1 niland-ward-camt-1998 pumo using calculators and computers in statistics camt98 45th annual...

1Niland-Ward-CAMT-1998

PUMO

USING CALCULATORS AND COMPUTERS IN

STATISTICS

CAMT98 45th Annual Conference San Antonio, Texas

July 23, 1998

Laura J. NilandMacArthur High School

2923 BittersSan Antonio, TX 78217

210-650-1100e-mail: [email protected]

Joe WardHealth Careers High School

4646 Hamilton WolfeSan Antonio, TX 78229

210-433-6575e-mail: [email protected]


PUMO

PREVIEW OF USING CALCULATORS AND

COMPUTERSIN

STATISTICS

• OVERVIEW OF GENERAL APPROACH TO PROBLEM ANALYSIS

•FOCUS ON THE COMBINED POWER OF REGRESSION MODELSAND COMPUTERS

•TWO-CATEGORY t- TEST FROM MOORE & MCCABE -IPSUSING REGRESSOIN MODELS

•THREE-CATEGORY ANOVA FROM MOORE & MCCABE USING REGRESSION MODELS

•MANATEE REGRESSION MODEL FROM MOORE & MCCABE


PUMO

Combining Regression Models and Statistical Software Students can:

-- Do useful, meaningful analyses AFTER the learning experience

that they could not do BEFORE. -- Analyze many different-appearing data analysis procedures

with one general approach.

-- Reduce the risk of unknowingly obtaining irrelevant output from statistical software.

-- More easily and correctly specify computational requirements to the computer.

-- Simplify communicating results of the analyses.

CONNECTING ANALYSIS OF VARIANCE(ANOVA)

ANDREGRESSION MODELS


PUMO

THE BIG PICTURE

Prediction Uncertainty OptimizationModeling

Problem Solving Through Data

Analysis

Mathematics Curriculum

Different DifferentDisciplines Statistics

Engineering

t-testsANOVA

Regression

Biological, Physical, SocialSciences

Linking

Linking


PUMO

Identify real-world problems1

2

3

4

5

67

Learn to use a computer

Learn to use statistical software

Use statistical software for computational requirements

Interpret results from statistical software

Translate to real-world actions

Translate questions of interest into mathematical models

ENRICHING A FIRST STATISTICS COURSE USING PREDICTION MODELS

AND STATISTICAL SOFTWARE


PUMO

Translate into Statistical ModelsGeneral form of:PREDICTION MODELSREGRESSION MODELSLINEAR MODELS

then

Y(Response)= P(redictions) + E(rrors)

Y(Response) = c1*X1 + c2*X2 + c3*X3 + . . . + c(last)* X(last) + E(rrors)Let

P(redictions) = c1*X1 + c2*X2 + c3*X3 + . . . + c(last)* X(last)

As expressed throughoutIntroduction to the Practice of Statistics by

Moore & McCabe

DATA = FIT + RESIDUAL


PUMO


PUMO PREDICTION is the

“Name of the Game”

• Predict BP Change Knowing TREATMENT (Calcium or Placebo)

• Predict Reading SCORE Knowing METHOD (Basal, Drta or Strat)

• Predict MANATEES Killed Knowing NUMBER of BOATS


PUMOWORKSHEET FOR PREDICTION MODELS FOR BLOOD PRESSURE STUDY C:\ALLWARD\ALLC\E\CAMT98\BLOODBLK.XLS

SEE PAGES 543-546 OF MOORE AND MCCABE--INTRODUCTION TO THE PRACTICE OF STATISTICS

Y = c1*X1 + c2*X2 + c3*X3 + . . . + c(last)*X(last) + E Y = P + E

MODEL # 1 Y = c11*U + E1 Y = 2.238*U + E1

Y = P1 + E1MODEL # 2 Y = c12*CALCIUM + c22*PLACEBO + E2 Y = 5.000*CALCIUM + (-0.273)*PLACEBO + E2

Y = P2 + E2MODEL # 2U Y = c13*U + c23*PLACEBO + E2 Y = 5.000*U + (-5.273)*PLACEBO + E2

Y = P2 + E2 MODEL # 1 MODEL # 2 MODEL # 2U

YO c11 YP YO - YP c12 c22 YP YO - YP c13(=c12) c23 YP YO - YP OBSERVED DATA 2.238 Predicted(P1) Error(E1) 5.000 -.273 Predicted(P2) Error(E2) 5.000 -5.273 Predicted(P2) Error(E2)

CASE GROUP DECREASE U (Estimate) (Residual) CALCIUM PLACEBO (Estimate) (Residual) U PLACEBO (Estimate) (Residual)1 CALCIUM 72 CALCIUM -4 1 2.238 -6.238 1 0 5.000 -9.000 1 0 5.000 -9.0003 CALCIUM 18 1 2.238 15.762 1 0 5.000 13.000 1 0 5.000 13.0004 CALCIUM 17 1 2.238 14.762 1 0 5.000 12.000 1 0 5.000 12.0005 CALCIUM -3 1 2.238 -5.238 1 0 5.000 -8.000 1 0 5.000 -8.0006 CALCIUM -5 1 2.238 -7.238 1 0 5.000 -10.000 1 0 5.000 -10.0007 CALCIUM 1 1 2.238 -1.238 1 0 5.000 -4.000 1 0 5.000 -4.0008 CALCIUM 10 1 2.238 7.762 1 0 5.000 5.000 1 0 5.000 5.0009 CALCIUM 11 1 2.238 8.762 1 0 5.000 6.000 1 0 5.000 6.00010 CALCIUM -211 PLACEBO -112 PLACEBO 12 1 2.238 9.762 0 1 -0.273 12.273 1 1 -0.273 12.27313 PLACEBO -1 1 2.238 -3.238 0 1 -0.273 -.727 1 1 -0.273 -.72714 PLACEBO -3 1 2.238 -5.238 0 1 -0.273 -2.727 1 1 -0.273 -2.72715 PLACEBO 3 1 2.238 .762 0 1 -0.273 3.273 1 1 -0.273 3.27316 PLACEBO -5 1 2.238 -7.238 0 1 -0.273 -4.727 1 1 -0.273 -4.72717 PLACEBO 5 1 2.238 2.762 0 1 -0.273 5.273 1 1 -0.273 5.27318 PLACEBO 2 1 2.238 -.238 0 1 -0.273 2.273 1 1 -0.273 2.27319 PLACEBO -11 1 2.238 -13.238 0 1 -0.273 -10.727 1 1 -0.273 -10.72720 PLACEBO -1 1 2.238 -3.238 0 1 -0.273 -.727 1 1 -0.273 -.72721 PLACEBO -3

Algebraic Algebraic Algebraic AlgebraicSum = 47 Sum = Sum = Sum =Sum of Sum of Sum of Sum of Squares = 1287 Squares = Squares = Squares =Average = 2.238 Average = Average = Average =

Total Sum of Squares = Total Sum of Squares = Total Sum of Squares =

WHAT DO ALL THREE MODELS HAVE IN COMMON?

DOES THIS SOUND LIKE SOMETHING YOU HAVE HEARD BEFORE?


PUMO

WORKSHEET FOR PREDICTION MODELS FOR BLOOD PRESSURE STUDY C:\ALLWARD\ALLC\E\CAMT98\BLOODANS.XLSSEE PAGES 543-546 OF MOORE AND MCCABE--INTRODUCTION TO THE PRACTICE OF STATISTICS


MODEL # 1 Y = c11*U + E1 Y = 2.238*U + E1

Y = P1 + E1MODEL # 2 Y = c12*CALCIUM + c22*PLACEBO + E2 Y = 5.000*CALCIUM + (-0.273)*PLACEBO + E2

Y = P2 + E2MODEL # 2U Y = c13*U + c23*PLACEBO + E2 Y = 5.000*U + (-5.273)*PLACEBO + E2


YO c11 YP YO - YP c12 c22 YP YO - YP c13(=c12) c23 YP YO - YP OBSERVED DATA 2.238 Predicted(P1) Error(E1) 5.000 -.273 Predicted(P2) Error(E2) 5.000 -5.273 Predicted(P2) Error(E2)

