Statistical Foundations — final assessment

Skills covered

Tell observational studies from experiments · Identify confounding variables · Identify sources of bias · Detect and correct nonresponse bias · Compare relative and absolute changes and rates · Judge causal claims · Separate statistical from practical significance · Classify measurement scales · Calculate a standard deviation · Flag outliers with the 1.5 × IQR rule · Calculate and use z-scores · Calculate the median absolute deviation · Calculate and interpret the coefficient of variation · Choose between n and n − 1 · Calculate a weighted mean · Describe the shape of a distribution · Choose a chart for the question and variable types · Build and read box plots · Judge normality from a Q-Q plot · Recognise misleading charts · Read ECDF plots · Read scatter plots · Write chart titles and summaries that state the finding · Apply the addition rule · Calculate conditional probabilities · Reason about base rates and predictive values · Apply Bayes' theorem · Distinguish independent from mutually exclusive events · Compute an expected value · Compute probabilities by counting · Use the complement rule · Calculate binomial probabilities · Check the binomial conditions · Calculate Poisson probabilities · Calculate normal probabilities · Solve inverse normal problems · Find critical values for one and two tails · Choose a distribution for a situation · Check a distributional assumption with data · Describe probability sampling designs · Allocate a stratified sample · Calculate the standard error of a mean · Distinguish the SD from the SE · Apply the central limit theorem · Judge when n is large enough for the CLT · Apply the finite population correction · Build a t interval for a mean · Choose between z and t, and explain why · Build an interval for a proportion · Choose between Wald and Wilson intervals · Build a Welch interval for a difference in means · Build an interval for a difference in proportions · Interpret a confidence interval correctly · Explain what makes an interval wider or narrower · Plan the sample size for a proportion · Build an interval from paired data · Plan the sample size for a mean · Formulate null and alternative hypotheses · Run a one-sample t-test · Run a two-sample t-test · Run a paired t-test · Test a single proportion · Compare two proportions · Compute and interpret a p-value · Reason about Type I and Type II errors · Plan power and sample size · Report and judge effect sizes · Control error rates across many tests · Choose an appropriate test · Interpret and communicate a test result