Inference and Experiments - AP Statistics

Range of values likely to contain a population parameter. Provides an estimate with associated uncertainty.

Distribution of sample means approximates normality as sample size increases. Foundation for statistical inference with large samples.

$t$-test. Uses the $t$-distribution when population standard deviation is unknown.

To confirm results are consistent and not due to random chance. Increases confidence in findings through repeated validation.

Probability of correctly rejecting a false null hypothesis. Power equals $1 - \beta$ where $\beta$ is Type II error rate.

Failing to reject a false null hypothesis. A false negative error with probability $\beta$.

Rejecting a true null hypothesis. A false positive error with probability $\alpha$.

Probability of observing data at least as extreme under $H_0$. Measures evidence against the null hypothesis.

$H_a$. Standard notation for the alternative hypothesis in statistics.

A result unlikely to occur by chance alone, below a threshold $p$-value. Indicates the result is not likely due to random variation.

Neither participants nor researchers know who receives treatment. Prevents bias from expectations affecting results.

A group that does not receive the treatment, used for comparison. Provides a baseline to measure treatment effects against.

To eliminate bias by evenly distributing confounding variables. Ensures treatment and control groups are comparable on average.

$\text{alpha}$ or $\text{α}$. Greek letter alpha represents the significance threshold.

Measure of data dispersion around the mean. Quantifies how spread out data points are.

Mean or median. Describes the central tendency of the distribution.

Grouping similar experimental units to reduce variability. Improves precision by controlling for known sources of variation.

Dividing population into subgroups and sampling each proportionally. Ensures all subgroups are adequately represented.

Ensures representation of all subgroups in the sample. Particularly useful when subgroups differ significantly.

$z^*$ = 1.96. Standard normal value capturing 95% of the distribution.

Study observing subjects without manipulation or intervention. Cannot establish causation, only association.

Wilcoxon signed-rank test. Does not assume normal distribution of data.

Extent to which results generalize to other contexts. Relates to the generalizability of study findings.

$t$-test. Uses the $t$-distribution when population standard deviation is unknown.

$H_0$. Standard notation for the null hypothesis in statistics.

To eliminate bias by evenly distributing confounding variables. Ensures treatment and control groups are comparable on average.

$H_a$. Standard notation for the alternative hypothesis in statistics.

Failing to reject a false null hypothesis. A false negative error with probability $\beta$.

Mean or median. Describes the central tendency of the distribution.