if normal blood cholestrol level is 5.8 mM
and a treatment caused a drop of 1.0 mM with a standard deviation of the difference of 2.0 mM
what is the minimum number of individuals that should be used in the drug trial to determine whether or not it is effective
i know you have to calculate t
i got t = mean of difference/s(difference)
which gave me t =0.5 but this would give n as infinity
this doesnt seem to be right but im not sure what or if ive gone wrong
thanks
To determine the minimum number of individuals needed for the drug trial, you can use a statistical test called the t-test.
The formula you mentioned, t = mean of difference/s(difference), is correct. It represents the t-value, which is a measure of the difference between the means relative to the variability in the data.
However, there seems to be an error in your calculation. Let's go through the correct steps:
1. Define the null and alternative hypotheses:
- Null hypothesis (H0): The drug is not effective. There is no significant difference in blood cholesterol levels before and after treatment.
- Alternative hypothesis (H1): The drug is effective. There is a significant decrease in blood cholesterol levels after treatment.
2. Calculate the t-value:
- To calculate the t-value, you need the mean (mean of difference) and the standard deviation (s(difference)) of the difference in blood cholesterol levels before and after treatment.
- In this case, the mean of the difference is -1.0 mM (a drop of 1.0 mM).
- The standard deviation of the difference is given as 2.0 mM.
Therefore, the t-value is calculated as:
t = mean of difference / s(difference)
= -1.0 mM / 2.0 mM
= -0.5
3. Determine the degrees of freedom (df):
- The degrees of freedom depend on the sample size (n) in the drug trial.
- The formula to calculate the degrees of freedom for a paired t-test is: df = n - 1.
4. Look up the critical t-value:
- The critical t-value depends on the desired level of significance (alpha) and the degrees of freedom (df).
- Let's assume a significance level of alpha = 0.05 for a two-tailed test (to account for the possibility of a significant increase or decrease in cholesterol levels).
- You can find the critical t-value in a t-table or use a statistics calculator with the appropriate values.
However, at this point, we have an issue. You calculated a t-value of -0.5, which implies an infinite number of individuals would be needed for the trial. This seems incorrect.
To further investigate the issue, we need more information. Are you given any other information about the desired level of significance (alpha) and the power of the statistical test? Additionally, information about the minimum effect size that would be considered clinically significant is helpful.
The sample size calculation generally considers the desired power (often 80% or 90%), alpha (usually 0.05), effect size, and variability of the data. With this information, we can determine an appropriate sample size using power analysis or sample size calculators.
Please provide any additional information, and I will be happy to guide you through the process of determining the minimum number of individuals needed for the trial.