Understand that standard error changes with the square root of the sample size.

Recognize, in context, the idea of ANOVA as comparing variance between groups to variance within groups.

Recognize when the Central Limit Theorem applies.

Recognize, in context, parts of a chi-squared test for independence (null, degrees of freedom, and observed vs expected rationale).

Recognize and construct examples to illustrate how correlation does not imply causation.

Interpret positive, negative, and zero correlation and transfer knowledge about associations to new context/situations.

 Identify the meaning of correlation and its relationship to the slope of the regression line.

Recognize how a change in units affects the variance (since variance is expressed in squared units).

Identify sample and population quantities in context and match to standard statistical notation. (Instructors: Please check alignment with your curriculum)

Reason how larger sample sizes decrease the p-value, all else being equal.

Reason how larger sample sizes decrease the p-value, all else being equal.

Reason about the factors that affect the width of a confidence interval (sample size, confidence level, standard deviation).

Recognize good properties of a bar graph.

Identify counterparts in the courtroom analogy for hypothesis test (innocence ≈ null; acquit ≈ fail to reject; etc.). Identify errors of Type I and II in context.

Contrast inferential and descriptive statistics with respect to their different goals and typical tools or outputs.

Apply relationships among alpha level, p-value, and the decision of a hypothesis test.

Applying Bayes' rule or examining marginal and conditional proportions in a table to see how, for rare conditions, most positive test results may be false positives.

Give 4 levels of measurement (nominal, ordinal, interval, ratio scales) in appropriate hierarchical order and identify examples of each level in a real-world context.

Reason about mean and median, and the effect of an outlier.

Reason about mean and median, and the effect of an outlier.

Explore Simpson’s paradox and recognize how a third variable might drive the relationship between two others.

 Recognize and apply the basic rules of probability and distinguish between their use.

Interpret basics of regression, including: checking assumptions, interpretation of slope, r, and r^2.

Apply margin of error in the context of a poll question, including that variability decreases with the square root of sample size.

Identify examples of biased (e.g. range) and unbiased (e.g. mean) estimators.

Identify factors that allow a sample of data to be representative of the population and distinguish between random and convenience samples.

Identify the null hypothesis (as opposed to the alternative hypothesis) for the most common situations.

Identify factors to consider when deciding how outliers should be treated, as well as factors for deciding if a study is worthwhile.

 Understand the definition of a P-value.

Reason about the meaning of and distinguish among observed, fitted, and residual values.