Univariate inferences about a mean
Download
1 / 24

Univariate Inferences about a Mean - PowerPoint PPT Presentation


  • 49 Views
  • Uploaded on

Univariate Inferences about a Mean. Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute of Networking and Multimedia. Scenarios. To test if the following statements are plausible

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Univariate Inferences about a Mean' - nuncio


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Univariate inferences about a mean

Univariate Inferences about a Mean

Shyh-Kang Jeng

Department of Electrical Engineering/

Graduate Institute of Communication/

Graduate Institute of Networking and Multimedia


Scenarios
Scenarios

To test if the following statements are plausible

A clam by a cram school that their course can increase the IQ of your children

A diuretic is effective

An MP3 compressor is with higher quality

A claim by a lady that she can distinguish whether the milk is added before making milk tea



Tests of hypotheses
Tests of Hypotheses

Developed by Fisher, Pearson, Neyman, etc.

Two-sided

One-sided




Student s t statistics
Student’s t-Statistics


Student s t distribution
Student’s t-distribution


Student s t distribution1
Student’s t-distribution


Student s t distribution2
Student’s t-distribution


Origin of the name student
Origin of the Name “Student”

  • Pseudonym of William Gossett at Guinness Brewery in Dublin around the turn of the 20th Century

  • Gossett use pseudonym because all Guinness Brewery employees were forbidden to publish

  • Too bad Guinness doesn’t run universities



Selection of a
Selection of a

  • Often chosen as 0.05, 0.01, or 0.1

  • Actually, Fisher said in 1956:

    • No scientific worker has a fixed level of significance at which year to year, and in all circumstances, he rejects hypotheses; he rather gives his mind to each particular case in the light of his evidence and hid ideas





Statistical significance vs practical significance
Statistical Significance vs. Practical Significance

  • The cram school claims that its course will increase the IQ of your child statistically significant at the 0.05 level

  • Assume that 100 students took the courses were tested, and the population standard deviation is 15

  • The actual IQ improvement to be statistically significant at 0.05 level is simply


More specific hypotheses
More Specific Hypotheses

  • Null hypothesis

  • Alternative hypothesis




Power
Power

  • The probability of concluding that the sample came from the H1distribution (i.e., concluding there is a significant difference), when it really did from the H1distribution (there is a difference)



Effective sizes
Effective Sizes

  • How many samples are required to validate the following claim of the cram school:

    • Our course will raise IQ levels of your child by 5 points

  • statistically significant at 0.05 level, and the type II error is 0.1

  • Normal IQ mean is 100, with standard deviation 15

  • Sample standard deviation is assumed to be 15, too



ad