What 3 factors affect study results?
Bias/confounding Chance Treatment/Therapy/Exposure etc
How are bias/confounding minimized?
Strong study design Randomization Masking/blinding
What is standard error of the mean?
Estimate of the standard deviation of all sample means --Describes the precision of the sample estimate --Based on variability and sample size --Measures “how far off” estimate is likely to be from population mean
How is standard error of the mean/proportion calculated?
Estimated std error of mean: s/sqrt(n)
- = population standard deviation ÷ square root of sample size
Estimated std error of proportion (p): sqrt(p(1-p)/n)
- (see image)
What is a confidence interval?
A range of “plausible values” for the true population value
How is confidence interval calculated?
Confidence interval = estimate (plus/minus) critical value x standard error
Standard error depends on...
variability and sample size
Critical value depends on...
sample size and confidence
What does statistical significance show?
Results are unlikely to be caused purely by chance
Define Type I error:
Rejecting the null hypothesis (there is a difference) when the null hypothesis is true (false negative)
The probability of obtaining the observed test statistic, or one more extreme, if the null hypothesis is true
Define Type II error:
Not rejecting the null hypothesis (no difference) when the null hypothesis is false (false positive)
P(Type II error) Probability of concluding there is no difference when a difference exists
Power = 1 - beta Study with good power is less likely to “miss” important differences
What is power dependent on?
- Type I error rate alpha
- Effect size (e.g. difference in means or proportions)
- Variability of outcome measure
- Sample size
Typically first 3 are fixed and sample size is increased to achieve >80% power
What are the steps in hypothesis testing?
1. State hypotheses 2. Choose significance level 3. Calculate appropriate test statistic and corresponding p-value 4. Decide whether evidence is sufficient to reject the null hypothesis
What is the alternative hypothesis?
The study or research hypothesis, want data to SUPPORT the alternative
What is the null hypothesis?
Converse of study hypothesis, want data to REJECT the null
How are hypotheses described?
One sided Two sided
Alpha = P(Type I error) The probability of rejecting the null hypothesis when it is true
- Probability of concluding there is a difference when no difference exist
- overstating the significance of your findings
What is the test statistic?
Test statistic = (Observed value - Hypothesized value)/Standard error of observed value