# Estimate the sample size

• I
• jaumzaum
In summary, the article states that a sample of 600 people would be needed to locate 200 people with an episode of major depression, but the article's calculations were incorrect and the correct number is 80 individuals.f

#### jaumzaum

Hello!
I will present an article tomorrow and I just found out the sample size calculation could be wrong (it's not my article).
It's very urgent, if someone could help me to confirm if the sample size calculation is right or wrong (and if so, help me to calculate the correct amount) this would save my presentation.
To explain about the article: It is a population based study to estimate the prevalence of major depression in Brazilian population.

As I was taught, the optimal sample size for a study can be calculated as:
##n = Z^2 p (1-p)/D^2##
Where Z = 1,96 for a confidence level of 95%
p is the estimated proportion
D is the sample error

The article says the following when calculating the sample size:
"To calculate the sample size, it was employed as parameters of sensitivity and specificity the value of 80%, acceptable error of 10 percentage points for more or less, and level of significance of 95%, being necessary to include around 200 subjects with and 200 without an episode of major depression disorder in the study. With a point prevalence of around 30% of depressive symptoms in the adult population of Pelotas , it was estimated that with a sample of around 600 individuals it would be possible to locate around 200 with an episode of major depression."

If I consider Z = 1,96, p = 0,3 and D = 0,1 I get 80 individuals, not 200 or 600.
Am I right considering these numbers?

Sorry if it's already too late, but I'm not clear on the meaning of the " Optimal size" for a sample. Optimal in what way/sense?

jaumzaum
Am I right considering these numbers?
I agree with your numbers: the only things I can think of regarding the original study are
• the first language of the author does not appear to be English which may lead to misinterpretation
• the "acceptable error of 10 percentage points for more or less" could mean an error band 10 pp wide i.e. ## \pm 5 \% ##, although that would give a sample size of 246.

jaumzaum
Sorry if it's already too late, but I'm not clear on the meaning of the " Optimal size" for a sample. Optimal in what way/sense?
In the sense of being the minimum sample size to provide an estimate with the desired confidence interval.

jaumzaum and WWGD
If I consider Z = 1,96, p = 0,3 and D = 0,1 I get 80 individuals, not 200 or 600.
I think p is actually 0.8 for both sensitivity and specificity, but that doesn't change the size much.

jaumzaum
Thanks @pbuk and @WWGD, I confirmed yesterday that the calculation in the article was indeed wrong.
p is 0.8 actually (what would give a Z of 61), sorry about that.
If we consider the error margin is 10% in total, we get around 200 individuals, but the article says specifically that it uses 10% for more or for less (this happens also in other calculations).

However, more people is not bad, just the calculations that we needed to change a bit!