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%