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6 Pages

### CLG Topic 10

Course: STAT 502, Fall 2011
School: Purdue University -...
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Word Count: 1079

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10 Topic Handout: ANCOVA &amp; RCBD Designs Learning Goals for this Activity: (1) Experience in the use of ANCOVA and RCBD Models; (2) An understanding of why such models are worthwhile. 10.1 Output for Example II (from notes) is given below on pages 1-2. Complete the analysis of this example (using the analysis of Example I completed in class as a guide). Make sure to consider the following: a. Assumptions...

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10 Topic Handout: ANCOVA & RCBD Designs Learning Goals for this Activity: (1) Experience in the use of ANCOVA and RCBD Models; (2) An understanding of why such models are worthwhile. 10.1 Output for Example II (from notes) is given below on pages 1-2. Complete the analysis of this example (using the analysis of Example I completed in class as a guide). Make sure to consider the following: a. Assumptions Assessment. b. Analysis with the covariate included. c. Compare to previous analysis (without the covariate). What changes? What stays the same? ANOVA MODEL The GLM Procedure Dependent Variable: y Source trt Error Corrected Total R-Square 0.013384 DF 2 6 8 Coeff Var 37.83138 Sum of Squares 1.55555556 114.6666667 116.2222222 Root MSE 4.371626 Mean Square 0.77777778 19.1111111 F Value 0.04 Pr > F 0.9604 y Mean 11.55556 t Tests (LSD) for y NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 6 Error Mean Square 19.11111 Critical Value of t 2.44691 Least Significant Difference 8.734 16 1 15 3 14 Means with the same letter are not significantly different. 2 13 1 2 3 12 GRP A A A Mean 12.000 11.667 11.000 N 3 3 3 trt 1 3 2 11 10 9 8 7 ANCOVA Interaction Model Source Square F Value x trt x*trt Error Corrected Total R-Square 0.873088 Pr > F Coeff Var 19.18864 1 3 6 2 1 DF Sum of Squares 1 2 2 3 8 9.66896458 87.46642860 4.33686046 14.7499686 116.2222222 Root MSE 2.217353 y Mean 11.55556 2 3 4 5 Di s e a s e trt Mean 9.66896458 43.73321430 2.16843023 4.9166562 1.97 8.89 0.44 0.2554 0.0548 0.6793 1 6 7 St age 2 3 8 9 r esi d 3 3 2 2 1 r e s i d 1 0 0 -1 -1 -2 -2 -3 -3 - 1. 5 -1 - 0. 5 0 N o r ma l 0. 5 ANCOVA MODEL 1. 5 6 7 8 9 10 11 12 13 14 15 16 17 pr ed Sum of Squares 97.1353932 19.0868290 116.2222222 Source Model Error Corrected Total DF 3 5 8 R-Square 0.835773 Root MSE 1.953808 Coeff Var 16.90795 1 Qu a n t i l e s Mean Square 32.3784644 3.8173658 F Value 8.48 Pr > F 0.0209 y Mean 11.55556 Source x trt DF 1 2 Type I SS 9.66896458 87.46642860 Mean Square 9.66896458 43.73321430 F Value 2.53 11.46 Pr > F 0.1724 0.0136 Source x trt DF 1 2 Type III SS 95.57983762 87.46642860 Mean Square 95.57983762 43.73321430 F Value 25.04 11.46 Pr > F 0.0041 0.0136 Least Squares Means Adjustment for Multiple Comparisons: Tukey-Kramer trt 1 2 3 y LSMEAN -1.1648624 10.3148399 25.5166892 Standard Error 2.8625918 1.1363118 2.9889270 Pr > |t| 0.7009 0.0003 0.0004 LSMEAN Number 1 2 3 Least Squares Means for Effect trt t for H0: LSMean(i)=LSMean(j) / Pr > |t| Dependent Variable: y i/j 1 2 3 10.2 1 3.877496 0.0263 4.739498 0.0118 2 -3.8775 0.0263 4.587099 0.0135 3 -4.7395 0.0118 -4.5871 0.0135 Suppose we are interested in determining if there are regional effects on the salaries of teachers. We obtain from DASL a dataset containing average teacher salaries for each state. The