biostats unit 2

sampling distribution

Distribution of a statistic from many samples.

Standard error (SE)

Typical distance between a sample statistic and the true population value.

Confidence interval (CI)

Range likely to contain the true population value.

Confidence level

Probability the CI includes the true value (e.g., 95%).

Critical value

Cutoff point for deciding extreme results.

The boundary on your sampling distribution that tells you what counts as “unusual” or “extreme” if the null hypothesis is true.

SE for sample mean

SE = standard deviation/square root of the sample size

estimates how much the sample mean varies from the population mean

SE for proportions

SE = square root sample proportion (1-sample proportion)/sample size

estimates how much the sample proportion varies from the true population proportion

Significance level (α)

Threshold for rejecting H₀; chance of Type I error.

Type 1 error

rejecting a true null hypothesis

Margin of error (ME)

How far a sample statistic might be from the true value.

equation for ME

ME = critical value * SE

Type II error

Not rejecting a false null

Null hypothesis (H₀)

“No effect” or “no difference” claim.

p-value

Probability of seeing data like ours if H₀ is true.

4 step hypothesis testing

1 state null and alternative hypothesis

2 choose method

3 compute test statistic and p value

4 conclusion

1 group proportion (categorical)

make a randomization distribution to find p-value

1 group mean (numerical)

model-based (t-test)

2 group proportions (categorical)

randomization distribution

2 group means (numerical)

randomization distribution

1 tailed test

tests one direction only

2 tailed test

tests both directions

when is t distribution used

used for small samples

z score

how many sd a value is from the mean

z score equation

value-mean/standard deviation

Central limit theorem

If you take many samples from a population and compute their means, the distribution of those sample means will be approximately normal, as long as the sample size is large enough.

pnorm() and pt() does what

it is the probability up to a z or t value

qnorm() and qt()

z or t value for a given probability

simulation-based inference

use repeated sampling to find patterns

randomization distribution

Distribution under H₀, made by shuffling data.

Model-based inference

Use formulas (normal/t) to find patterns.

Bootstrap distribution

Distribution made by resampling with replacement.

Resampling within groups

Resample separately for each group.