You have just been assigned to work on a team of public health experts whose goal is to design and implement a study regarding diet and autism. On the team, you appear to have the most statistical expertise and everyone looks to you for advice on these types of questions!

The team is very interested in the gluten-free, casein-free (GFCF) diet which may eliminate certain proteins from the diet and therefore alleviate some symptoms experienced by children with autism. The team leader says there is only enough funding to sample 40 children with autism and compare their GI (gastrointestinal) symptoms before and after implementing a GFCF diet. GI symptoms will be assessed both before the diet and after the diet using a quality of life (QOL) tool.

a) Because you understand the importance of using resources well, you ask the team leader to see the power calculations associated with this choice in sample size. The entire team looks at you with a blank stare. Please explain to them the importance of power to this study in terms that a non-statistician can understand.

Include answers to what is power? what would happen in the context of this study if the power were low, and why that is not good? what level(s) of power would you suggest?

The attention span of your team is limited – so please be brief.

b) Now that the team fully understands the details of designing a study with an appropriate number of subjects, please calculate the power for such a study using a two-sided alpha level (type 1 error) of 0.05, to show a mean difference of 5 units in GI symptoms QOL score with a standard deviation of 12 units.

Provide your recommendation on whether the sample size stated is sufficient for this study.