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Preliminaries
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At a general/broad overview level:
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Recall the 6 steps of the statistical method of investigation is and why it is needed in science and other fields
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Recognize that variation is pervasive
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Explain why probability can be used to measure randomness
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Recognize different ways of representing and summarizing data.
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Be able to identify observational units and variables in a dataset.
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Terminology: see Preliminaries glossary
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6 Jan 2014. Section P.1
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Understand why anecdotal evidence is unreliable
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Follow an example of the 6 step method of statistical investigation.
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Distinguish types of variables.
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Distinguish observational units and variables
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Know organization and expectations of class.
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8 Jan 2014. Section P.2
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Explain why statistics is needed to interpret data
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Describe distributions in terms of shape and basic statistics.
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Use graphs to describe and answer questions about data.
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10 Jan 2014. Section P.3
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Distinguish different sources of variability
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Define probability in terms of long-run frequency.
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Practice simulation as a way to model processes
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Chapter 1
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Be able to measure the strength of evidence in the case of a single binary variable.
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Justify a conclusion about data using p-values and standardized statistics
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Terminology: see Chapter 1 glossary
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13 Jan 2014. Section 1.1
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Distinguish between a statistic and a parameter
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Explain each step the 3S method for measuring the strength of evidence (statistic, simulate, strength)
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Explain why a chance model can be used to evaluate a statement about real data
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Justify using coin flipping and simulation using the one-proportion applet to simulate a 50/50 binary random process
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Qualitatively compare real data to the outcome of a random process.
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15 Jan 2014. Section 1.2
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Simulate a non-50/50 binary random process.
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Use a random process to simulate the outcomes of a null hypothesis
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Associate non-random processes with alternative hypotheses
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Relate 'null and alternative' hypotheses to the 3S method and the 6 step method of statistical investigation.
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Relate null hypothesis, null distribution, and random process
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Define p-value
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Graphically interpret a p-value using a distribution.
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Use a p-value to make a statement about the strength of evidence
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Become more comfortable with the difference between a statsitic and a parameter
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17 Jan 2014. Section 1.3
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Describe what the standard deviation is supposed to measure
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Calculate the standard deviation of a set of data
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Standardize a statistic using a null distribution
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Use a standardized statistic to make a statement about the strength of evidence
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17-22 Jan 2014. Section 1.4 (homework)
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Identify three factors that affect the strength of evidence
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Explain how and why they affect it (i.e. whether they would make the p-value and standardized statistic larger or smaller)
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Be able to decide whether to use a one- or two-sided test based on the research question and prior knowledge.
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Link the decision to do a one-sided or two-sided test to how an alternative hypothesis is formulated
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22 Jan 2014. Section 1.5
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Relate the theory-based alternative to the simulation part of the 3S method.
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Use the normal distribution to evaluate the strength of evidence.
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Memorize formula for calculating the appropriate standard deviation of the null distribution for sample proportions.
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Know when the theory-based approach is invalid and understand that the simulation-based approach is valid more often.
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Use the one-proportion applet to experiment and build your intuition about the central limit theorem
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Chapter 2
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Appreciate properties of and be able to generate a simple random sample
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Recognize biased sampling methods
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Be able to critique the validity of a study based on its sampling scheme
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Apply tests of significance to random samples from populations
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Be able to measure the strength of evidence for a single quantitative variable
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Distinguish type I and type II errors
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Terminology: see the Chapter 2 section summaries
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24 Jan 2014. Section 2.1
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Distinguish a sample from a population.
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Describe the relationship between samples, populations, statistics, and parameters
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Distinguish between quantitative and categorical variables
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Interpret a histogram
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Identify the population in a description of a study design.
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Decide between different possible populations that a sample may represent
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Describe how to use a sampling frame to generate a simple random sample
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Relate bias to sampling methodology
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Distinguish simple random samples, convenience samples, and proportional samples.
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Connect the sampling scheme to the generalizability of a study
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27 Jan 2014. Section 2.2
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Understand how the property of resistance to outliers can be used to choose a statistic to use
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Justify using the median vs. the mean as a statistic to summarize a set of data
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Use the 3S strategy to draw inferences about a quantitative variable
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Understand the relationship between the formulas for the z-statistic and the t-statistic
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Use a theory based method (one-sample t-test) to draw inferences about a population mean
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29 Jan 2014. Section 2.3
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Relate p-values to significance levels
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Use a significance level to draw a conclusion about the strength of evidence.
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Construct a "truth table" to define type I and type II errors.
