In: Statistics and Probability
a) The researchers are trying to identify a strategy that would decrease the prevalence of peanut allergy in infants. For this, they are using a strategy of either giving peanuts or not giving peanuts in the early infancy between 8 and 11 months. Hence they are trying to answer whether giving an early peanut rich diet can decrease the prevalence of peanut allergy in the infants.
b) The treatment variable is an explanatory variable. It determines the treatment options provided in a given study. Here the treatment options are whether to have a peanut-rich diet or not.
The response variable is the one that is measured as a result of varying the explanatory or the treatment variable. Hence the response variable here is the prevalence of peanut allergy.
c) The subjects were assigned to groups in a randomized fashion. The groups weren't inherent based on some pre-existing traits. And hence whether a certain subject would receive peanut-diet or not was randomized. Hence this is an instance of a randomized study with appropriate controls. Therefore it is a controlled experiment and not an observational study.
d) The experiment was performed as mentioned in the question and the prevalence of peanut-allergy was assessed in the individuals based on whether they were treated with a peanut-rich diet or not. And as can be seen, there was a significant decrease in the prevalence of peanut allergy when the subjects were treated with a peanut-rich diet. This was observed irrespective of whether the infants had tested positive or negative for the skin-prick test.
Thus, the conclusion based on these results is that irrespective of their prior condition, if the infants are provided with a peanut-rich diet in the period between 4 and 11 months, their chance of having peanut allergy decreases.
e) The experiment was designed in a controlled fashion. This is not merely an observational study. Hence there is causality that can be inferred from here. And hence the results are reliable.
f) The population from which the children were selected isn't mentioned here. However, all of these are infants with either eczema or egg allergy or both. Hence the results apply to the infants who have these conditions.
g) The p-value is a measure of the probability that the results obtained are due to chance. Here, in both the cases (whether the infants were positive or negative to the skin prick test), the p-values for the prevalence of peanut allergy shows a value less than 0.05. This value is for the difference in the prevalence with or without treatment a peanut-rich diet. Hence, the conclusion drawn that the introduction of peanuts at an earlier age is effective in reducing peanut allergies is statistically significant. This is what the p-value indicates. That there is less than 5% chance of the resuls being due to random chance event.