dataset also has another variable that is known to be related to teacher salary and that is average expenditure per student. Using the output below (and the following questions as guideposts), analyze the data to determine if there are regional differences in salary. Note: The entire dataset and description may be found at http://lib.stat.cmu.edu/DASL/Stories/EducationalSpending.html. a. Consider the assignment of regions (see below). Comment. b. Consider the analysis of covariance (see page 3-4). Perform the analysis and draw appropriate conclusions. (Side question: Why are the Type I / III SS different?) c. If we had just done an ANOVA and ignored the covariate (see page 5), would we have drawn any incorrect conclusions? Consider the one-way ANOVA what conclusions would you draw? d. Is there any additional output that you wish you had to examine? proc freq; tables region; run; Cumulative Cumulative Region Frequency Percent Frequency Percent ENC 5 9.80 5 9.80 ESC 4 7.84 9 17.65 MA 3 5.88 12 23.53 MN 8 15.69 20 39.22 NE 6 11.76 26 50.98 PA 5 9.80 31 60.78 SA 9 17.65 40 78.43 WNC 7 13.73 47 92.16 WSC 4 7.84 51 100.00 ADDITIONAL REGIONAL INFORMATION ENC = Indiana, Michigan, Ohio, Illinois, Wisconsin, ESC = Kentucky, Alabama, Tennessee, Mississippi MA = New York, Pennsylvania, New Jersey MN = Wyoming, New Mexico, Utah, Montana, Idaho, Colorado, Arizona, Nevada NE = Maine, Vermont, Rhode Island, New Hampshire, Massachusettes, Connecticut PA = Washington, Oregon, California, Alaska, Hawaii SA = Maryland, Virginia, North Carolina, Georgia, Deleware, District of Columbia, West Virginia, South Carolina, Florida WNC = Minnesota, Missouri, South Dakota, Kansas, Iowa, North Dakota, Nebraska WSC = Arkansas, Oklahoma, Louisiana, Texas Source Model Error Total R-Square 0.765853 Source Spend Region DF 9 41 50 SumofSquares 679.7466365 207.8215988 887.5682353 Coeff Var 9.191611 DF 1 8 Mean Square 75.5274041 5.0688195 Root MSE 2.251404 Type I SS 606.4901533 73.2564832 F Value 14.90 Pr > F <.0001 Pay Square 606.4901533 9.1570604 F Mean 24.49412 Mean Value 119.65 1.81 Pr > F <.0001 0.1037 Source DF Type III SS Mean Square F Value Spend 1 382.2488496 382.2488496 75.41 Region 8 73.2564832 9.1570604 1.81 The GLM Procedure Least Squares Means Adjustment for Multiple Comparisons: Tukey-Kramer Pr > F <.0001 0.1037 Region Pay LSMEAN Standard Error Pr > |t| LSMEAN Number ENC 26.6220761 1.0069028 <.0001 1 ESC MA MN NE PA SA WNC WSC 24.5768606 23.2072148 25.1035843 22.7431288 26.3157257 24.2792555 23.5503181 23.9822325 1.1986906 1.4091828 0.8025782 0.9279276 1.0771737 0.7504688 0.8573429 1.1572955 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 2 3 4 5 6 7 8 9 Least Squares Means for Effect Region t for H0: LSMean(i)=LSMean(j) / Pr > |t| Dependent Variable: Pay i/j 1 3 4 5 6 7 8 9 1.308531 0.9230 1 2 1.968314 0.5729 1.179985 0.9563 2.831038 0.1374 0.20742 1.0000 1.865574 0.6399 2.32408 0.3521 1.722737 0.7295 0.696142 0.9986 -0.37278 1.0000 1.182952 0.9557 -1.0189 0.9818 0.210387 1.0000 0.710787 0.9984 0.37201 1.0000 -1.1453 0.9632 0.282011 1.0000 -1.88155 0.6296 -0.67163 0.9989 -0.20379 1.0000 -0.40748 1.0000 1.90748 0.6127 -0.88334 0.9927 0.750146 0.9976 1.333031 0.9152 0.807512 0.9960 -2.57577 0.2281 -1.28729 0.9294 -0.63366 0.9993 -0.82263 0.9955 1.551596 0.8242 1.967604 0.5733 1.418739 0.8841 0.639696 0.9992 0.215306 1.0000 2 -1.30853 0.9230 3 -1.96831 0.5729 -0.69614 0.9986 4 -1.17998 0.9563 0.37278 1.0000 1.145301 0.9632 5 -2.83104 0.1374 -1.18295 0.9557 -0.28201 1.0000 -1.90748 0.6127 6 -0.20742 1.0000 1.018901 0.9818 1.881553 0.6296 0.883341 0.9927 2.575774 0.2281 7 -1.86557 0.6399 -0.21039 1.0000 0.671629 0.9989 -0.75015 0.9976 1.287291 0.9294 -1.5516 0.8242 8 -2.32408 0.3521 -0.71079 0.9984 0.203789 1.0000 -1.33303 0.9152 0.633655 0.9993 -1.9676 0.5733 -0.6397 0.9992 9 -1.72274 0.7295 -0.37201 1.0000 0.40748 1.0000 -0.80751 0.9960 0.822631 0.9955 -1.41874 0.8841 -0.21531 1.0000 -0.30403 1.0000 0.304026 1.0000 ONE-way ANOVA Sum of Squares 297.4977869 590.0704484 887.5682353 Source Region Error Corrected Total DF 8 42 50 R-Square 0.335183 Root MSE 3.748239 Coeff Var 15.30261 Mean Square 37.1872234 14.0492964 Pr > F 0.0190 Pay Mean 24.49412 Tukey's Studentized Range (HSD) Test for Pay Alpha 0.05 Error Degrees of Freedom 42 Error Mean Square 14.0493 Critical Value of Studentized Range 4.62238 Minimum Significant Difference 7.7029 Harmonic Mean of Cell Sizes 5.059112 NOTE: Cell sizes are not equal. GRP B B B B B B B B Means with the same letter are not significantly different. 10.3 F Value 2.65 Mean 29.640 27.933 26.540 24.289 24.213 23.850 22.643 21.650 21.000 A A A A A A A N 5 3 5 9 8 6 7 4 4 Region PA MA ENC SA MN NE WNC WSC ESC This problem is adapted from Devore, Probability and Statistics for Engineering. We want to test the power consumption for five different brands of a dehumidifier. Because power consumption will be different at different humidity levels, it was determined to control the humidity levels for this experiment and block on this variable. Thus each brand was tested at each of four different humidity levels (ranging from moderate to heavy). a. Pages 5-6 of the output show the analysis for the humidifier data. Using the output provided, determine the results of this analysis. b. Suppose that the interaction plot looked like the one shown at the bottom of page 6. How would your analysis change? ANALYSIS FOR HUMIDIFIER DATA proc sort data=h; by brand humidity; symbol1 v=dot i=join; proc gplot data=ex1807; plot power*humidity = brand; run; proc glm; class humidity brand; model power = humidity brand; lsmeans brand / adjust=tukey pdiff tdiff; output out=diag p=pred r=resid; run; p o we r 1100 1000 900 800 700 600 1 2 3 4 h u mi d i t y br and 1 2 3 4 5 Source humidity brand Error Corrected Total Sum of Squares 53231.0000 116217.7500 1671.0000 171119.7500 DF 4 3 12 19 R-Square 0.990235 Coeff Var 1.362242 Mean Square 13307.7500 38739.2500 139.2500 Root MSE 11.80042 F Value 95.57 278.20 power Mean 866.2500 The GLM Procedure Least Squares Means Adjustment for Multiple Comparisons: Tukey brand 1 2 3 4 5 LSMEAN Number 1 2 3 4 5 power LSMEAN 797.500000 843.500000 839.000000 914.000000 937.250000 Least Squares Means for Effect brand t for H0: LSMean(i)=LSMean(j) / Pr > |t| Dependent Variable: power i/j 1 1 2 3 4 5 5.512838 0.0010 4.973539 0.0024 13.96186 <.0001 16.74824 <.0001 2 3 4 5 -5.51284 0.0010 -4.97354 0.0024 0.539299 0.9813 -13.9619 <.0001 -8.44902 <.0001 -8.98832 <.0001 -16.7482 <.0001 -11.2354 <.0001 -11.7747 <.0001 -2.78638 0.0978 -0.5393 0.9813 8.449023 <.0001 11.2354 <.0001 8.988323 <.0001 11.7747 <.0001 2.78638 0.0978 Hypothetical Interaction Plot for LAST question. p o we r 1100 1000 900 800 700 600 1 2 3 4 h u mi d i t y br and 1 2 3 4 5 Pr > F <.0001 <.0001
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Purdue University - Main Campus - STAT - 502
Topic 11 Handout: Two Way Analysis of VarianceLearning Goals: (1) Learn how to analyze two factors in ANOVA; (2) Understandand be able to properly interpret interactions.11.1Pages 2 and 3 show six possible interaction plots for an analysis of drugeff
