Chapter 2, Problem 64CR

The article “Rethinking Calcium Supplements” (US Airways Magazine, October 2010) describes a study investigating whether taking calcium supplements increases the risk of heart attack. Consider the following four study descriptions. For each study, answer the following five questions:

Study 1: Every heart attack patient and every patient admitted for an illness other than a heart attack during the month of December at a large urban hospital was asked if he or she took calcium supplements. The researchers found that the proportion of heart attack patients who took calcium supplements was significantly higher than the proportion of patients admitted for other illnesses who took calcium supplements.

Study 2: Two hundred people were randomly selected from a list of all people living in Minneapolis who receive Social Security. Each person in the sample was asked whether or not they took calcium supplements. These people were followed for 5 years, and whether or not they had a heart attack during the 5-year period was noted. The researchers found that the proportion of heart attack victims in the group taking calcium supplements was significantly higher than the proportion of heart attack victims in the group not taking calcium supplements.

Study 3: Two hundred people were randomly selected from a list of all people living in Minneapolis who receive Social Security. Each person was asked to participate in a statistical study, and all agreed to participate. Those who had no previous history of heart problems were instructed to take calcium supplements. Those with a previous history of heart problems were instructed not to take calcium supplements. The participants were followed for 5 years, and whether or not they had a heart attack during the 5-year period was noted. The researchers found that the proportion of heart attack victims in the calcium supplement group was significantly higher than the proportion of heart attack victims in the no supplement group.

Study 4: Four hundred people volunteered to participate in a 10-year study. Each volunteer was assigned at random to either group 1 or group 2. Those in group 1 took a daily calcium supplement. Those in group 2 did not take a calcium supplement. Those proportion who suffered a heart attack during the 10-year study period was noted for each group. The researchers found that the proportion of heart attack victims in group 1 was significantly higher than the proportion of heart attack victims in group 2.

To determine

1. 1. Identify the study as an observational study or an experiment.
2. 2. Decide whether the study was conducted by taking a random selection from the population.
3. 3. Decide whether the assignment to experimental groups was done randomly.
4. 4. Explain whether it can be concluded that calcium supplements can increase the risk of heart attack.
5. 5. Conclude whether it is reasonable to generalize the results of the study to a larger population and identify the concerned population.

Answer to Problem 64CR

Study 1:

1. 1. The given study is an observational study.
2. 2. No, the study was not conducted by taking a random selection from the population.
3. 3. No, the assignment to groups was not done randomly.
4. 4. No, it cannot be concluded that calcium supplements can increase the risk of heart attack.
5. 5. No, it is not reasonable to generalize the results of the study to a larger population.

Study 2:

1. 1. The given study is an observational study.
2. 2. Yes, the study was conducted by taking a random selection from the population.
3. 3. No, the assignment to groups was not done randomly.
4. 4. No, it cannot be concluded that calcium supplements can increase the risk of heart attack.
5. 5. Yes, it is reasonable to generalize the results of the study to a larger population; the concerned population is the population of Minneapolis residents receiving Social Security.

Study 3:

1. 1. The given study is an experiment.
2. 2. Yes, the study was conducted by taking a random selection from the population.
3. 3. No, the assignment to groups was not done randomly.
4. 4. No, it cannot be concluded that calcium supplements can increase the risk of heart attack.
5. 5. No, it is reasonable to generalize the results of the study to a larger population.

Study 4:

1. 1. The given study is an experiment.
2. 2. No, the study was not conducted by taking a random selection from the population.
3. 3. Yes, the assignment to groups was done randomly.
4. 4. Yes, it can be concluded that calcium supplements can increase the risk of heart attack.
5. 5. No, it is reasonable to generalize the results of the study to a larger population.

Explanation of Solution

The given information relates to four studies conducted in order to verify whether taking calcium supplements could increase the risk of heart attack.

Study 1:

The study was conducted in a large urban hospital, in the month of December. The researchers asked every patient who had heart attack and who were admitted for some illness other than heart attack, admitted at the hospital during the given time, whether or not they took calcium supplements. It was concluded that the proportion of patients with heart attack who had taken calcium supplements was much higher than the proportion of patients with some other illness who had taken calcium supplements.

1.

Observational study:

A study, in which, the researcher observes the individuals in a sample taken from the population of interest, without actually attempting to influence the outcomes, is called an observational study. A good observational study involves a sample that represents the population well.

Experiment:

A study, in which, the researcher attempts to influence the outcomes or the response variables by manipulating the explanatory variables or the variables that are supposed to affect the response variables, is called an experiment. A good experiment randomly allocates the observations to the different combinations of the explanatory variables.

In this study, the researcher does not determine whether a patient takes calcium supplements. The researcher merely questions the patients regarding taking calcium supplements and computes the proportions.

Thus, the given study is an observational study.

2.

The researchers did not select the subjects of the study by using any random methods. Rather, they collected the data from every patient who was admitted to the hospital during the given time.

