Class Notes (838,386)
Canada (510,872)
Statistics (475)
STAT 231 (84)
Lecture

Week 7 lecture Slides.pdf

13 Pages
59 Views
Unlock Document

Department
Statistics
Course
STAT 231
Professor
Matthias Schonlau
Semester
Fall

Description
Home Page Statistical Inference Title Page • We have looked at the sampling distribution of estimators and confidence intervals Contents • Look at the idea of a hypothesis test and the p -value scale of evidence Page 46 of 77 Go Back Full Screen Close Quit •First• Prev •Next •Last • Go Back •Full Screen •Close •Quit                                     Home Page Testing statistical hypotheses Title Page • Thereareoftenhypothesesthatastatisticianorscientistmight want to “test” in the light of observed data. Contents • Two important types of hypotheses are (1) that a parameter vector θ has some specified value θ ; we 0 denote this as H 0: θ = θ 0. (2) that a random variable Y has a specified probability distri- bution, say with p.d.f. f (y) ; we denote this as H : Y ∼ 0 0 Page 47 of 77 f 0y) . • We shall concentrate on the first of these. Go Back Full Screen Close Quit     •Firs•Prev •Next•Last•Go Back •Full Scre•Close•Quit                   Home Page Statistical approach Title Page • Assume that the hypothesis H 0will be tested using some ran- dom data “Data”. Contents • Defineateststatistic(alsocalledadiscrepancymeasure) D = g(Data) that is constructed to measure the degree of “agree- ment” between Data and the hypothesis H 0. • It is conventional to define D so that D =0 represents the best possible agreement between the data and H 0, and so that the larger D is, the poorer the agreement. Page 48 of 77 • Once specific observed “data” have been collected, let d = obs Go Back g(data ) be the corresponding observed value of D . • To test H , we now calculate the observed significance level Full Screen (also called the p-value), defined as Close p − value = Pr(D ≥ d ;H ), obs 0 (5) Quit where the notation “ ;H 0 ” means “assuming H 0is true”. •Fir•Prev•NextLast•Go Bac•Full Scr•Clos•Quit                                 Home Page Meaning of p -value Title Page • If p-value is close to zero then we are inclined to doubt that H 0 is true, because if it is true the probability of getting agree- Contents ment as poor or worse than observed is small. • This makes the alternative explanation that H 0 is false more appealing. • In other words, we must accept that one of the following two statements is correct.: Page 49 of 77 (a) H 0 is true but by chance we have observed data that indi- cate poor agreement with H 0, or Go Back (b) H 0 is false. Full Screen Close Quit       • Firs•Prev•Next •Last•Go Back•Full Scree•Close•Quit                               Home Page Meaning of p -value Title Page • In summary, the p -value is a numerical scale which measures the strength of evidence in the data against some hypothesis. Contents • It is a number between 0 and 1 • The smaller the value the more evidence against the hypoth- esis. • In order to have an agreement about what ‘small’ means the following scale is often used, but you should not take it as Page 50 of 77 anything but a rule of thumb. Go Back Full Screen Close Quit       •First•Prev •Next •Last •Go Back •Full Screen•Close •Quit                               Home Page Meaning of p -value Title Page Significance level Interpretation p> 0.10 no evidence against the hypothesised value 0.05
More Less

Related notes for STAT 231

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit