Conclusions from experiments

The method of data collection has a major influence on whether a relationship can be interpreted as causal.

In an observational study, there is often the potential for a lurking variable to underlie an observed relationship.

In contrast, it is possible to conclude from a well-designed experiment that the controlled variable does affect the response.

In a well designed experiment, the observed relationships will be causal.

Note however that the experiment must be well designed in order to come to conclusions about causal relationships. In a badly designed experiment, lurking variables can still cause difficulties with interpretation.

Vitamin C and colds

To test whether vitamin C reduces the risk of catching a cold, a 1961 French study involved 279 skiers over two periods of 5-7 days. Skiers in one group of 139 were given 1 gram ascorbic acid (vitamin C) per day whereas those in the other group were given a tablet that looked similar but had no active ingredient (called a placebo). None of the skiers knew which of the treatments they had received.

     Cold      No cold  
Ascorbic acid 17 122
Placebo 31 109

From this table, we can calculate that 12% of those who were given vitamin C got colds and 22% of those given the placebo got colds. A statistical test comparing these percentages gives moderately strong evidence of a difference (p-value = 0.027). From the design of the experiment, we can conclude:

There is moderately strong evidence that use of vitamin C reduces the probability of getting a cold for skiers.

Comb weight of chicks

An experiment was conducted as part of an investigation into the effect of two hormones on the growth of male chicks. Twenty two chicks were used in the experiment and half were selected at random and given testosterone, the other half receiving dehydroandrosterone. The comb weights of the chicks (mg) are shown below.

     testosterone     dehydroandrosterone  
    57
120
101
137
119
117
104
  73
  53
  68
118
89
30
82
50
39
22
57
32
96
31
88
Mean 97 56

A statistical test shows that there is very strong evidence that the mean comb weight of the chicks getting testosterone is higher than that of the chicks getting dehydroandrosterone. From the design of the experiment, we can conclude that:

There is very strong evidence that giving chicks testosterone results in heavier combs than dehydroandrosterone.