Problem 1
1. JB with a two tailed hypothesis test. He discusses outliers a bit for extra discussion.
https://youtu.be/q1D4Di1KWLc
2. Problem 2 on this worksheet is an example of a 95% CI on one population mean. It is based on problem10.5 in the textbook.
https://drive.google.com/file/d/0B0G6ga3ykYRHeXcxNjdkNmRlYWc/view
3. There is an example on pages 393-395 worked out in the textbook.
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Problems 2 and 6. Both are one way analysis of variance (a.k.a AOV or Anova) problems with the AOV table given along with the sample means for each group.
A link to our textbook reference for chapter 11
link: https://drive.google.com/file/d/19Td_GXTWTIi_G9IL-Uj_qcXyP_4Be2IL/view
First some quick intro video:
Introduction to the AOV Procedure
a. Introduction to One Way Analysis of Variance (ANOVA)
link: https://youtu.be/QUQ6YppWCegb. ANOVA. An Intro to Formulas
link: https://youtu.be/fFnOD7KBSbw
c. A Numerical Example of a One Way ANOVA
link: https://youtu.be/WUoVftXvjiQ
d. Comparing Among k Means in ANOVA when F - Test is Significant. First Basic Procedure.
link: https://youtu.be/kO8t_q-AXHE
e. A quick intro to Tukeys multiple comparison procedure. A common approach more popular than LSD procedure discussed in d. above. The Tukey procedure will not be on the exam Spring 2020.
link: https://youtu.be/lpdFr5SZR0Q
f. Finding the Approximate P-Value from F - test Using Textbook F - tables
link: https://youtu.be/XdZ7BRqznSA
g. AOV worksheet
link
h. AOV Worksheet Answers (Sorry its a home scan :-) )
link:
i. Book Exercises for One Way Anova. Three problems are listed but pay particular attention to 11.12. It is very similar to exam questions 2 and 6. Problems 11.12 (a,b,c) , 11.13 (b,d) , 11.14 (a,b)
link: https://drive.google.com/file/d/1Zcr5ZO77L_AVu5Sv1kX65iU5XRZC_fle/view?usp=sharing
a. Eric's handwritten solutions to the textbook problems 11.12 (a,b,c) , 11.13 (b,d) , 11.14 (a,b)
link: https://drive.google.com/file/d/0B0G6ga3ykYRHUnRfYUxjaHMtVzQ/view
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Problem 3.
Chapter 12 Topics. Simple Linear Regression
Chapter 12 Textbook Reference from our B1 Text
link: https://drive.google.com/file/d/1pXBOqJPuLJG-BKSe3hPsbK1ne62suJ3T/view?usp=sharing
a. Intro to Linear Regression and Correlation Coefficient (r).
OpenStax Version
(A short 4 min video, at minute 3 a quick intro to
Pearson's Correlation Coefficient is presented)
link: https://youtu.be/mPvtZhdPBhQ
b. Inference About the Slope b1, and Understanding Regression Output
from Software. OpenStax Version
link: https://youtu.be/depiT-hTaGA
c. Examples of Outliers in Regression. Discussion of 'Leverage' and 'Influence'
in a Regression Analysis.
link: https://youtu.be/jZEKAlo1E54
d. Interpretation of B0, B1, assumptions for linear regression, and R-Squared.
link: https://youtu.be/z8DmwG2G4Qc
e. Introduction to Linear Regression Marin Stats Version.
link: https://youtu.be/vblX9JVpHE8
f. Intro to Linear Regression JB Stats Version
link: https://youtu.be/KsVBBJRb9TE
g. Discussion of Linear Regression that Puts Several Concepts Together
JB Stats Version
link: https://youtu.be/xIDjj6ZyFuw
Practice Problems and Materials.
Potency and Temperature Worksheet:
Notice we run this analysis for the worksheet in both R and SAS. Notice how to find the important information in both of these common statistics software packages. This worksheet is very similar to the exam question 3.
h.The R Software Printout.
link: https://drive.google.com/file/d/0B0G6ga3ykYRHWnNwVnllTlhwcHc/view
i. The worksheet (last pages) with Associated SAS software printout
link: https://drive.google.com/file/d/0B0G6ga3ykYRHcGg3a2pkWlBLZG8/view
j. The worksheet answers.
link: https://drive.google.com/file/d/0B0G6ga3ykYRHR3ViWl9wUmJWblU/view?usp=sharing
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Problems 4 and 7. Analysis of Categorical Data
We will be testing for relationships among the row and column variables in cross classification frequency tables. We will use a new testing distribution. So far we have used Z, t, and F. Now we add the Chi Square distribution.
a. Intro to the Chi Square Distribution.
link
b. Textbook reference:
link
c. Example of an analysis of a 2 x 3 Table. Problem 7 is also a 2 x 3 table. Notice this analysis procedure uses the Chi Square Distribution https://youtu.be/L1QPBGoDmT0
d. More details about the Chi Square Distribution. Using the Chi Square table and using software.
This gives information on drawing rejections regions for Chi Square tests and figuring out p-values with book tables. Software is also discussed. https://youtu.be/HwD7ekD5l0g
e. A Chi-Square Table: Chi-Square table
f. Review pages 602-607 in the book. I would pay particular attention to example 14.5
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Problem 5. The Non Parametric Kruskal Wallis Procedure.
When we want to compare 2 or more groups and the assumptions of the t test and anova are not met a plan b is a non parametric procedure. There are several such procedures and we are going to focus on the Kruskal- Wallis. Basically to get around the assumption problem we do an analysis on the ranks of the data.
a. A video of a guy doing a really good job explaining the procedure. This problem he is doing is very similar to question 5 on the exam. Notice that the Kruskal - Wallis procedure also uses the Chi Square Distribution with df = k - 1 , where k is the number of groups being compared. https://youtu.be/q1D4Di1KWLc
b. The textbook goes through an easy to follow example of comparing four groups with the KW procedure on pages 650-654. nonparametric book reference link
c. Text book problem solutions by H.G. Textbook problems 15.33 and 15.37