Purdue University - Main Campus - STAT - 502
Topic 12 Handout: CARS exampleLearning Goals: (1) Explore the difference between balanced and unbalanced ANOVAdesigns; (2) Further understanding of interactions; (3) Learn about confounding of effectsin ANOVA.The questions are based on the following s
Purdue University - Main Campus - STAT - 502
Topic 13 Handout: Random EffectsLearning Goals: (1) Understand the differences between fixed effects and random effectsmodels; (2) Be able to identify effects as either fixed or random; (3) Be able to utilize EMS(expected mean squares) to determine (a)
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #1Coverage: KKMN Chapters 1-3Name: _SCORE: _ of 30Instructions: Although I do encourage you to work together both in and outside of class, remember thatcollaboration on homework problems should be minimal and everyone should creat
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #1Coverage: KKMN Chapters 1-3Name: _SCORE: _ of 30Instructions: Although I do encourage you to work together both in and outside of class, remember thatcollaboration on homework problems should be minimal and everyone should creat
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #2Coverage: KKMN Chapters 4-7Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!#1.(3 pts) Briefly explain the difference between the following two equations. Do either of theseconstitute a complete statemen
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #3Coverage: KKMN Chapter 8-9Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!Please note that HW problems generally do not require any SAS coding.#1.(6 points) KKMN Problem 8.03 as stated. Please note that
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #4Coverage: KKMN Chapter 9Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!Please note that HW problems generally do not require SAS coding.#1.(6 points) KKMN Problem 9.02.#2.(4 points) KKMN Problem 9.03
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #5Coverage: KKMN Chapters 10 &amp; 12Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!Please note that HW problems generally do not require SAS coding.#1.(7 points) KKMN Problem 10.07. Ignore the questions in
Purdue University - Main Campus - STAT - 502
Topic 1 Basic StatisticsKKMN Chapters 1-31Topic OverviewCourse Syllabus &amp; ScheduleReview: Basic StatisticsTerminology: Being able to CommunicateDistributions: Normal, T, FHypothesis Testing &amp; Confidence IntervalsSignificance Level &amp; Power2Textb
Purdue University - Main Campus - STAT - 502
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Purdue University - Main Campus - STAT - 502
CLG Activity #1Please discuss questions 3.1-3.6from the handout.CLG Activity #1Q1: Research Questions?Is there an effect of smoking on SBP?Is body size associated to SBP?Can any combination of the three variablesbe used to predict SBP?CLG Activit
Purdue University - Main Campus - STAT - 502
Topic 3 Multiple Regression AnalysisRegression on Several PredictorVariables(Chapter 8)1Topic OverviewSystolic Blood Pressure ExampleMultiple Regression ModelsSAS Output for RegressionMulticollinearity2Systolic Blood Pressure DataIn this topic
Purdue University - Main Campus - STAT - 502
Topic 4 CLG Addendum1CLG Activity #1In your groups, please attempt thefirst set of questions. These willinvolve computing various extrasums of squares.2Question 4.1 &amp; 4.2Univariate and bivariate issues that mayaffect modeling include:For HSM, H
