This lesson will introduce the connection between correlation and causality. It is 1 of 4 in the series titled "Correlation and Causation." Includes short quiz. [5:19]
This lesson will introduce the connection between correlation and causality. It is 2 of 4 in the series titled "Correlation and Causation." Includes short quiz. [6:14]
This lesson will introduce the connection between correlation and causality. It is 4 of 4 in the series titled "Correlation and Causation." Includes short quiz. [3:02]
Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise).
Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.
Samples and ProbabilityType of Unit: ConceptualPrior KnowledgeStudents should be able to:Understand the concept of a ratio.Write ratios as percents.Describe data using measures of center.Display and interpret data in dot plots, histograms, and box plots.Lesson FlowStudents begin to think about probability by considering the relative likelihood of familiar events on the continuum between impossible and certain. Students begin to formalize this understanding of probability. They are introduced to the concept of probability as a measure of likelihood, and how to calculate probability of equally likely events using a ratio. The terms (impossible, certain, etc.) are given numerical values. Next, students compare expected results to actual results by calculating the probability of an event and conducting an experiment. Students explore the probability of outcomes that are not equally likely. They collect data to estimate the experimental probabilities. They use ratio and proportion to predict results for a large number of trials. Students learn about compound events. They use tree diagrams, tables, and systematic lists as tools to find the sample space. They determine the theoretical probability of first independent, and then dependent events. In Lesson 10 students identify a question to investigate for a unit project and submit a proposal. They then complete a Self Check. In Lesson 11, students review the results of the Self Check, solve a related problem, and take a Quiz.Students are introduced to the concept of sampling as a method of determining characteristics of a population. They consider how a sample can be random or biased, and think about methods for randomly sampling a population to ensure that it is representative. In Lesson 13, students collect and analyze data for their unit project. Students begin to apply their knowledge of statistics learned in sixth grade. They determine the typical class score from a sample of the population, and reason about the representativeness of the sample. Then, students begin to develop intuition about appropriate sample size by conducting an experiment. They compare different sample sizes, and decide whether increasing the sample size improves the results. In Lesson 16 and Lesson 17, students compare two data sets using any tools they wish. Students will be reminded of Mean Average Deviation (MAD), which will be a useful tool in this situation. Students complete another Self Check, review the results of their Self Check, and solve additional problems. The unit ends with three days for students to work on Gallery problems, possibly using one of the days to complete their project or get help on their project if needed, two days for students to present their unit projects to the class, and one day for the End of Unit Assessment.
Students extend their understanding of compound events. They will compare experimental results to predicted results by calculating the probability of an event, then conducting an experiment.Key ConceptsStudents apply their understanding of compound events to actual experiments.Students will see there is variability in actual results.Goals and Learning ObjectivesContinue to explore compound independent events.Compare theoretical probability to experimental probability.
Students begin learning about compound events by considering independent events. They will consider everyday objects with known probabilities. Students will represent sample spaces using lists, tables, and tree diagrams in order to calculate the probability of certain events.Key ConceptsCompound events are introduced in this lesson, building upon what students have learned about determining sample space and probabilities of single events.Terms introduced are:multistage experiment: an experiment in which more than one action is performedcompound events: the combined results of multistage experimentsindependent events: compound events in which the outcome of one does not affect the outcome of the otherGoals and Learning ObjectivesLearn about compound events and sample spaces.Use different tools to find the sample space (tree diagrams, tables, lists) of a compound event.Use ratio and proportion to solve problems.SWD: Go over the mathematical language used throughout the module. Make sure students use that language when discussing problems in this lesson.
Students will continue to apply their understanding of compound independent events. They will calculate probabilities and represent sample spaces with visual representations.Key ConceptsStudents continue to solve problems with compound events. The formula for calculating the probability of independent events is introduced:P(A and B) = P(A) ⋅ P(B)Goals and Learning ObjectivesDeepen understanding of compound events using lists, tables, and tree diagrams.Learn about the Fundamental Counting Principle.
Students continue to extend their understanding of compound events by comparing independent and dependent events. This includes drawing the sample space to understand how the first event does or does not affect the second event. Students will solve problems with dependent compound events.Key ConceptsStudents will learn about the differences between dependent and independent events.Events are independent if the outcome of an event does not influence the outcome of the others.Events are dependent if the outcome of an event does influence the outcome of the others.The difference can be observed by drawing a diagram to represent the sample space. For dependent events, the sample space is smaller.Goals and Learning ObjectivesUnderstand the difference between independent and dependent compound events.Draw diagrams for dependent compound events.Solve compound event problems.
Psychology is designed to meet scope and sequence requirements for the single-semester introduction to psychology course. The book offers a comprehensive treatment of core concepts, grounded in both classic studies and current and emerging research. The text also includes coverage of the DSM-5 in examinations of psychological disorders. Psychology incorporates discussions that reflect the diversity within the discipline, as well as the diversity of cultures and communities across the globe.Senior Contributing AuthorsRose M. Spielman, Formerly of Quinnipiac UniversityContributing AuthorsKathryn Dumper, Bainbridge State CollegeWilliam Jenkins, Mercer UniversityArlene Lacombe, Saint Joseph's UniversityMarilyn Lovett, Livingstone CollegeMarion Perlmutter, University of Michigan
By the end of this section, you will be able to:
Explain what a correlation coefficient tells us about the relationship between variables
Recognize that correlation does not indicate a cause-and-effect relationship between variables
Discuss our tendency to look for relationships between variables that do not really exist
Explain random sampling and assignment of participants into experimental and control groups
Discuss how experimenter or participant bias could affect the results of an experiment
Identify independent and dependent variables
This video explains the different types of study designs used in statistics. [9:51]
Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.