CASE GROUP DECREASE U (Estimate) (Residual) CALCIUM PLACEBO (Estimate) (Residual) U PLACEBO (Estimate) (Residual)1 CALCIUM 7 1 2.238 4.762 1 0 5.000 2.000 1 0 5.000 2.0002 CALCIUM -4 1 2.238 -6.238 1 0 5.000 -9.000 1 0 5.000 -9.0003 CALCIUM 18 1 2.238 15.762 1 0 5.000 13.000 1 0 5.000 13.0004 CALCIUM 17 1 2.238 14.762 1 0 5.000 12.000 1 0 5.000 12.0005 CALCIUM -3 1 2.238 -5.238 1 0 5.000 -8.000 1 0 5.000 -8.0006 CALCIUM -5 1 2.238 -7.238 1 0 5.000 -10.000 1 0 5.000 -10.0007 CALCIUM 1 1 2.238 -1.238 1 0 5.000 -4.000 1 0 5.000 -4.0008 CALCIUM 10 1 2.238 7.762 1 0 5.000 5.000 1 0 5.000 5.0009 CALCIUM 11 1 2.238 8.762 1 0 5.000 6.000 1 0 5.000 6.00010 CALCIUM -2 1 2.238 -4.238 1 0 5.000 -7.000 1 0 5.000 -7.00011 PLACEBO -1 1 2.238 -3.238 0 1 -0.273 -.727 1 1 -0.273 -.72712 PLACEBO 12 1 2.238 9.762 0 1 -0.273 12.273 1 1 -0.273 12.27313 PLACEBO -1 1 2.238 -3.238 0 1 -0.273 -.727 1 1 -0.273 -.72714 PLACEBO -3 1 2.238 -5.238 0 1 -0.273 -2.727 1 1 -0.273 -2.72715 PLACEBO 3 1 2.238 .762 0 1 -0.273 3.273 1 1 -0.273 3.27316 PLACEBO -5 1 2.238 -7.238 0 1 -0.273 -4.727 1 1 -0.273 -4.72717 PLACEBO 5 1 2.238 2.762 0 1 -0.273 5.273 1 1 -0.273 5.27318 PLACEBO 2 1 2.238 -.238 0 1 -0.273 2.273 1 1 -0.273 2.27319 PLACEBO -11 1 2.238 -13.238 0 1 -0.273 -10.727 1 1 -0.273 -10.72720 PLACEBO -1 1 2.238 -3.238 0 1 -0.273 -.727 1 1 -0.273 -.72721 PLACEBO -3 1 2.238 -5.238 0 1 -0.273 -2.727 1 1 -0.273 -2.727

Algebraic Algebraic Algebraic AlgebraicSum = 47 Sum = 47.000 .000 Sum = 47.000 .000 Sum = 47.000 .000Sum of Sum of Sum of Sum of Squares = 1287 Squares = 105.190 1181.810 Squares = 250.818 1036.182 Squares = 250.818 1036.182Average = 2.238 Average = 2.238 .000 Average = 2.238 .000 Average = 2.238 .000

Total Sum of Squares = 1287.000 Total Sum of Squares = 1287.000 Total Sum of Squares = 1287.000

WHAT DO ALL THREE MODELS HAVE IN COMMON? SUM OF SQUARES OF THE PREDICTED (ESTIMATED) VALUES + SUM OF SQUARES OF THE ERRORS (RESIDUALS) = SUM OF SQUARES OF THE OBSERVED RESPONSE (DEPENDENT) VALUES

DOES THIS SOUND LIKE SOMETHING YOU HAVE HEARD BEFORE? PYTHAGOREAN THEOREM


PUMOPredict BP Change Knowing TREATMENT

(Calcium or Placebo)

Is there a "significant" difference between the mean Blood PressureChange for the Calcium and Placebo groups?

Hypothesis 1: There is NO DIFFERENCE between the mean Blood PressureChange for the Calcium and Placebo groups.

ASSUMED MODEL: (Model #2) Y = c12*CALCIUM + c22*PLACEBO + E2 Y = 5.000*CALCIUM +(-0.273)*PLACEBO + E2

RESTRICTED MODEL: (Model #1) Y = c11*U + E1Y = 2.238*U + E1

F = (SSERESTR - SSEASSUM) / (PREDASSU - PREDREST) (SSEASSUM) / (NUMCASES - PREDASSU)

WHERE --

1181.810 = SSERESTR = SUM OF SQUARES OF ERRORS IN THE RESTRICTED MODEL1036.182 = SSEASSUM = SUM OF SQUARES OF ERRORS IN THE ASSUMED MODEL 2 = PREDASSU = NUMBER OF PREDICTORS IN THE ASSUMED MODEL 1 = PREDREST = NUMBER OF PREDICTORS IN THE RESTRICTED MODEL 21 = NUMCASES = NUMBER OF CASES (OBSERVATIONS)

(SSERESTR - SSEASSUM) = (1181.810 - 1036.182) = 145.628

(PREDASSU - PREDREST) = NUMERATOR DEGREES OF FREEDOM = (2 -1) = 1

(SSERESTR - SSEASSUM) / (PREDASSU - PREDREST) = 145.628/1

(NUMCASES - PREDASSU) = DENOMINATOR DEGREES OF FREEDOM = 21 - 2 = 19

(SSEASSUM) / (NUMCASES - PREDASSU) = 1036.810/19 = 54.569

F = (145.628/1) = 145.628 = 2.669 (1036.810/19) 54.569

WRITE YOUR CONCLUSION:


PUMO

************************************************************************ BEGIN SYSTOLIC BLOOD PRESSURE STUDY, MOORE AND MCCABE CHAPTER 7, PAGE 543 USING THE POOLED TWO-SAMPLE t PROCEDURES CREATE APROPRIATE VARIABLES FOR MOORE AND MCABE PAGE 543 USE BLOODCAL DATA LET U = 1 LET CALCIUM = 0 LET PLACEBO = 0 IF GROUPID$ = "CALCIUM" THEN LET CALCIUM = 1 IF GROUPID$ = "PLACEBO" THEN LET PLACEBO = 1 SAVE BLOODVAR RUN ********************************************************************* COMPUTE MODELS FOR TWO-SAMPLE t-test *************************************************************** MODEL # 1 IS -- MGLH MODEL DECREASE = U (This model gives the AVERAGE DECREASE for the 21 subjects --GRAND MEAN)

MODEL CONTAINS NO CONSTANT.

DEP VAR:DECREASE N:21 MULTIPLE R: 0.286 SQUARED MULTIPLE R: 0.082 ADJUSTED SQUARED MULTIPLE R:.082 STANDARD ERROR OF ESTIMATE:7.687

VARIABLE COEFFICIENT STD ERROR STD COEF TOLERANCE T P(2 TAIL)

U 2.238 1.677 0.286 1.000 1.334 0.197

ANALYSIS OF VARIANCE

SOURCE SUM-OF-SQUARES DF MEAN-SQUARE F-RATIO P

REGRESSION 105.190 1 105.190 1.780 0.197 RESIDUAL 1181.810 20 59.090********************************************************************

ESTIMATE RESIDUAL DECREASE U

CASE 1 2.238 4.762 7.000 1.000 CASE 2 2.238 -6.238 -4.000 1.000 CASE 3 2.238 15.762 18.000 1.000 CASE 4 2.238 14.762 17.000 1.000 CASE 5 2.238 -5.238 -3.000 1.000 CASE 6 2.238 -7.238 -5.000 1.000 CASE 7 2.238 -1.238 1.000 1.000 CASE 8 2.238 7.762 10.000 1.000 CASE 9 2.238 8.762 11.000 1.000 CASE 10 2.238 -4.238 -2.000 1.000 CASE 11 2.238 -3.238 -1.000 1.000 CASE 12 2.238 9.762 12.000 1.000 CASE 13 2.238 -3.238 -1.000 1.000 CASE 14 2.238 -5.238 -3.000 1.000 CASE 15 2.238 0.762 3.000 1.000 CASE 16 2.238 -7.238 -5.000 1.000 CASE 17 2.238 2.762 5.000 1.000 CASE 18 2.238 -0.238 2.000 1.000 CASE 19 2.238 -13.238 -11.000 1.000 CASE 20 2.238 -3.238 -1.000 1.000 CASE 21 2.238 -5.238 -3.000 1.000


PUMO

MODEL #2 IS -- MGLH MODEL DECREASE = CALCIUM + PLACEBO (This model gives the AVERAGE DECREASE for CALCIUM and PLACEBO groups)


DEP VAR:DECREASE N: 21 MULTIPLE R: 0.441 SQUARED MULTIPLE R: 0.195 ADJUSTED SQUARED MULTIPLE R:.153 STANDARD ERROR OF ESTIMATE: 7.385


CALCIUM 5.000 2.335 0.441 1.000 2.141 0.045 PLACEBO -0.273 2.227 -0.025 1.000 -0.122 0.904



REGRESSION 250.818 2 125.409 2.300 0.128 RESIDUAL 1036.182 19 54.536*******************************************************************************