Hence, the study was not conducted by taking a random selection from the population.

3.

The two groups here are: the patients who took calcium supplements and the patients who did not take calcium supplements.

Now, the researchers did not decide who took the supplements and who did not.

Hence, the assignment to groups was not done randomly.

4.

The study is an observational study. Now, it is known that a cause-and-effect relationship can only be established by using a designed experiment. It is impossible to determine whether one variable affects the other, from an observational study.

Hence, it cannot be concluded that calcium supplements can increase the risk of heart attack.

5.

The hospital at which the study is performed in the month of December is a large urban hospital. The patients coming to such a hospital for treatments cannot be considered as a representative of all patients in general, seeking treatment at all hospitals all the year round.

Now, it is known that the conclusions of a study can be generalized to a larger population, if the study is conducted under situations representing those of a larger population.

Hence, it is not reasonable to generalize the results of the study to a larger population.

Study 2:

1.

The study was conducted on 200 randomly selected people from Minneapolis, receiving Social Security. Each person was asked whether they took calcium supplements, at the beginning of the study and thereafter followed over a period of 5 years. At the end, the cases of heart attack during the period was noted for each and the proportion revealed a higher proportion of people getting heart attacks had taken calcium supplements, than those who did not.

In this study, the researcher does not determine whether a patient takes calcium supplements. The researcher merely questions the patients regarding taking calcium supplements and conducts the study.

Thus, the given study is an observational study.

2.

The researchers selected the subjects of the study by using random methods.

Hence, the study was conducted by taking a random selection from the population.

3.

The two groups here are: the patients who took calcium supplements and the patients who did not take calcium supplements.

Now, the researchers did not decide who took the supplements and who did not.

Hence, the assignment to groups was not done randomly.

4.

The study is an observational study. Now, it is impossible to determine whether one variable affects the other, from an observational study.

Hence, it cannot be concluded that calcium supplements can increase the risk of heart attack.

5.

The sample was taken from the population of Minneapolis residents receiving Social Security. Thus, it represents only the said population and not any other population.

Hence, it is reasonable to generalize the results of the study to a larger population; the concerned population is the population of Minneapolis residents receiving Social Security.

Study 3:

1.

The study was conducted on 200 randomly selected people from Minneapolis, receiving Social Security. Those who had had heart attack before were asked to stop taking supplements, if they did. Those who did not have heart attack before were asked to start taking the calcium supplements. The study was conducted over a period of 5 years. It was found that a higher proportion of people with heart attacks were found in the group that took the supplements, than those who did not.

In this study, the researcher determines whether a patient takes calcium supplements or not, during the period of the study. Thus, the researcher influences the outcome to some extent, by controlling the administration of supplements.

Thus, the given study is an experiment.

2.

The researchers selected the subjects of the study by using random methods.

Hence, the study was conducted by taking a random selection from the population.

3.

The two groups of interest here are: the patients who took calcium supplements and the patients who did not take calcium supplements.

Now, the researchers did not decide who took the supplements and who did not, before the beginning of the study. They simply asked those with heart attack to stop talking it and those with no history of heart attack to start taking it. The researchers did not control who had had heart attack before.

Hence, the assignment to groups was not done randomly.

4.

Although the study is an experiment, the researcher does not decide who receives the treatment and who does not. Thus, it is impossible to determine whether the supplements caused the heart attack.

Hence, it cannot be concluded that calcium supplements can increase the risk of heart attack.

5.

The sample was taken from the population of Minneapolis residents who are receiving Social Security. However, there was a mixture of people who took supplements and who did not, along with those who had heart attacks and those who did not. Thus, it is difficult to use this sample to decide whether it represents any population in particular.

Hence, it is not reasonable to generalize the results of the study to a larger population.

Study 4:

1.

The study was conducted on 400 volunteers over a period of 10 years. The volunteers were divided into 2 groups- group 1 took the calcium supplement, group 2 did not. It was found that a higher proportion of people with heart attacks were found in group 1, than in group 2.

In this study, the researcher determines whether a patient takes calcium supplements or not, during the period of the study. Thus, the researcher influences the outcome to some extent, by controlling the administration of supplements.

Thus, the given study is an experiment.

2.

The researchers did not select the subjects of the study by using random methods. Rather, the subjects were volunteers.

Hence, the study was not conducted by taking a random selection from the population.

3.

The two groups of interest here are: the patients who took calcium supplements and the patients who did not take calcium supplements. The researchers assigned the volunteers to these groups using random methods.

Hence, the assignment to groups was done randomly.

4.

As the study is an experiment and the researcher decides who receives the treatment and who does not, it is possible to determine whether the supplements caused the heart attack.

Hence, it can be concluded that calcium supplements can increase the risk of heart attack.

5.

The subjects studied in the sample were volunteers. As a result, it is not known which particular populations they come from.

Hence, it is not reasonable to generalize the results of the study to a larger population.