Question

ADHD? OR JUST YOUNGEST IN THE CLASS?

A study¹ indicates that the youngest children in a school grade are more likely to be diagnosed with attention-deficit/hyperactivity disorder (ADHD) than their older peers in the same grade. The study involved 937,943 children between 6 and 12 years old in British Columbia, Canada. The cutoff date for entering school in any year in British Columbia is December 31^st, so in any given class, those born late in the year are almost a year younger than those born early in the year. Is it possible that the younger students are being over-diagnosed with ADHD?

Boys: ADHD or Just Young?

The table below shows the number of boys diagnosed with ADHD based on the quarter of the year in which they were born, as well as the proportion of boys born during that quarter.

Birth Date	ADHD Diagnoses	Proportion of Births
Jan-Mar	6880	0.244
Apr-Jun	7982	0.258
Jul-Sep	9161	0.257
Oct-Dec	8945	0.241

Table 1 ADHD diagnoses and birth date for boys


¹Morrow, R., et al., “Influence of relative age on diagnosis and treatment of attention-deficit/hyperactivity disorder in children,” Canadian Medical Association Journal, April 17, 2012; 184(7): 755–762.

(a) What is the total number of boys diagnosed with ADHD in the sample?

Total number of boys = Enter your answer in accordance to the question statement

(b) For the null hypothesis, use the overall proportion of births in a quarter to give the null proportion for that quarter. Compute the expected number of ADHD diagnoses for each quarter under this hypothesis.

Answer 1

(a)

the total number of boys diagnosed with ADHD in the sample = 6880 + 7982 + 9161 + 8945 = 32968

So,

Answer is:

32968

(b)

the expected number of ADHD diagnoses for each quarter under this hypothesis is got as follows:

Birth date	the expected number of ADHD diagnoses for each quarter under this hypothesis
Jan - Mar	32968 X 0.244 = 8044
Apr - Jun	32968 X 0.258 = 8506
Jul - Sep	32968 X 0.257 = 8473
Oct - Dec	32968 X 0.241 = 7945

So,

Answer is:

the expected number of ADHD diagnoses for each quarter under this hypothesis is as follows:

Birth date	the expected number of ADHD diagnoses for each quarter under this hypothesis
Jan - Mar	8044
Apr - Jun	8506
Jul - Sep	8473
Oct - Dec	7945