Classroom Resource

P-Value as a Benchmark in Experimental Research | Prediction by the Numbers

Subject Area

Mathematics

Grade(s)

8, 9, 10, 11, 12

Overview

Learn about the origins and meaning of “p-value,” a statistical measure of the probability that has become a benchmark for success in experimental science, in this video from NOVA: Prediction by the Numbers. In the 1920s and 1930s, British scientist Ronald A. Fisher laid out guidelines for designing experiments using statistics and probability to judge results. He proposed that if experimental results were due to chance alone, they would occur less than 5 percent (0.05) of the time. The lower the p-value, the less likely the experimental results were caused by chance. Use this resource to stimulate thinking and questions about the use of statistics and probability to test hypotheses and evaluate experimental results.

Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.44

Explain whether two events, A and B, are independent, using two-way tables or tree diagrams. [Algebra I with Probability, 38]

Unpacked Content

UP:MA19.8A.44

Vocabulary

  • Independent event
  • Probability
  • Dependent event
  • Event
  • Two-way table
  • Tree diagram
  • Simple event
  • Compound event

Knowledge

Students know:
  • Methods to find probability of simple and compound events.

Skills

Students are able to:
  • Interpret the given information in the problem.
  • Accurately determine the probability of simple and compound events.
  • Accurately calculate the product of the probabilities of two events.

Understanding

Students understand that:
  • Events are independent if one occurring does not affect the probability of the other occurring, and that this may be demonstrated mathematically by showing the truth of P(A & B) = P(A) x P(B).
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.45

Compute the conditional probability of event A given event B, using two-way tables or tree diagrams. [Algebra I with Probability, 39]

Unpacked Content

UP:MA19.8A.45

Vocabulary

  • Conditional probability
  • Independence
  • Probability
  • Sample space
  • Simple event
  • Compound event

Knowledge

Students know:
  • Methods to find probability of simple and compound events.
  • Techniques to find conditional probability.

Skills

Students are able to:
  • Accurately determine the probability of simple and compound events.
  • Accurately determine the conditional probability P(A given B) from a sample space or from the knowledge of P(A&B) and the P(B).

Understanding

Students understand that:
  • The independence of two events is determined by the effect that one event has on the outcome of another event.
  • The occurrence of one event may or may not influence the likelihood that another event occurs.
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.46

Recognize and describe the concepts of conditional probability and independence in everyday situations and explain them using everyday language. [Algebra I with Probability, 40]

Unpacked Content

UP:MA19.8A.46

Vocabulary

  • Conditional probability
  • Independence
  • Probability

Knowledge

Students know:
  • Possible relationships and differences between the simple probability of an event and the probability of an event under a condition.

Skills

Students are able to:
  • Communicate the concepts of conditional probability and independence using everyday language by discussing the impact of the occurrence of one event on the likelihood of the other occurring.

Understanding

Students understand that:
  • The occurrence of one event may or may not influence the likelihood that another event occurs (e.g., successive flips of a coin
  • First toss exerts no influence on whether a head occurs on the second, drawing an ace from a deck changes the probability that the next card drawn is an ace).
  • Events are independent if the occurrence of one does not affect the probability of the other occurring.
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.47

Explain why the conditional probability of A given B is the fraction of B’s outcomes that also belong to A, and interpret the answer in context. [Algebra I with Probability, 41]

Unpacked Content

UP:MA19.8A.47

Vocabulary

  • Conditional probability
  • Probability
  • Simple events
  • Compound events
  • Sample space
  • Independent events
  • Dependent events

Knowledge

Students know:
  • Possible relationships and differences between the simple probability of an event and the probability of an event under a condition.

Skills

Students are able to:
  • Accurately determine the probability of simple and compound events.
  • Accurately determine the conditional probability P(A given B) from a sample space or from the knowledge of P(A&B) and the P(B).

Understanding

Students understand that:
  • Conditional probability is the probability of an event occurring given that another event has occurred.
Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.26

Describe the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Unpacked Content

UP:MA19.A2.26

Vocabulary

  • Sample surveys
  • Experiments
  • Observational studies
  • Randomization

Knowledge

Students know:
  • Key components of sample surveys, experiments, and observational studies.
  • Procedures for selecting random samples.

Skills

Students are able to:
  • Use key characteristics of sample surveys, experiments, and observational studies to select the appropriate technique for a particular statistical investigation.

Understanding

Students understand that:
  • Sample surveys, experiments, and observational studies may be used to make inferences made about the population.
  • Randomization is used to reduce bias in statistical procedures.
Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.33

Use data from a randomized experiment to compare two treatments; limit to informal use of simulations to decide if an observed difference in the responses of the two treatment groups is unlikely to have occurred due to randomization alone, thus implying that the difference between the treatment groups is meaningful.

Unpacked Content

UP:MA19.A2.33

Vocabulary

  • Randomized experiment
  • Significant
  • Parameters

Knowledge

Students know:
  • Techniques for conducting randomized experiments.
  • Techniques for conducting simulations of randomized experiment situations.

Skills

Students are able to:
  • Design and conduct randomized experiments with two treatments.
  • Draw conclusions from comparisons of the data of the randomized experiment.
  • Design, conduct, and use the results from simulations of a randomized experiment situation to evaluate the significance of the identified differences.

Understanding

Students understand that:
  • Differences of two treatments can be justified by a significant difference of parameters from a randomized experiment.
  • Statistical analysis and data displays often reveal patterns in data or populations, enabling predictions.
Link to Resource
https://aptv.pbslearningmedia.org/resource/nvpn-sci-pvalue/p-value-as-a-benchma…

CR Resource Type

Audio/Video

Resource Provider

PBS
Accessibility

Accessibility

Video resources: includes closed captioning or subtitles
License

License Type

Custom

Custom License Type (URL)

https://aptv.pbslearningmedia.org/help/terms-of-use/#.YD-bCNhKiUk

Approved Date

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