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Concepts in Statistics
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Lumen Learning: Waymaker Concepts in Statistics Learning Outcomes is licensed under CC-BY 4.0
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Outcomes
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Module 1: Types of Statistical Studies and Producing Data
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1.1Types of Statistical Studies
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1.1.1From a research question, determine the goal of a statistical studyGoals of Statistical Studies
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1.1.2Determine if a study is an experiment or an observational studyExperiments vs. Observational Studies
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1.1.3From a description of a statistical study, determine the goal of the studyDetermine the Goals of Statistical Studies
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1.1.4Based on the study design, determine what types of conclusions are appropriateDrawing Conclusions from Statistical Studies
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1.2Sampling
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1.2.1For an observational study, critique the sampling plan. Recognize implications and limitations of the planCritiquing Sampling Plans
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1.3Conducting Experiments
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1.3.1Identify features of experiment design that controls the effects of confoundingControlling the Effects of Confounding
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Module 2: Summarizing Data Graphically and Numerically
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2.1Categorical vs. Quantitative Data
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2.1.1Distinguish between quantitative and categorical variables in contextCategorical vs. Quantitative Data
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2.2Dotplots
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2.2.1Describe the distribution of quantitative data using a dotplotDescribing Data Distribution Using Dotplots
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2.3Histograms
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2.3.1Describe the distribution of quantitative data using a histogramDescribing Data Distribution Using Histograms
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2.4Measures of Center
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2.4.1Use mean and median to describe the center of a distributionUsing Means and Medians to Describe the Center of Distributions
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2.5Measures of Spread
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2.5.1Use a five-number summary and a boxplot to describe a distributionFive-Number Summaries and Boxplots
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2.6Describing a Distribution
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2.6.1Use mean and standard deviation to describe a distributionUse Means and Standard Deviation to Describe Distributions
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Module 3: Examining Relationships: Quantitative Data
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3.1Scatterplots
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3.1.1Use a scatterplot to display the relationship between two quantitative variables. Describe the overall pattern (form, direction, and strength) and striking deviations from the patternUse Scatterplots to Describe the Relationship Between Variables
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3.2Linear Relationships
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3.2.1Use a correlation coefficient to describe the direction and strength of a linear relationship. Recognize its limitations as a measure of the relationship between two quantitative variablesUse Correlation Coefficients to Describe Linear Relationships
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3.3Association vs. Causation
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3.3.1Distinguish between association and causation. Identify lurking variables that may explain an observed relationshipDifference Between Association and Causation
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3.4Linear Regression
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3.4.1For a linear relationship, use the least-squares regression line to model the pattern in the data and to make predictionsUse the Least-Squares Regression Line
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3.5Assessing the Fit of a Line
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3.5.1Use residuals, standard error, and r2 to assess the fit of a linear modelAssess the Fit of Linear Models
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Module 4: Nonlinear Models
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4.1Exponential Relationships
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4.1.1Use an exponential model (when appropriate) to describe the relationship between two quantitative variables. Interpret the model in contextUse an Exponential Model to Describe Relationships
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Module 5: Relationships in Categorical Data with Intro to Probability
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5.1Two-Way Tables
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5.1.1Analyze the relationship between two categorical variables using a two-way tableUsing Two-Way Tables to Analyze Relationships
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5.1.2Calculate marginal, joint, and conditional percentages and interpret them as probability estimatesCalculating Marginal, Joint, and Conditional Percentages
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5.1.3Analyze and compare risks using conditional probabilitiesComparing Risks Using Conditional Probabilities
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5.1.4Create a hypothetical two-way table to answer more complex probability questionsCreating Hypothetical Two-Way Tables
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Module 6: Probability and Probability Distributions
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6.1Another Look at Probability
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6.1.1Interpret (in context) a probability as a long-run relative frequency of an eventInterpreting Probablities in Context
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6.2Probability Rules
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6.2.1Reasons from probability distributions, using probability rules, to answer probability questionsAnswering Probability Questions
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6.2.2Use conditional probability to identify independent eventsIdentifying Independent Events
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6.3Discrete Probability Distribution
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6.3.1Distinguish between discrete random variables and continous random variablesDiscrete and Continuous Random Variables
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6.3.2Use probability distributions for discrete and continuous random variables to estimate probabilities and identify unusual eventsEstimate Probababilities and Identify Unusual Events
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6.4Continuous Probability
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6.4.1Use a probability distribution for a coninuous random variable to estimate probabilities and identify unusual eventsUse Probability Distribution to Identify Unusual Events
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6.5Normal Random Variables
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6.5.1Use a normal probability distribution to estimate to probabilities and identify unusual eventsUsing Normal Probability Distributions
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Module 7: Linking Probability to Statistical Inference
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7.1Distribution of Sample Proportions
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7.1.1Describe the sampling distribution for sample proportions and use it to identify unusual (and more common) sample resultsDescribe Sampling Distributions
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7.1.2Distinguish between a sample statistic and a population parameterDifference Between Sample Statistics and Population Parameters
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7.1.3Use a z-score and the standard normal model to estimate probabilities of specified eventsUse Z-Scores to Estimate Specified Events
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7.2Statistical Inference
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7.2.1Find a confidence interval to estimate a population proportion when conditions are met. Interpret the confidence interval in contextUse Confidence Intervals to Estimate Population Proportions
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7.2.2Test a hypothesis about a population proportion using a simulated sampling distribution or a normal model of the sampling distribution. State a conclusion in contextTest a Population Proportion Hypothesis
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Module 8: Inference for One Proportion
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8.1Estimating a Population Proportion
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8.1.1Recognize situations that call for testing a claim about a population proportion or estimating a population proportionKnow When to Test Population Proportion Claims
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8.1.2Construct a confidence interval to estimate a population proportion when conditions are met. Interpret the confidence interval in contextContructing Confidence Intervals
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8.1.3For a confidence interval, interpret the meaning of a confidence level and relate it to the margin of errorInterpret the Meaning of Confidence Levels
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8.2Hypothesis Testing
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8.2.1Given claim about a population, determine null and alternative hypothesesDetermine Null and Alternative Hypotheses
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8.2.2Recognize the logic behind a hypothesis test and how it relates to the P-valueUnderstanding the Logic Behind Hypothesis Tests
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8.2.3Recognize type I and type II errorsType l and Type ll Errors
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8.3Hypothesis Test for a Population Proportion
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8.3.1Recognize when a situation calls for testing a hypothesis about a population proportionKnow When to Test Population Proportions
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8.3.2Conduct a hypothesis test for a population proportion. State a conclusion in contextConducting Hypothesis Tests for Population Proportions
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8.3.3Interpret the P-value as a conditional probability in the context of a hypothesis test about a population proportionInterpreting P-Values About Population Proportions
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8.3.4Distinguish statistical significance from practical importanceStatistical Significance vs. Practical Importance
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Module 9: Inference for Two Proportions
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9.1Distribution of Differences in Sample Proportions
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9.1.1Recognize when to use a hypothesis test or a confidence interval to compare two population proportions or to investigate a treatment effect for a categorical variableKnow When to Use a Hypothesis Test or Confidence Interval