Determining Sample Size for Studying Sodium Consumption and Hypertension

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In summary: 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.
  • #1
Jadan89
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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 :)))
 
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  • #2
Jadan89 said:
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)
 
  • #3
I like Serena said:
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!
 
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  • #4
Jadan89 said:
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... :confused:
As long as we're only "estimating population sizes", I think we shouldn't take a test to detect a specific elevation into account.
 
  • #5
I like Serena said:
... but we have no information about the population's standard deviations... we only have information about how reliable a test to detect elevation is... :confused:
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!
 
  • #6
Jadan89 said:
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. :eek:

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. :)
 
  • #7
I like Serena said:
To be honest, I don't understand what they mean with the test for elevation either. :eek:

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! :)
 

1. How is population size estimated?

Population size can be estimated using various methods, such as direct counting, mark-recapture, and sampling. Direct counting involves physically counting every individual in a population. Mark-recapture involves marking a subset of individuals, releasing them back into the population, and then estimating the population size based on the ratio of marked to unmarked individuals in subsequent samples. Sampling involves collecting data from a smaller portion of a population and using statistical methods to extrapolate the population size.

2. What is the importance of estimating population size?

Estimating population size is important for numerous reasons. It can help inform conservation efforts, track changes in population over time, and aid in resource management. It can also provide valuable information for understanding the impacts of human activities on a population and predicting potential future changes in population size.

3. What are the limitations of population size estimation methods?

Each population size estimation method has its own limitations. For example, direct counting may be difficult or impossible for certain species that are elusive or live in inaccessible areas. Mark-recapture requires assumptions about the proportion of marked individuals in subsequent samples, which may not always hold true. Sampling methods may also be influenced by the chosen sampling area and the variability of the population within that area.

4. How does population size estimation differ between species?

The methods used to estimate population size can vary between species due to differences in behavior, habitat, and other factors. For example, mark-recapture may be more suitable for a highly mobile species, while direct counting may be more appropriate for a sedentary species. Additionally, the accuracy of population size estimates may also differ between species due to varying levels of uncertainty and variability within populations.

5. Can population size be accurately estimated for all species?

Population size estimation can be challenging for certain species, especially those that are rare or difficult to observe. In these cases, alternative methods such as genetic markers or aerial surveys may be used. However, there may still be limitations and uncertainties associated with these methods, so accurate estimation may not always be possible for all species.

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