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Understanding statistics
 





Module 3: Interpreting Data

8. What relationships are possible between variables?

A. Causation




Causation is when a change in the explanatory variable causes a change in the response variable. For example in Module 1 the relationship between feeding babies on mother's breast milk and their early resistance to some contagious diseases was of this type.

However, this relationship is not always as obvious as you might think and sometimes what you think is the explanatory variable turns out to be the response variable, as is shown in this example.




Test your knowledge


Question

You are considering two variables - hotel occupancy rates and advertising sales for the same hotel. Select the appropriate variable type for each variable.
  1. hotel occupancy rates
  2. advertising sales for the same hotel
Answer
Show details for Click here for answersClick here for answers

B. Other contributing variables

The explanatory variable contributes to but is not the sole cause of the response variable. There is at least one other variable that needs to be taken into account because it contributes to the response. For example, in the debate about the relationship between smoking and lung cancer there might be other interacting variables, such as working conditions involving working with asbestos, or working in highly polluted environments, that could increase the likelihood of someone developing lung cancer (Gustavssonn, Nyberg et.al 2002).

C. Common Response




Common response is when changes in X and Y are caused by changes in a third variable Z. For example, there exists a moderate correlation between a person's Tertiary Entrance Rank (TER) and his/her grade point average (GPA) for the first year at university. Do high TERs cause high GPAs? Surely not! Instead both observed variables are responding to other variables such as knowledge, ability, or study habits.

D. Confounding Variable




Confounding Variable is when changes in Y are caused by changes in X and by changes in a third variable Z. The role of confounding variables has been discussed at some length already.

In all of these cases the data would show an association between the two variables. In observational studies, it is difficult to argue that an association shows that one variable causes the changes observed in the other variable. But we can use observational data to show strong association.


Scenario

A double-blind study [Hurt, Dale et.al 1994] examined the effectiveness of nicotine patches which dispense nicotine into the blood. The participants in the study were volunteers who smoked more than 20 cigarettes/day, were in good health and wanted to quit smoking. The 240 volunteers were randomly assigned to either a nicotine patch group or a placebo patch group and each was placed on an intervention (quit) program recommended by the National Cancer Institute. This program involved counselling before, during and months after the 8-week period for which the volunteers had to wear their patches.

After the 8-week period 46% of the nicotine patch group and 20% of the placebo patch group had quit smoking completely. After a year the quit level was 27.5% for the nicotine patch group and 14.2% for the placebo patch group.

The researchers also discussed the effect of other smokers in the volunteer's home. With other smokers at home, after the 8-week patch therapy 31% of volunteers with nicotine patches had quit. With no smokers at home 58% of volunteers with nicotine patches had quit. In the placebo group the proportions who quit were the same whether there were smokers at home or not.

 


Test your knowledge


Question

What were the researchers trying to find out?
  1. Whether nicotine patches were effective in helping people to stop smoking.
  2. Whether nicotine patches increase the success rate of intervention programs.
  3. Whether having others who smoke at home makes it harder to stop smoking.
  4. Whether an intervention program is effective.
Answer

Show details for Click here for answersClick here for answers

Test your knowledge


Question

Match the variable type to the variable
Answer

Show details for Click here for answersClick here for answers
  1. The presence of other smokers in the home.
  2. The use of nicotine patches
  3. The use of an intervention program
  4. Quitting smoking
  1. explanatory
  2. response
  3. control
  4. contributing

If you were observant, you might have noticed that the presence of smokers in the home did not seem to affect the quit rate of those volunteers on the placebo patch and intervention program. Can you propose an explanation for this observation?

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