Difference between revisions of "Stat 202 Discussion"

Revision as of 22:50, 31 October 2018

Broad Objectives

Single Variable Descriptive Statistics

• Understand the traditional way of structuring data (datasets, tables, cases, variables, values).
• Be able to recognize the types of variables in a data set (quantitative, identifier, categorical (ordinal, nominal, binary)).
• Understand that different analyses and displays are appropriate for different types of variables.
• Understand the concept of a distribution of a variable (what values the variable takes and how often it takes those values).
• Describe the distribution of a single quantitative variable (histogram, box plot, QQ plot, shape, outliers, center, spread, modes, symmetry, skewness, normal/bell shaped, mean, median, standard deviation, Q1, Q3, IQR, percentiles).
• Describe the outliers in single quantitative variables (tails, 1.5 IQR rule), and know which measures are resistant to outliers (resistant) and which are sensitive to outliers (not resistant), and what that means.
• Describe the distribution of a single categorical variable (bar plot, pie chart, frequency table).
• Understand the concept of and apply transformations of a variable (e.g. z-score, change of units, log) and know the special properties of a linear transformation.
• Understand what it means for data (a quantitative variable) to fit a Normal model with parameters (revealed by histogram, QQ-Plot, including typical noise) and know how to make predictions based on that assumption.
• Understand descriptions of Normal and other models with density curves.

Paired Variables Descriptive Statistics

• Describe the relationship between a categorical variable and a quantitative variable (series of histograms, side-by-side box plots).
• Describe the relationship between pairs of quantitative variables (scatter plots).
• Know what it means for a pair of quantitative variables to fit a linear model with scatter.
• Know that correlation and regression are only appropriate for pairs of quantitative variables that fit a linear model with scatter.
• Describe the linear relationship between quantitative variables with correlation and regression, and know the properties of these analyses.
• Know the difference between outliers for a relationship between variables, and outliers for individual variables, understand the influence of influential data points.
• Know the concept of, and how to compute, residuals of a regression analysis.
• Know the significance of R^2 in assessing the fraction of variance explained by linear regression between two quantitative variables.
• Know that neither correlation nor association implies causation.

Design of Experiments

[Coming soon...]

Probability

• Understand and use set notation (element of, subset of, union, intersection, complement of, null set, disjoint sets).
• Understand and apply the terminology of probability (random phenomenon, sample space, outcomes, events, independent sets) and the rules/"axioms" of probability.
• Understand the mathematical concept of a function to be able to apply it to the definition of a random variable.
• Know and understand the definition of a random variable as a function mapping a sample space of a random phenomenon to real numbers, and be able to give important examples of random variables (coin toss, die toss, sampling, binomial).
• Know how to compute the mean and standard deviation of a discrete random variable from its probability table.
• Know how to apply formulas to compute means, variances, and standard deviations of sums, differences, and linear transformations of independent and correlated random variables.
• Know the assumptions behind the use of a Binomial model, and recognize situations when this model is applicable.
• Use the Binomial calculator to make predictions in StatCrunch; know how to use other StatCrunch calculators (geometric, Normal, Uniform) and when they apply.

Sampling Distributions

[Coming soon ...]

Inference

[Coming soon...]