Difference between revisions of "Objectives 2018F"

Revision as of 16:47, 27 October 2018

Objectives for Exam 1

• In looking at side-by-side box plots, be able to tell which distribution has the greatest median, and which has the least median.
• In looking at side-by-side box plots, be able to tell which distribution has the greatest IQR, and which has the least IQR.
• In looking at side-by-side box plots, be able to tell which distribution has the least and greatest Q1 and Q3.
• In looking at side-by-side box plots (both modified and unmodified), be able to tell which distribution has the greatest and least values (i.e. min/max).
• In looking at side-by-side box plots (modified) be able to tell which show that suspected outliers are present.
• Know the 1.5*IQR Rule for suspected outliers. Be able to use this rule to:
• Plug in a "where" function into StatCrunch/Summary Stats to count (statistic = n) the number of outliers in a box plot when they are too many/too close to count by hand on the image.
• Given a distribution, identify the cases and the variables.
• Given a list of variables, identify which are nominal, ordinal, binary, identifier/label, or quantitative. Be able to justify your answers, not just provide guesses.
• Make a stem plot from data.
• Be able to follow the direction: "make a stem plot and split stems."
• Be able to follow the direction: "make a stem plot and trim stems" and/or "make a stem plot and trim and split stems."
• Know to put gaps in a stem plot when appropriate.
• Know what type of variable is described by each of the following: a bar graph, pie chart, stem plot, histogram, box plot.
• Know how to describe in words the distribution of a quantitative variable, in terms of shape (unimodal, bimodal, multimodal, symmetric, skewed to left, skewed to right), outliers (how many and where they are, e.g. upper tail, lower tail, or both), center (mean and median), spread (standard deviation, and 5 number summary).
• Know that a distribution is skewed to the side of the longer tail, but alternatively, and perhaps more precisely, a distribution is skewed left if its mean is less than its median, and skewed right if its mean is greater than its median---the longer tail pulls the mean toward it, as the mean is more sensitive to outliers.
• Know how to compute the mean and median, and the standard deviation and the 5 number summary of a variable from data in StatCrunch.
• If a distribution has two or more isolated modes, know how to use a "where" function to separate the modes so that summary statistics can be derived for each mode in isolation.
• Know which summary statistics are resistant to outliers (i.e. "resistant") and which are sensitive to outliers (i.e. "not resistant"). Also understand why.
• Know that describing the distribution of a variable conveys "what values the variable takes, and how often it takes those values." Know the similarities and differences between describing distributions of categorical and quantitative variables.
• In StatCrunch, know how to derive a frequency table for a categorical variable to describe its distribution.

Objectives for Exam 2

Chapter 5

• Find mean and standard deviation, and other summary statistics, for a quantitative variable.
• Given the mean and standard deviation for the raw data, compute the z-score for particular data points.
• Given the mean and standard deviation for the raw data, compute the raw score for particular z-scores.
• Interpret a z-score as the number of standard deviations of a data point above the mean.
• Know that, after transforming data to z-scores, the mean of the z-scores is 0.
• Know that, after transforming data to z-scores, the standard deviation of the z-scores is 1.
• Know that, after transforming data to z-scores, the shape of the z-score distribution (gaps, modes, symmetry, skewness) is the 'same as the original.
• Given several Normal probability QQ-plots, identify which looks most Normal (it will be obvious).
• Use the Normal calculator in StatCrunch to compute percentiles and related quantities.
• Know the parameters for the standard Normal model (mean 0, standard deviation 1).
• Know that if the data follow a Normal distribution, the z-scores follow a standard Normal distribution.
• Know that if the data do NOT follow a Normal distribution, the z-scores do NOT follow Normal distribution either, standard or otherwise, although mean of the z-scores is always 0 and the standard deviation is always 1.

Chapter 6

• Know what it means for two variables to be associated, (knowing the value of one variable tells you something about the value of the other that you would not know otherwise).
• Be able to describe an association in terms of its form, strength, and direction.
• Be able to identify outliers for the relationship between the variables as possibly distinct from outliers in just one variable alone.
• Know the difference between explanatory variables and response variables, and which goes on which axis.
• Know how to draw a scatter plot.
• Know how to identify an association between two variables as linear, possibly with scatter.
• Know how to compute the correlation between two variables.

Chapters 7 & 8

• Know how to perform a simple linear regression to describe the relationship between a response and an explanatory variable.
• Know that if the explanatory and response variables are switched, the regression line changes, even when plotted on the same axes (unless there is no scatter in the data).
• Know that both correlation and simple linear regression are only appropriate if the form of the association between the variables is linear.
• Know that both correlation and simple linear regression are only appropriate for quantitative variables. (The book does discuss alternatives for ordinal variables, but we didn't cover those in any detail.)
• Know that both correlation and simple linear regression can be sensitive to outliers. Outliers can make the interpretation of results of correlation and regression suspect, and not descriptive of the rest of the data.
• Likewise, know that if a strong association between variables is nonlinear, the correlation coefficient will not reveal the full strength of the association.
• Know that the best way to discern the appropriateness of the linear model (on which both correlation and simple linear regression are based) is by looking at the residuals of the simple linear regression. The linear model is appropriate if the residuals are a horizontal band of points around zero, with no structure. Be able to plot the residuals versus X-values for this purpose.

Chapter 13 & 14 & 15

• Know what a set is, what an element of a set is, and what a subset of a set is.
• Know the symbols for "subset," "element of," "empty set," "intersection," "union," and "complement of."
• Know what it means for two sets to be disjoint.
• Given two sets, find their union and intersection.
• Be able to identify the sample space of a random phenomenon (set of outcomes).
• Be able to list all the events of random phenomenon with two or three outcomes (remember than an event can have 0, 1, 2, or more outcomes).
• Given a sample space and an event find the complement of the event.
• Remember and be able to apply the 5 rules of probability.
• Know the interpretation of independent events, together with Rule 5 which defines them mathematically.
• Know that a random variable assigns, as a function, a number to each outcome of a random phenomenon.
• Be able to give an example of a random variable defined on the set of outcomes of the throw of a four sided die with colors labeling the sides.
• Be able to give an example of a random variable defined on the set of outcomes of ten coin tosses.
• Be able to give an example of a random variable defined on the set of outcomes of three students sampled from our thirty-student class.
• Be able to compute the mean of a discrete random variable.
• Be able to compute the standard deviation of a discrete random variable.

Chapter 16: Probability Models

• Bernoulli Trials
• Geometric Model
• Binomial Model
• Approximating Binomial Model with Normal Model
• Uniform Model