Recall the news report from npr.org, which was part of Homework Assignments 4 an
ID: 3175965 • Letter: R
Question
Recall the news report from npr.org, which was part of Homework Assignments 4 and 6 and is posted on canvas: "Early bedtime for preschoolers might help reduce obesity risk later". There were three groups of preschoolers (early to bed, lessthanorequalto 8 pm; middle, 8-9pm; and late to bed, greaterthanorequalto 9 pm). The news report focused on two of the groups (a subset of all the data) and claimed that "preschoolers who went to bed late - after 9 pm - were still twice as likely to develop obesity in their teens as the early-to-bed group". However, the researchers could have done a total of three comparisons. In other words, the researchers could have compared the risk of obesity in: preschoolers who went to bed before 8 pm to preschoolers who went to bed between 8 and 9pm; preschoolers who went to bed before 8 pm to preschoolers who went to bed after 9pm; and preschoolers who went to bed between 8 and 9pm to preschoolers who went to bed after 9pm. In Homework Assignment 6, we reported that the p-value for a test of the relative risk of obesity in preschoolers who went to bed after 9pm compared to preschoolers who went to bed before 8pm was less than 0.0002. The exact p-value is 0.00015. a) Given the number of comparisons (tests) the researchers could have made, how should the researchers adjust their alpha (significance) level for the individual test comparing preschoolers who went to bed after 9pm to preschoolers who went to bed before 8pm, if the overall alpha level is 0.05? b) Given this adjusted alpha, would you still conclude that the relative risk of obesity comparing preschoolers who went to bed after 9 pm to preschoolers who went to bed before 8pm is significantly different (greater) than 1?Explanation / Answer
A.
The overall significance for the family of comparisons = 5%
Number of comparisons = 3
That means the total permissible false positives for the entire family of 3 comparisons is 5%.
The researchers should reduce the value of alpha for each individual comparison by dividing the overall value of alpha by 3 (Answer).
So the new alpha should be = 0.05/3 = 0.016
B.
Corresponding to the alpha the overall value of p = 0.05
Applying Benforni correction to determine the significance level for the pair (sleeping before < 8 PM vs sleeping > 9 PM):
The new significance (adjusted alpha) = 0.05/3 = 0.016
So, the p value observed for this pair (< 8 PM vs > 9 PM sleeping time) = 0.0002 which is much smaller as compared to even the adjusted alpha value of 0.016.
What does it mean,
There is a higher risk of obesity between the preschoolers who went to bed < 8 PM than the kids who went to bed after 9 PM. So, we can conclude that the relative risk of obesity between the two groups is more than 1. (Answer)
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