Students can break down complex problems into their component pieces, identify which of these components are important to the hypothesis that you are testing, apply the appropriate statistical test, and, of course, to quantify the uncertainty inherent in your conclusion and your data. Much of the field of applied statistics, and therefore this course, is about attributing variation to either 'noise' or 'signal' and logically justifying the steps you take in analyzing data sets.

Students can contribute to a wide range of project scopes, including, but not limited to:

• Descriptive statistics: location, spread, displaying data: students will compute and distinguish between descriptors of the location and spread of data such as mean, mode, median and standard deviation, interquartile range. They will explain the effect of bias and non-random sampling on moments.
• Data Visualization: Students will display data with appropriate visual tools.
• Quantifying uncertainty: students will qualitatively interpret and quantify common descriptions of uncertainty, such as confidence intervals and standard error.
• Probability: Frequentist and Bayesian probability; students will re-construct from first principles the laws of basic probability, including conditional and Bayesian logic.
• Hypothesis Testing principles and some simple applications inclyding Binomial test and Chi-squared (contingency and goodness of fit). Students will define and describe the relationship between type I errors, type II errors, power, and sample size. Students will calculate an example of inflated alpha given simultaneous multiple tests (i.e., GWAS). Students will construct binomial, normal, and Poisson distributions. Students will select the appropriate statistical test and will calculate the test value and associate p-value.
• Students will justify their conclusion and will offer support in the form of calculating a confidence interval.
• Normal Distribution: Students will interpret and compute z- scores and assess any assumptions that z-scores include.
• T-tests, ANOVA, correlation, Regression, General Linear Models: Students will assess and contrast common statistical tests and apply them to novel problems appropriately by incorporating an evaluation of assumptions and experimental design concerns.
• Students will compute common statistical tests, including t-tests, ANOVA, correlation, regression, and general linear models, including ANCOVA.
• Non-parametric statistics, Computationally intensive methods and Maximum likelihood: Students will conduct statistical tests when the test's assumptions are violated will compare the results of the standard parametric test with their analogous non-parametric test. Students will be able to identify the nonparametric alternative to each parametric test. Students will evaluate the effects of using an inappropriate test (or a test when its assumptions are violated) on alpha and beta.
• Students will identify when it is appropriate to use computational methods such as Bootstrap and apply them to problems.
• Students will calculate Maximum Likelihood Estimates (MLE) and explain when they are used, and contrast them to Bayes' theorem.
• Experimental Design: Students will identify specific and common errors in poor experimental design and describe poor design's qualitative effects. Students will analyze the results of poor experimental design on common statistical tests' ability to discriminate against the null hypothesis (power). Students will be able to calculate the sample size necessary to obtain sufficient power for the study. Students will be able to calculate effect size and summarize the challenges and benefits of meta-analysis.