Team Based Statistics

Learning Outcomes

• B: Can I work with the basic building blocks of statistics?

  • B1: I can distinguish types and subcategories of variables.

  • B2: I can identify different sampling techniques.

  • B3: Given a sample of data, I can generate visualizations to represent it's variables.

  • B4: Given a sample of data, I can identify or compute different measures of centrality.

  • B5: Given a sample of data, I can identify or compute different measures of variation, and identify outliers.

• P: Can I compute probabilities and identify properties of probability distributions?

  • P1: I can compute and interpret probabilities of events, including compound events involving operations.

  • P2: I can compute and interpret probability of events involving conditional probabilities.

  • P3: I can utilize Bayes Theorem in the computation and interpretation of probabilities.

  • P4: I can compute and interpret probabilities from the probability distribution of a random variable, as well as compute and interpret the expectation, variance and standard deviation of a random variable.

  • P5: I can compute and interpret the expectation, variance and standard deviation of linear combinations of random variables.

• D: Can I work with the foundational probability distributions of statistics?

  • D1: I can compute and interpret probabilities given bounds, and bounds given probabilities for the standard normal variable.

  • D2: I can compute and interpret probabilities given bounds, and bounds given probabilities for general normal variables.

  • D3: I can count ordered and unordered selections of objects, with or without repitition.

  • D4: I can compute and interpret probabilities for binomial random variables.

  • D5: I can use the normal approximation for binomial random variables to compute probabilities and bounds.

• F: Can I perform the fundamental tasks of statistical inference?

  • F1: I can identify point estimates for parameters of interest.

  • F2: I can find a confidence interval for the true proportion of a categorical variable, given a sample, and interpret the meaning of this interval.

  • F3: I can test hypothesis about the true proportion of a categorical variable, given a sample: stating the null and alternative hypothesis, computing a $p$-value, explaining the meaning of the $p$-value and drawing a conclusion.

• C: Can I perform inference for categorical variables?

  • C1: I can identify the sample size neccesary for a confidence interval to have a given margin of error.

  • C2: I can perform hypothesis tests and compute confidence intervals for the differences of proportions, and explain the results.

  • C3: I can use ${\chi }^2$ tests to test the goodness of fit of a sample, and explain the results.

  • C4: I can use ${\chi }^2$ tests to test the independence of categorical variables and explain the results.

• N: Can I perform inference for numerical variables?

  • N1: I can compute and interpret probabilities given bounds, and bounds given probabilities for standard $t$-variables.

  • N2: I can perform hypothesis tests and compute confidence intervals for the means of numerical variables, and explain the results.

  • N3: I can perform hypothesis tests and compute confidence intervals for the means of differences of paired numerical variables, and explain the results.

  • N4: I can perform hypothesis tests and compute confidence intervals for the differences of means of numerical variables, and explain the results.

  • N5: I can find the sample size of a numerical variables needed to find confidence intervals with given margin of errors, and detect differences in means given a power.

  • N6: I can use ANOVA to test if variation between groups can be explained solely through the variation within groups and explain the results.

• R: Can I perform regression for paired numerical variables?

  • R1: I can compute and interpret the correlation coefficient and it's square for a regression analysis.

  • R2: I can find the parameters for the regression line, explain the parameters, and use it to make predictions from the linear model.

  • R3: I can perform hypothesis tests and compute confidence intervals for the parameters of the regression line and explain the results.