more moderate/heavy drinkers among men than women (strength of relationship 98-37=61%)

 Alcohol consumption Male Female Teetotaller/occasional drinker 37% 98% Moderate/heavy drinker 63% 2% Total 100% 100%

4. The relationship points the same way but it’s weaker for those with higher level of education. (strength of relationship for those without higher education: 96-29=67%, for those with higher education: 100-46=54%).

 No higher eduaction With higher education Alcohol consumption Male Female Alcohol consumption Male Female Teetotaller/occasional drinker 29% 96% Teetotaller/occasional 46% 100% Moderate/heavy drinker 71% 4% Moderate/heavy 54% 0% Total 100% 100% Total 100% 100%