Purdue University - Main Campus - STAT - 502
Topic 4 Extra Sums of Squaresand the General Linear TestUsing Partial F Tests in MultipleRegression Analysis(Chapter 9)1Recall: Types of Tests1.ANOVA F Test: Does the group of predictorvariables explain a significant percentage of thevariation i
Purdue University - Main Campus - STAT - 502
CLG ActivityIn CLGs, please attempt Activity#1 from the handout for Topic 5.Note that this activity builds on theone we used for Topic #4.15.1 (a) &amp; (b)2GPA, HSM | HSS , HSE , SATM , SATVr2GPA , HSE | HSMr6.835== 0.061105.65 + 6.8352.48=
Purdue University - Main Campus - STAT - 502
Topic 5 Partial Correlations; Diagnostics &amp;Remedial MeasuresChapters 10 &amp; 141OverviewReview: MLR Tests &amp; Extra SSPartial Correlations Think Extra SS beingused to compute Extra R2Of the variation left to explain.How much isexplained by adding anot
Purdue University - Main Campus - STAT - 502
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Purdue University - Main Campus - STAT - 502
Topic 7 Other Regression IssuesReading: Some parts ofChapters 11 and 15OverviewConfounding (Chapter 11)Interaction (Chapter 11)Using Polynomial Terms (Chapter 15)Regression: Primary GoalsWe usually are focused on one of thefollowing goals:Predic
Purdue University - Main Campus - STAT - 502
Topic 8 One-Way ANOVASingle Factor Analysis of VarianceReading: 17.1, 17.2, &amp; 17.5Skim: 12.3, 17.3, 17.41OverviewNote: Entire topic constitutes some reviewas this would be the last thing you coveredin 501. We will cover it perhaps insomewhat more
Purdue University - Main Campus - STAT - 502
Topic 8 One-Way ANOVASingle Factor Analysis of VarianceReading: 17.1, 17.2, &amp; 17.5Skim: 12.3, 17.3, 17.41OverviewNote: Entire topic constitutes some reviewas this would be the last thing you coveredin 501. We will cover it perhaps insomewhat more
Purdue University - Main Campus - STAT - 502
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Purdue University - Main Campus - STAT - 502
Topic 10 ANCOVA &amp; RCBDAnalysis of Covariance (Ch. 13)Randomized Complete BlockDesigns (Ch. 18)1ReviewRecall the idea of confounding. Suppose I want todraw inference about a certain predictor.If meaningfully different interpretations would bemade
Purdue University - Main Campus - STAT - 502
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Purdue University - Main Campus - STAT - 502
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Purdue University - Main Campus - STAT - 502
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Purdue University - Main Campus - STAT - 502
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Purdue University - Main Campus - STAT - 506
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Purdue University - Main Campus - STAT - 506
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STAT 506Homework 5For most problems you will still need to access the data in the PRG1 folder. Use the libname statement we learned toload this each time you work on your assignments calling the library orion. I tried to bold the parts where I expectyo
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STAT 506Homework 6For most problems you will need to access the data in the PRG2 folder. Use the libname statement we learned to loadthis each time you work on your assignments calling the library orion. I tried to bold the parts where I expect you toa
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Purdue University - Main Campus - STAT - 506
