{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# lect3 - IE 410 Notes for Lecture 3 THE ANALYSIS OF...

This preview shows pages 1–13. Sign up to view the full content.

IE 410 Notes for Lecture 3 THE ANALYSIS OF VARIANCE (or ANOVA) One Sample T-test: H 0 : μ = μ 0 Two-Sample T-test: H 0 : μ 1 = μ 2 (Two populations have the same mean)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: Which tennis ball brand bounces higher, Penn or Wilson? Get (say) 3 balls of each brand: Drop each from 10 feet onto concrete OBSERVE: height of bounce (the response variable Y)
Single Factor Analysis of Variance (a.k.a. One-way ANOVA) H 0 : μ 1 = μ 2 = μ 3 = ..... = μ k Test if the mean of several populations are all the same H 1 : at least one mean is different

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example : Does fertilizer type effect yield from an acre of corn? Factor = "fertilizer type" Factor levels ( treatments) = types "1", "2", "3", & "4" H 0 : μ 1 = μ 2 = μ 3 = μ 4 H 1 : at least one different Y(i,j) = yield (bushels) from the jth field treated with fertilizer i
Basic Model of a data set: Assume the factor (call it Factor A) is at " a " levels, and that n observations are taken within each level Let y(i,j) be the response for the jth observation within the ith level of Factor A.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
FACTOR A 1 2 3 ....... a ----------------------------------------- y(1,1) y(2,1) y(3,1) ...... y(a,1) y(1,2) y(2,2) y(3,2) y(a,2) . . Obs. . . y(1,n) y(2,n) y(3,n) ..... y(a,n)
Each y(i,j) is a random variable. Once the expt has been conducted, we will have numbers that are outcomes of the random variables. If we repeated the expt, we would get different outcomes Sampling is assumed to be RANDOM

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Statistical Models: Two Basic Types depending on the situation FIXED vs. RANDOM Effects models Example : y(i,j) =SAT score of randomly students from University i Factor A = University at levels "Lehigh", "Laughyette", "Michigan" Randomly select students from each school, and record their SAT score in the dataset.
FIXED Effects: Interested only in the 3 schools, Lehigh, Laff, and UofM H 0 : μ lehigh = μ laff = μ UofM

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
RANDOM Effects Model Suppose you wanted to test whether or not the mean SAT scores were the same at all American universities. How would you do it ? From the population of American Universities, you might randomly select "a" universities to study. From each of these universities, you might randomly select students, and record their scores in the dataset. H 0 : Mean SAT scores are equal at all American Univ’s
Fixed Effects: Interested in making inference only about those treatments (factor levels) included in the study. Random Effects: Interested in making inference about a large population of treatments from which those studied are a representitive random sample.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Basic Relevance: For the One-way ANOVA i) The statistical tests are the same for Fixed and Random ii) The power of the tests is different For Multi-factor ANOVA the tests are different as well.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern