Fractures of the spine are common and serious among women with advanced osteoporosis (low mineral density in the bones). Can taking strontium ranelate help? A large medical trial was conducted to investigate this question. Researchers recruited $1649$women with osteoporosis who had previously had at least one fracture for an experiment. The women were assigned to take either strontium ranelate or a placebo each day. All the women were taking calcium supplements and receiving standard medical care. One response variable was the number of new fractures over $3$years.

a. Describe a completely randomized design for this experiment.

b. Explain why it is important to keep the calcium supplements and medical care the same for all the women in the experiment.

c. The women who took strontium ranelate had statistically significantly fewer new fractures, on average, than the women who took a placebo over a $3$-year period. Explain what this means to someone who knows little statistics.

A completely randomized experiment allocates all participants of the group at random.

Let us allocate a unique number to $1649$women each between $1$and $1649$(including both the numbers).

Draw randomly $825$unique numbers between $1$and $1649$(including both the numbers), that can be done by using a random digits table or technology, or by using slips of papers.

According to $825$selected integers, the corresponding $825$women will be assigned to the Strontium ranelate treatment, whereas the remaining $824$women will be assigned to the placebo treatment.

Two variables are confounded when their effects cannot be distinguished from each other on a response variable.

In the experiment, if we do not keep the calcium supplements and the medical care the same for all women,we cannot then be sure that the differences amongthe treatments are due to treatment, calcium supplements or medical care.

That means the medical care and the calcium supplements will confound the results, i.e., we will not be able to distinguish their effects on the results from the treatments effects.

Furthermore, because of the confusion, we will then be unable to prove any causation.

“Statistically significant” means that the differences have been so large that they are unlikely to be due to chance.

“The women who took strontium ranelate had statistically significantly fewer new fractures, on average than the women who took a placebo over a $3$-year period”.

This means that women who took strontium ranelate had on average so many fewer new fractions compared to women who took placebo and that is unlikely to be due to chance.