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Purdue University - Main Campus - STAT - 506
Chapter 3: Working with SAS Syntax3.1 Mastering Fundamental Concepts3.2 Diagnosing and Correcting Syntax Errors1Chapter 3: Working with SAS Syntax3.1 Mastering Fundamental Concepts3.2 Diagnosing and Correcting Syntax Errors2Objectives3Identify t
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Chapter 4: Getting Familiar withSAS Data Sets4.1 Examining Descriptor and Data Portions4.2 Accessing SAS Data Libraries4.3 Accessing Relational Databases (Self-Study)1Chapter 4: Getting Familiar withSAS Data Sets4.1 Examining Descriptor and Data P
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Purdue University - Main Campus - STAT - 506
Chapter 6: Reading Excel Worksheets6.1 Using Excel Data as Input6.2 Doing More with Excel Worksheets (Self-Study)1Chapter 6: Reading Excel Worksheets6.1 Using Excel Data as Input6.2 Doing More with Excel Worksheets (Self-Study)2Objectives3Use th
Purdue University - Main Campus - STAT - 506
Chapter 7: Reading Delimited Raw Data Files7.1 Using Standard Delimited Data as Input7.2 Using Nonstandard Delimited Data as Input1Chapter 7: Reading Delimited Raw Data Files7.1 Using Standard Delimited Data as Input7.2 Using Nonstandard Delimited D
Purdue University - Main Campus - STAT - 506
Chapter 8: Validating and Cleaning Data8.1 Introduction to Validating and Cleaning Data8.2 Examining Data Errors When Reading Raw Data Files8.3 Validating Data with the PRINT and FREQ Procedures8.4 Validating Data with the MEANS andUNIVARIATE Procedu
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Purdue University - Main Campus - STAT - 511
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Purdue University - Main Campus - STAT - 511
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Purdue University - Main Campus - STAT - 511
Homework1_Spring2012Page 1Homework1_Spring2012Page 2Homework1_Spring2012Page 3Homework1_Spring2012Page 4
Purdue University - Main Campus - STAT - 511
Homework2Page 1Homework2Page 2Homework2Page 3Homework2Page 4
Purdue University - Main Campus - STAT - 511
Homework3Page 1Homework3Page 2Homework3Page 3Homework3Page 4Homework3Page 5
Purdue University - Main Campus - STAT - 511
STAT 511-2 Homework 1Page 1STAT 511-2 Homework 1Page 2STAT 511-2 Homework 1Page 3STAT 511-2 Homework 1Page 4STAT 511-2 Homework 1Page 5STAT 511-2 Homework 1Page 6STAT 511-2 Homework 1Page 7
Purdue University - Main Campus - STAT - 511
STAT 511-2 Homework 2Page 1STAT 511-2 Homework 2Page 2STAT 511-2 Homework 2Page 3STAT 511-2 Homework 2Page 4
Purdue University - Main Campus - STAT - 511
STAT 511 Homework 3Page 1STAT 511 Homework 3Page 2STAT 511 Homework 3Page 3STAT 511 Homework 3Page 4
Purdue University - Main Campus - STAT - 511
STAT 511-2 Homework 4 SolutionsPage 1STAT 511-2 Homework 4 SolutionsPage 2STAT 511-2 Homework 4 SolutionsPage 3
Purdue University - Main Campus - STAT - 511
Statistics 511: Statistical MethodsDr. LevinePurdue UniversityFall 2011Lecture 6: Populations, Samples and ProcessesDevore: Section 1.1-1.2Oct, 2011Page 1Statistics 511: Statistical MethodsDr. LevinePurdue UniversityFall 2011Populations and Sa
Purdue University - Main Campus - STAT - 511
Statistics 511: Statistical MethodsDr. LevinePurdue UniversityFall 2011Lecture 2: Measures of Location and VariabilityDevore: Section 1.3-1.4Oct, 2011Page 1Statistics 511: Statistical MethodsDr. LevinePurdue UniversityFall 2011Sample mean The