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)

Define p-value:

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)

Define beta:

P(Type II error) Probability of concluding there is no difference when a difference exists

Define power:

Power = 1 - beta Study with good power is less likely to “miss” important differences

What is power dependent on?

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- 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

Define alpha:

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