ESTIMATE RESIDUAL DECREASE CALCIUM PLACEBO

CASE 1 5.000 2.000 7.000 1.000 0.000 CASE 2 5.000 -9.000 -4.000 1.000 0.000 CASE 3 5.000 13.000 18.000 1.000 0.000 CASE 4 5.000 12.000 17.000 1.000 0.000 CASE 5 5.000 -8.000 -3.000 1.000 0.000 CASE 6 5.000 -10.000 -5.000 1.000 0.000 CASE 7 5.000 -4.000 1.000 1.000 0.000 CASE 8 5.000 5.000 10.000 1.000 0.000 CASE 9 5.000 6.000 11.000 1.000 0.000 CASE 10 5.000 -7.000 -2.000 1.000 0.000 CASE 11 -0.273 -0.727 -1.000 0.000 1.000 CASE 12 -0.273 12.273 12.000 0.000 1.000 CASE 13 -0.273 -0.727 -1.000 0.000 1.000 CASE 14 -0.273 -2.727 -3.000 0.000 1.000 CASE 15 -0.273 3.273 3.000 0.000 1.000 CASE 16 -0.273 -4.727 -5.000 0.000 1.000 CASE 17 -0.273 5.273 5.000 0.000 1.000 CASE 18 -0.273 2.273 2.000 0.000 1.000 CASE 19 -0.273 -10.727 -11.000 0.000 1.000 CASE 20 -0.273 -0.727 -1.000 0.000 1.000 CASE 21 -0.273 -2.727 -3.000 0.000 1.000


PUMO

********************************************************************* MODEL #2U -- MGLH MODEL DECREASE = CONSTANT + PLACEBO (In this model the coefficient of CONSTANT gives the AVERAGE DECREASE for CALCIUM and the coefficient of PLACEBO is the DIFFERENCE between the AVERAGE DECREASE of PLACEBO and CALCIUM)

DEP VAR:DECREASE N: 21 MULTIPLE R: 0.351 SQUARED MULTIPLE R: 0.123 ADJUSTED SQUARED MULTIPLE R:.077 STANDARD ERROR OF ESTIMATE: 7.385


CONSTANT 5.000 2.335 0.000 . 2.141 0.045 PLACEBO -5.273 3.227 -0.351 1.000 -1.634 0.119



REGRESSION 145.628 1 145.628 2.670 0.119 RESIDUAL 1036.182 19 54.536

*********************************************************************** ESTIMATE RESIDUAL DECREASE PLACEBO

CASE 1 5.000 2.000 7.000 0.000 CASE 2 5.000 -9.000 -4.000 0.000 CASE 3 5.000 13.000 18.000 0.000 CASE 4 5.000 12.000 17.000 0.000 CASE 5 5.000 -8.000 -3.000 0.000 CASE 6 5.000 -10.000 -5.000 0.000 CASE 7 5.000 -4.000 1.000 0.000 CASE 8 5.000 5.000 10.000 0.000 CASE 9 5.000 6.000 11.000 0.000 CASE 10 5.000 -7.000 -2.000 0.000 CASE 11 -0.273 -0.727 -1.000 1.000 CASE 12 -0.273 12.273 12.000 1.000 CASE 13 -0.273 -0.727 -1.000 1.000 CASE 14 -0.273 -2.727 -3.000 1.000 CASE 15 -0.273 3.273 3.000 1.000 CASE 16 -0.273 -4.727 -5.000 1.000 CASE 17 -0.273 5.273 5.000 1.000 CASE 18 -0.273 2.273 2.000 1.000 CASE 19 -0.273 -10.727 -11.000 1.000 CASE 20 -0.273 -0.727 -1.000 1.000 CASE 21 -0.273 -2.727 -3.000 1.000


PUMO

See the results of this analysis in Example 7.12, pp. 544-546 inMoore and McCabe

INTRODUCTION to the PRACTICE of STATISTICSSecond Edition, 1993

by W.H. Freeman


PUMO WORKSHEET FOR PREDICTION MODELS FOR READING STUDY C:\ALLWARD\ALLC\E\NCTM\WASHDC98\NCTMAK98\READANS.XLSSEE PAGE 725 OF MOORE AND MCCABE--INTRODUCTION TO THE PRACTICE OF STATISTICS


MODEL # 1 Y = c11*U + E1 Y = 9.788*U + E1

Y = P1 + E1MODEL # 2 Y = c12*BASAL + c22*DRTA + c32*STRAT + E2 Y = 10.500*BASAL + 9.727*DRTA + 9.136*STRAT + E2

Y = P2 + E2MODEL # 2U Y = c13*U + c23*DRTA + c33*STRAT + E2 Y = 10.500*BASAL - .773*DRTA - 1.364*STRAT + E2


YO c11 YP YO - YP c12 c22 c32 YP YO - YP c13=c12 c23 c33 YP YO - YP OBSERVED DATA 9.788 Predicted Error 10.500 9.727 9.136 Predicted Error 10.500 -.773 -1.364 Predicted Error