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Chapter 3
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Estimate the size of the effect of a non-random process on the data
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Justify a conclusion about data using a confidence interval
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Master 4 different ways of constructing a confidence interval and relate them to each other
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Explain how biases in sampling methods affect confidence intervals
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Terminology: see the Chapter 3 section summaries
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31 Jan 2013. Section 3.1
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Make the conceptual link between significance testing and whether a value is a plausible value for a parameter
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Define a confidence interval
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Relate a confidence level to a significance level.
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Explain the connection between confidence level and the range of plausible parameter values
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3 Feb 2014. Section 3.2
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Relate the term margin-of-error to confidence intervals.
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Use the 2SD method (and its generalization "the Empirical Rule") to generate confidence intervals for population proportions and know when this method is valid.
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Use the theory-based method to generate confidence intervals and to explain where the Empirical Rule comes from
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Memorize the formula for the theory-based confidence interval for a proportion
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5 Feb 2013. Section 3.3
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Use the Empirical Rule to generate a confidence intervals for a population mean and know when this method is valid
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Use the t-distribution (theory-based) to generate a confidence interval for a population mean and know when this is valid
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5 Feb 2013 also. Section 3.4
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Explain how and why sample size and confidence level affect the width of confidence intervals and be able to justify this using the theory-based confidence interval formulas and simulations
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7 Feb 2014. Bootstrap confidence intervals [not in textbook]
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Understand how the relationship between sample and population is analogous to the relationship be statistics and parameter
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Justify sampling with replacement from a sample to represent sampling from a population based on the above relationship
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Connect the idea of sampling to the idea of bootstrapping
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Use percentiles to construct a bootstrapped confidence interval
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10 Feb 2014. Section 3.5B
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Understand the distinction between statistical and practical significance
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Define power of a test
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Identify factors that affect the power of a test
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Describe how power relates to the null hypothesis
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Chapter 4
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Evaluate whether the design of a study allows causal conclusions to be drawn
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Terminology: see Chapter 4 glossary
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12 Feb 2014. Section 4.1
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Distinguish and identify explanatory and response variables in a study
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Define and identify confounding variables.
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Explain how confounding variables affect the ability to draw causal conclusions.
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19 Feb 2014. Section 4.2
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Identify the two places where randomization can come into study design and distinguish between them (random sampling and random assignment)
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Explain why the processes of unit selection and explanatory group formation affect the scope of conclusions
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Distinguish observational from experimental studies
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Explain why causal conclusions cannot be drawn from observational studies (and any circumstances when they can).
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19,20 Feb 2014. Section 4.3 (homework)
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Identify and calculate the statistic in a paired design study.Be able to identify the statistic and explain the logic of a paired design.
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Use a paired design to draw a conclusion
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Identify where randomization comes into paired design studies.
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Chapter 5.
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Apply the 6 step statistical investigation method to the case of data on two groups with one binary variable
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Terminology: see Chapter 5 glossary; also sensitivity, specificity, positive predictive value, negative predictive value
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21 Feb 2014. Section 5.1
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Construct a contingency table from a data table
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Make a segmented bar graph from a data table
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Identify observation units and variables in a two-variable dataset.
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Calculate conditional proportions from a contingency table
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21 Feb 2014. Section 5.2 (inference)
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Apply the 3S method to a dataset that involves comparing two sample proportions (two groups, one binary variable)
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Explain the logic of the scrambling strategy of simulation. Compare shuffling cards to the applet
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Relate the scrambling strategy of simulation to previous strategies
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Use the two-way table inference applet to draw conclusions about two proportions
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24 Feb 2014. Section 5.2 (estimation)
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Use the 2SD method to produce confidence intervals for the difference between two proportions
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Use bootstrapping to produce confidence intervals for the difference between two proportions
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Identify factors that affect p-values and confidence intervals for the two groups, one binary variable situation and explain why they have their effects
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Explain how confidence levels and significant levels affect the process of drawing conclusions
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24 Feb 2014. Section 5.3
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Use the normal distribution to test for and estimate differences between two proportions
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Relate the theory-based approach to the simulation based approach
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Explain the boxes in the two-proportion theory based inference applet and use it to interpret the data in this chapter
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Memorize and interpret the formulas for the two proportion theory-based approach
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26 Feb 2014. Sensitivity, specificity, positive predictive value, negative predictive value
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Understand how to interpret medical test results in the context of a 2x2 contingency table
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Contrast the usefulness and intuitiveness of counts vs. proportions in interpreting 2x2 tables
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Chapter 6
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Apply the 7 step method to data with two groups, one quantitative variable
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Terminology: see Chapter 6 glossary
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28 Feb 2014. Section 6.1
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Use dotplots and summary statistics to display, summarize, and compare distributions of quantitative data.
