Preface Learning Outcomes and Usage
The material in this book is designed to answer the following big questions and develop the following skills.
Learning Outcomes
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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.
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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.
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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.
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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.
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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.
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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.
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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.
This is an active learning text driven by in class activities meant to be worked on in small groups, with guidance from the instructor. For a more traditional text see the excellent https://www.openintro.org/ on which much of this material is based.