CASE GROUP SCORE U (Estimate) (Residual) BASAL DRTA STRAT (Estimate) (Residual) U DRTA STRAT (Estimate) (Residual)1 BASAL 4 1 9.788 -5.788 1 0 0 10.500 -6.500 1 0 0 10.500 -6.5002 BASAL 6 1 9.788 -3.788 1 0 0 10.500 -4.500 1 0 0 10.500 -4.500

cut here …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. ……………..21 BASAL 7 1 9.788 -2.788 1 0 0 10.500 -3.500 1 0 0 10.500 -3.50022 BASAL 9 1 9.788 -.788 1 0 0 10.500 -1.500 1 0 0 10.500 -1.50023 DRTA 7 1 9.788 -2.788 0 1 0 9.727 -2.727 1 1 0 9.727 -2.72724 DRTA 7 1 9.788 -2.788 0 1 0 9.727 -2.727 1 1 0 9.727 -2.727

cut here …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. ……………..43 DRTA 8 1 9.788 -1.788 0 1 0 9.727 -1.727 1 1 0 9.727 -1.72744 DRTA 10 1 9.788 .212 0 1 0 9.727 .273 1 1 0 9.727 .27345 STRAT 11 1 9.788 1.212 0 0 1 9.136 1.864 1 0 1 9.136 1.86446 STRAT 7 1 9.788 -2.788 0 0 1 9.136 -2.136 1 0 1 9.136 -2.136

cut here …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. …………….. ……………..65 STRAT 5 1 9.788 -4.788 0 0 1 9.136 -4.136 1 0 1 9.136 -4.13666 STRAT 8 1 9.788 -1.788 0 0 1 9.136 -1.136 1 0 1 9.136 -1.136

Algebraic Algebraic Algebraic AlgebraicSum = 646 Sum = 646 .000 Sum = 646.000 .000 Sum = 646.000 .000Sum of Sum of Sum of Sum of Squares = 6916 Squares = 6322.970 593.030 Squares = 6343.545 572.455 Squares = 6343.545 572.455Average = 9.788 Average = 9.788 .000 Average = 9.788 .000 Average = 9.788 .000

Total Sum of Squares = 6916.000 Total Sum of Squares = 6916.000 Total Sum of Squares = 6916.000

WHAT DO ALL THREE MODELS HAVE IN COMMON? SUM OF SQUARES OF THE PREDICTED (ESTIMATED) VALUES + SUM OF SQUARES OF THE ERRORS (RESIDUALS) = SUM OF SQUARES OF THE OBSERVED RESPONSE (DEPENDENT) VALUES



PUMO

Predict Reading SCORE Knowing METHOD

(Basal, Drta or Strat)

Are there "significant" differences between the mean Reading SCORES forthe Basal, Drta and Strat groups?

Hypothesis 1: There are no differences between the mean ReadingSCORES for the Basal, Drta and Strat groups?

ASSUMED MODEL: (Model #2) Y = c12*BASAL + c22*DRTA + c32*STRAT + E2 Y = 10.500*BASAL + 9.727*DRTA + 9.136*STRAT + E2

RESTRICTED MODEL: (Model #1) Y = c11*U + E1 Y = 9.788*U + E1


WHERE --593.030 = SSERESTR = SUM OF SQUARES OF ERRORS IN THE RESTRICTED MODEL572.455 = SSEASSUM = SUM OF SQUARES OF ERRORS IN THE ASSUMED MODEL 3 = PREDASSU = NUMBER OF PREDICTORS IN THE ASSUMED MODEL 1 = PREDREST = NUMBER OF PREDICTORS IN THE RESTRICTED MODEL 66 = NUMCASES = NUMBER OF CASES (OBSERVATIONS)