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Develop intuition about how variance within vs. between groups affects the ability to draw conclusions about differences between the groups
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28 Feb 2013. Section 6.2
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Apply the 3S method to a dataset that involves comparing two quantitative sample statistics (two groups, one quantitative variable)
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Use the 2SD method to produce confidence intervals for the difference between two statistics
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Use bootstrapping to produce confidence intervals for the difference between two statistics
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Identify some factors that affect p-values and confidence intervals for the two groups, one quantitative variable situation and explain why they have their effects
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Explain the options in the randomization test with quantitative response applet and use it to interpret data in this chapter
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3 Mar 2014. Section 6.3
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Compare and contrast the t-distribution with the normal distribution
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Explain why a t-distribution is used to compare means of two groups and not a normal distribution
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Use the t-distribution to test for and estimate differences between two means
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Know the formula for the t statistic
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Relate the theory-based approach to the simulation based approach
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|
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Use the theory-based inference applet to interpret data in this chapter
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Chapter 9
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Develop statistics for comparing means across multiple groups
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Utilize simulation-based approaches to compare several means
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Understand roles of within-group and between-group variability in assessing significance
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|
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Apply and interpret results of theory-based approach (ANOVA F test)
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|
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Understand the link between the F distribution, F test, and F statistic
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Realize that either simulation or theory-based approaches can be used to assess the significance of an F statistic
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Consider follow-up multiple comparison analyses
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Terminology: see Chapter 9 glossary
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|
![collapse V](Expanded.png) |
3 and 5 March 2014. Section 9.1
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Justify making a new statistical test vs. mutliple pairwise tests
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Invent a statistic for comparing means across multiple groups
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Present a statistic comparing within vs. between group variation (F statistic)
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Use the 3S method to draw inferences about group differences using the F statistic
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Motivate the MAD statistic in the case of quantitative response variables
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Use the 3S method to draw inferences about group differences using the MAD statistic
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|
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7 March 2014. Section 9.1-2 continued
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Understand the motivation behind the F statistic and how to calculate it
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Explain and calculate "degrees of freedom" and know how it figures into theory-based approaches
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|
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Explain what the mean-square column in an ANOVA table means.
|
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|
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Interpret what a significant result in an ANOVA means.
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Use bootstrapping to calculate confidence intervals for the statistics that compare means across multiple groups
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|
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Construct post-hoc confidence intervals for differences between means
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|
![collapse V](Expanded.png) |
Chapter 10
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|
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Plot data with two quantitative variables
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Interpret the form and interpret, measure, and test the direction and strength of association in a scatterplot
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|
![*](LeafRowHandle.png) |
Terminology: see Chapter 10 glossary (terms relevant to sections 10.1-4)
|
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|
![collapse V](Expanded.png) |
10 March 2014. Section 10.1
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Identify observational units and variables in the case of paired data with two different variables
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|
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Distinguish this case from the matched-pairs case of 4.3
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|
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Construct a scatterplot from data
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Qualitatively describe the form, strength, and direction of an association from a scatterplot
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Identify any unusual observations in a scatterplot
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Construct the correlation coefficient statistic based on desired properties
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|
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Infer the strength and direction of an association from a correlation coefficient
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|
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Demonstrate why a correlation coefficient is agnostic about the form of an association
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|
![collapse V](Expanded.png) |
12 March 2014. Section 10.2-3
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Calculate a correlation coefficient from data and see how it summarizes strength and direction of an association and when it is valid
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|
![*](LeafRowHandle.png) |
Estimate correlations visually - practice with the correlation guessing game applet
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|
![*](LeafRowHandle.png) |
Use the 3S method to test hypotheses about the correlation coefficient
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|
![*](LeafRowHandle.png) |
Use bootstrapping to compute confidence intervals for the correlation coefficient
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|
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Define the regression line in terms of how it summarizes the data
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|
![*](LeafRowHandle.png) |
Interpret the slope and intercept of such a line and relate the slope to the correlation coefficient
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|
![collapse V](Expanded.png) |
14 March 2014. Section 10.4
|
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Use the 3S method to test hypotheses about the regression slope
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Use bootstrapping to compute confidence intervals for the regression slope
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14 March 2014. Conclusion
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Catalog the different types of simulation strategies we have used
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Integrate the different situations and strategies into a common framework using the 6-step method and the 3S strategy.
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Make a flowchart for statistical investigation based on data type and data shape (best to do as the course progresses)
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Distinguish between estimation and inference and explain the roles of each
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