MHB Determining Sample Size for Studying Sodium Consumption and Hypertension

[Jadan89]

You are interested in studying the relationship between sodium consumption and the development of hypertension. 32% of Americans are hypertensive (systolic blood pressure>140), and a further 29% are prehypertensive (140≥SBP>120). Detecting a 1 mm Hg SBP elevation with 80% power at the 0.05% significance level will require 1709 study participants.

How many total people will you have to identify to have 1709 normotensives (SBP≤120mmhg) for your study? How many will you have to identify if you just exclude hypertensives?

Thank you )

 

[I like Serena]

You are interested in studying the relationship between sodium consumption and the development of hypertension. 32% of Americans are hypertensive (systolic blood pressure>140), and a further 29% are prehypertensive (140≥SBP>120). Detecting a 1 mm Hg SBP elevation with 80% power at the 0.05% significance level will require 1709 study participants.

How many total people will you have to identify to have 1709 normotensives (SBP≤120mmhg) for your study? How many will you have to identify if you just exclude hypertensives?

Thank you )

Hi Jadan89! Welcome to MHB! ;)

Suppose we need $n$ persons to find 1709 normotensives.
Then we can expect that $n\cdot 32\%$ have hypertension and $n\cdot 29\%$ are prehypertensive.
The remainder must be normotensive.
If we have 1709 normotensives, how big must $n$ be? (Wondering)

 

[Jadan89]

Hi Jadan89! Welcome to MHB! ;)

Suppose we need $n$ persons to find 1709 normotensives.
Then we can expect that $n\cdot 32\%$ have hypertension and $n\cdot 29\%$ are prehypertensive.
The remainder must be normotensive.
If we have 1709 normotensives, how big must $n$ be? (Wondering)

Hello! Thank you for welcoming me and the reply!

I should have probaby added this to the original post, but shouldn't the effect size and standard deviation be calculated somehow? or am overthinking this too much?

Thanks again!

 

[I like Serena]

Hello! Thank you for welcoming me and the reply!

I should have probaby added this to the original post, but shouldn't the effect size and standard deviation be calculated somehow?

Thanks again!

... but we have no information about the population's standard deviations... we only have information about how reliable a test to detect elevation is...
As long as we're only "estimating population sizes", I think we shouldn't take a test to detect a specific elevation into account.

 

[Jadan89]

... but we have no information about the population's standard deviations... we only have information about how reliable a test to detect elevation is...
As long as we're only "estimating population sizes", I think we shouldn't take a test to detect a specific elevation into account.

I only assumed we had to use the effect size and standard deviation to calculate the sample size because we were provided with information about the power and significance level. Also, I am not totally sure of what "elevation" means in this problem.

Thanks!

 

[I like Serena]

I only assumed we had to use the effect size and standard deviation to calculate the sample size because we were provided with information about the power and significance level. Also, I am not totally sure of what "elevation" means in this problem.

Thanks!

To be honest, I don't understand what they mean with the test for elevation either.

Still, it's the wrong way around.
First we set a hypothesis, in this case that high sodium consumption results in hypertension.
Then we pick a sample, and measure the effects of sodium on hypertension before and after some treatment or some such.
As I understand the question, we want to know how big the sample should be to contain sufficient normotensitives before applying the treatment and checking the result on hypertension with our test.

Anyway, if you can get clarification about what is meant exactly with that test for elevation, that would help. :)

 

[Jadan89]

To be honest, I don't understand what they mean with the test for elevation either.

Still, it's the wrong way around.
First we set a hypothesis, in this case that high sodium consumption results in hypertension.
Then we pick a sample, and measure the effects of sodium on hypertension before and after some treatment or some such.
As I understand the question, we want to know how big the sample should be to contain sufficient normotensitives before applying the treatment and checking the result on hypertension with our test.

Anyway, if you can get clarification about what is meant exactly with that test for elevation, that would help. :)

Thank you, that makes a lot more sense. I was probably confused and overthinking the question because of all the other extra information provided in the problem.

I appreciate the help! :)