(PREDASSU - PREDREST) = NUMERATOR DEGREES OF FREEDOM = (3-1) = 2

(SSERESTR - SSEASSUM) / (PREDASSU - PREDREST) =20.575/2 = 10.288



F = (20.575/2) = 10.288 = 1.132 (572.455/63) 9.087



PUMO

BEGIN READING STUDY, MOORE AND MCCABE CHAPTER 10, PAGE 725 USING THE ONE-WAY ANOVA MODEL CREATE APROPRIATE VARIABLES FOR MOORE AND MCABE PAGE 725 AND FOR CONTRASTS ON PAGE 739 USE READING DATA LET U = 1 LET BASAL = 0 LET DRTA = 0 LET = STRAT = 0 IF GROUPID$ = "BASAL" THEN LET BASAL = 1 IF GROUPID$ = "DRTA" THEN LET DRTA = 1 IF GROUPID$ = "STRAT" THEN LET STRAT = 1 CONTRAST #1 MuB = .5*(MuD + MuS) LET DPHB = DRTA + (.5*BASAL) CONTRAST #2 MuD = MuS LET SPHB = STRAT + (.58*BASAL) LET DPS = DRTA + STRAT SAVE READVAR RUN ********************************************************************* COMPUTE MODELS FOR ONE-WAY ANOVA USING SCORE ON PAGE 725 (OR PRE3 PAGE 795) OF MOORE & MCCABE RESULTS ARE ON PAGE 729. *************************************************************** MODEL # 1 IS -- MGLH MODEL SCORE = U (This model gives the AVERAGE SCORE for the 21 subjects --GRAND MEAN)


DEP VAR: SCORE N: 66 MULTIPLE R: 0.956 SQUARED MULTIPLE R: 0.914 ADJUSTED SQUARED MULTIPLE R: .914 STANDARD ERROR OF ESTIMATE: 3.021


U 9.788 0.372 0.956 1.000 26.3260.000



REGRESSION 6322.970 1 6322.970 693.039 0.000 RESIDUAL 593.030 65 9.124****************************************************************************8

ESTIMATE RESIDUAL SCORE U

CASE 1 9.788 -5.788 4.000 1.000 CASE 2 9.788 -3.788 6.000 1.000 CASE 3 9.788 -0.788 9.000 1.000 CASE 4 9.788 2.212 12.000 1.000 CASE 5 9.788 6.212 16.000 1.000 CASE 6 9.788 5.212 15.000 1.000 CASE 7 9.788 4.212 14.000 1.000 CASE 8 9.788 2.212 12.000 1.000 CASE 9 9.788 2.212 12.000 1.000 CASE 10 9.788 -1.788 8.000 1.000----------------- CUT HERE ----------------------------


PUMO

MODEL # 2 MGLH

MODEL SCORE = BASAL + DRTA + STRAT

(This model gives the AVERAGE SCORE for BASAL, DRTA and STRAT groups)




BASAL 10.500 0.643 0.592 1.000 16.338 0.000 DRTA 9.727 0.643 0.549 1.000 15.136 0.000 STRAT 9.136 0.643 0.515 1.000 14.216 0.000



REGRESSION 6343.545 3 2114.515 232.707 0.000 RESIDUAL 572.455 63 9.087*********************************************************************************

ESTIMATE RESIDUAL SCORE BASAL DRTA

STRAT

CASE 1 10.500 -6.500 4.000 1.000 0.000 CASE 1 0.000 CASE 2 10.500 -4.500 6.000 1.000 0.000 CASE 2 0.000---------------CUT HERE --------------------------- CASE 21 10.500 -3.500 7.000 1.000 0.000 CASE 21 0.000 CASE 22 10.500 -1.500 9.000 1.000 0.000 CASE 22 0.000 CASE 23 9.727 -2.727 7.000 0.000 1.000 CASE 23 0.000 CASE 24 9.727 -2.727 7.000 0.000 1.000 CASE 24 0.000---------------- CUT HERE ------------------------ CASE 43 9.727 -1.727 8.000 0.000 1.000 CASE 43 0.000 CASE 44 9.727 0.273 10.000 0.000 1.000 CASE 44 0.000 CASE 45 9.136 1.864 11.000 0.000 0.000 CASE 45 1.000 CASE 46 9.136 -2.136 7.000 0.000 0.000 CASE 46 1.000----------------CUT HERE----------------------------- CASE 65 9.136 -4.136 5.000 0.000 0.000 CASE 65 1.000 CASE 66 9.136 -1.136 8.000 0.000 0.000 CASE 66 1.000


PUMO

MODEL #2U -- MGLH

MODEL SCORE = CONSTANT + DRTA + STRAT

(In this model the coefficient of CONSTANT gives the AVERAGE SCORE

for BASAL, the coefficient of DRTA is the DIFFERENCE between

the AVERAGE SCORE of DRTA and BASAL and the coefficient of STRAT is

the DIFFERENCE between the AVERAGE SCORE of STRAT and BASAL)



CONSTANT 10.500 0.643 0.000 . 16.338 0.000 DRTA -0.773 0.909 -0.122 0.750 -0.850 0.398 STRAT -1.364 0.909 -0.214 0.750 -1.500 0.139




