1 / 7

Statistical Inference

Statistical Inference. “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” (H.G. Wells, 1946)

jnewby
Download Presentation

Statistical Inference

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Statistical Inference • “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” (H.G. Wells, 1946) • “There are three kinds of lies: white lies, which are justifiable; common lies, which have no justification; and statistics.” (Benjamin Disraeli) • “Statistics is no substitute for good judgment.” (unknown)

  2. Statistical Inference • Suppose – • A mechanical engineer is considering the use of a new composite material in the design of a vehicle suspension system and needs to know how the material will react under a variety of conditions (heat, cold, vibration, etc.) • An electrical engineer has designed a radar navigation system to be used in high performance aircraft and needs to be able to validate performance in flight. • An industrial engineer needs to validate the effect of a new roofing product on installation speed. • A motorist must decide whether to drive through a long stretch of flooded road after being assured that the average depth is only 6 inches.

  3. Statistical Inference • What do all of these situations have in common? • How can we address the uncertainty involved in decision making? • a priori • a posteriori

  4. Probability • A mathematical means of determining how likely an event is to occur. • Classical (a priori): Given N equally likely outcomes, the probability of an event A is given by, • where n is the number of different ways A can occur. • Empirical (a posteriori): If an experiment is repeated M times and the event A occurs mA times, then the probability of event A is defined as,

  5. The Role of Probability in Statistics • In statistical inference, we want to make general statements about the population based on measurements taken from a sample. • How will all suspension systems produced with the new composite behave? • How will the radar navigation system perform in all aircraft? • What speed improvements will we obtain for all roofing applications using the new product? • To answer these questions, we ___________ from the population and hope to generalize the results.

  6. Observations & Statistical Inference • Example, • An experiment is designed to determine how long it takes to install a roof using a new product. • Experiment • Design • Result: t = 2.32 sec/ft2, P = 0.023 • p – value:

  7. Descriptive Statistics • Numerical values that help to characterize the nature of data for the experimenter. • Example: The absolute error in the readings from a radar navigation system was measured with the following results: • the sample mean, x = _________________________ • the sample median, x = _____________ 17 22 39 31 28 52 147 ~

More Related