Lecture 12 9/18/24 Flashcards
What is the null hypothesis?
there is no difference between/among groups
What is the alternative hypothesis?
there is a difference between/among groups
What is random error?
-absence of precision
-may result in underestimation or overestimation of true value
-measurement device has precision limitations
What is sampling error?
the difference between the measured value and the true value when random error occurs
What is systematic error/bias?
-absence of validity
-error having a nonzero mean, so that its effect is not reduced when observations are averaged
-deviations from true value all occur in the same direction
What are the characteristics of chance?
-random error occurs by chance
-not predictable
-always present
-increased sample size decreases random error
What is a type 1 error with respect to the null hypothesis?
-rejecting the null hypothesis when it is true
-we find a difference where none exists
What is a type 2 error with respect to the null hypothesis?
-accepting the null hypothesis when it is false
-we do not find a difference where one exists
What is a p-value?
-probability that the observed differences could be due to chance
-probability of making a type 1 error
What is power?
-probability that you will find a statistically significant difference when it exists and is of a certain magnitude
-probability of being able to identify an effect if one exists
-analogous to sensitivity
Why is a large sample size preferred?
it will always increase statistical power and allow for the detection of both large and small effect sizes regardless of population variation
Why is it important to calculate sample size?
to know the sufficient number of patients needed to detect a clinically important difference if it exists
Which aspects of sample size calculation are decided by the investigator?
-minimum effect size
-probability of type 1 error
-probability of type 2 error
Which aspects of sample size calculation are determined by the data?
-variability of the data
-rate of events
What non-statistical considerations must be taken into account when determining sample size?
-resources
-objectives of the study
What statistical considerations must be taken into account when determining sample size?
-precision of the estimate
-effect size
-expected variation in the data
-level of confidence
-significance level/type 1 error
-power to detect real effects
Why do continuous outcomes possess the most precision and accuracy?
due to the “true zero” that allows for measurement of both distance and magnitude
Why do categorical outcomes and ordinal outcomes lack precision and accuracy?
due to observation biases
What must be done to increase precision?
use a larger sample size
What are the benefits of a larger effect size?
-increased statistical power
-decreased sample size
What is effect size?
difference between means or proportions due to treatment
How does population variation impact sample size?
the more variation expected of the outcome, the larger the sample size required to draw accurate conclusions
What is a confidence interval?
estimated range of values which is likely to include an unknown population parameter (typically 95% likely)
How does a confidence interval differ from a point estimate?
a point estimate is a single value given to estimate a population parameter, while a confidence interval provides a range of values that is likely to contain the point estimate
What is suggested when the confidence interval contains the null value?
suggests that the parameter is not statistically significant from the null
What are the characteristics of underpowered studies?
-small sample size
-statistically non-significant results and low power make studies inconclusive
