Portney: Chapter 23 Flashcards
What is probability?
The likelihood that any one event will occur, given all the possible outcomes
Essential to understand inferential statistics
Represented by a lowercase p
Relationship to normal distribution
Implies uncertainty – what is likely to happen
What is sampling error?
The tendency for sample values to differ
from population values
The variance properties of a sampling
distribution of means
What are confidence intervals?
Estimating population parameters
- Point estimate, e.g. mean
- Confidence intervals
Confidence intervals are a range of scores that is likely contain the population parameter, with a certain level of confidence
Confidence interval for a sample mean:
CI= X ±(z)sX ; z = 1.96 for p = .05 (95% confidence)
How do you interpret confidence intervals?
The correct interpretation of a 95% confidence interval is that if we were to repeat sampling many times, 95% of the time our confidence interval would contain the true population mean.
Increase confidence by decreasing precision
(e.g., 99% confidence interval)
What is a null hypothesis?
H0
No difference
Observed difference between the groups by change, which states that the group means are not different and come from the same population.
Indicates observed differences are sufficiently small and considered 0.
What is an alternative hypothesis?
H1
There is a difference
States the treatment is effective and that the effect is too large to be considered a result of chance alone.
May be stated with or without direction
- nondirectional: no specific group mean is expected to be larger
- directional: expected direction of difference between sample means
Superiority and non-inferiority trials
Most of the time when researchers design a randomized trial, they are looking to show that a new intervention is more effective than a placebo or standard treatment. Such studies are considered superiority trials because their aim is to demonstrate that one treatment is “superior” to another.
A non-inferiority trial focuses on demonstrating that the effect of a new intervention is the same as standard care, in an effort to show that it is an acceptable substitute. This approach is based on the intent to show no difference, or more precisely that the new treatment is “no worse” than standard care.
What is a type I mistake?
mistakenly finding a difference
Level of significance
- Alpha (α): probability of making a Type I error
Interpreting probability values
What is a type II mistake?
mistakenly finding no difference
Probability of making a Type II error: Beta (β)
Statistical power: 1 – β
What is power?
Power is the probability that a test will lead to rejection of the null hypothesis, or the probability of attaining statistical significance.
What are the determinants of statistical power?
P = power (1 – β)
A = alpha level of significance
N = sample size
E = effect size
What is a priori analysis?
estimates sample size
What is a post hoc analysis?
determines power
What is a one-tailed test?
One-tailed test more powerful
- Should only be used when the relevant difference is only in one direction
- Directional hypothesis
What is a two-tailed test?
allows for possibility that difference may be positive or negative
nondirectional hypothesis