***************************************************************************** ESTIMATE RESIDUAL SCORE DRTA STRAT

CASE 1 10.500 -6.500 4.000 0.000 0.000 CASE 2 10.500 -4.500 6.000 0.000 0.000-------------- CUT HERE ----------------------------- CASE 21 10.500 -3.500 7.000 0.000 0.000 CASE 22 10.500 -1.500 9.000 0.000 0.000 CASE 23 9.727 -2.727 7.000 1.000 0.000 CASE 24 9.727 -2.727 7.000 1.000 0.000---------------- CUT HERE ----------------------------- CASE 43 9.727 -1.727 8.000 1.000 0.000 CASE 44 9.727 0.273 10.000 1.000 0.000 CASE 45 9.136 1.864 11.000 0.000 1.000 CASE 46 9.136 -2.136 7.000 0.000 1.000--------------- CUT HERE -------------------------------------- CASE 65 9.136 -4.136 5.000 0.000 1.000 CASE 66 9.136 -1.136 8.000 0.000 1.000


PUMO

See the results of this analysis in Example 10.6, pp. 725-732 inMoore and McCabe


by W.H. Freeman


PUMO

WORKSHEET FOR PREDICTION MODELS FOR MANATEE ANALYSIS C:\ALLWARD\ALLC\E\NCTM\WASHDC98\NCTMAK98\MANATBLK.XLSSEE PAGE 674 OF MOORE AND MCCABE -- INTRODUCTION TO THE PRACTICE OF STATISTICS


MODEL # 1 Y = c11*U + E1 Y = 29.429*U + E1

Y = P1 + E1MODEL # 2 Y = c12*U + c22*BOATS + E2 Y = -41.430*U + .125*BOATS + E2

Y = P2 + E2 MODEL # 1 MODEL # 2

YO c11 YP YO - YP c12 c22 YP YO - YP

OBSERVED DATA 29.42860 Predicted Error -41.43040 0.125 Predicted ErrorCASE BOATS MANATEES U (Estimate) (Residual) U BOATS (Estimate) (Residual)

1 447 132 460 21 1 29.429 -8.429 1 460 16.006 4.9943 481 24 1 29.429 -5.429 1 481 18.628 5.3724 498 16 1 29.429 -13.429 1 498 20.751 -4.7515 513 24 1 29.429 -5.429 1 513 22.624 1.3766 512 207 526 15 1 29.429 -14.429 1 526 24.247 -9.2478 559 34 1 29.429 4.571 1 559 28.367 5.6339 585 33 1 29.429 3.571 1 585 31.614 1.38610 614 33 1 29.429 3.571 1 614 35.235 -2.23511 645 39 1 29.429 9.571 1 645 39.105 -.10512 675 43 1 29.429 13.571 1 675 42.851 .14913 711 50 1 29.429 20.571 1 711 47.346 2.65414 719 47

Algebraic Algebraic AlgebraicSum = 7945 412 Sum = Sum =Sum of Sum of Sum of Squares =4618597.000 14056.000 Squares = Squares =Average = 567.500 29.429 Average = Average =

Total Sum of Squares = Total Sum of Squares =

WHAT DO THESE TWO MODELS HAVE IN COMMON?

DOES THIS SOUND LIKE SOMETHING YOU HAVE HEARD BEFORE?


PUMO

WORKSHEET FOR PREDICTION MODELS FOR MANATEE ANALYSIS C:\ALLWARD\ALLC\E\NCTM\WASHDC98\NCTMAK98\MANATANS.XLS

SEE PAGE 674 OF MOORE AND MCCABE -- INTRODUCTION TO THE PRACTICE OF STATISTICS


MODEL # 1 Y = c11*U + E1 Y = 29.429*U + E1

Y = P1 + E1MODEL # 2 Y = c12*U + c22*BOATS + E2 Y = -41.430*U + .125*BOATS + E2

Y = P2 + E2 MODEL # 1 MODEL # 2

YO c11 YP YO - YP c12 c22 YP YO - YP

OBSERVED DATA 29.42860 Predicted Error -41.43040 0.125 Predicted ErrorCASE BOATS MANATEES U (Estimate) (Residual) U BOATS (Estimate) (Residual)

1 447 13 1 29.429 -16.429 1 447 14.383 -1.3832 460 21 1 29.429 -8.429 1 460 16.006 4.9943 481 24 1 29.429 -5.429 1 481 18.628 5.3724 498 16 1 29.429 -13.429 1 498 20.751 -4.7515 513 24 1 29.429 -5.429 1 513 22.624 1.3766 512 20 1 29.429 -9.429 1 512 22.499 -2.4997 526 15 1 29.429 -14.429 1 526 24.247 -9.2478 559 34 1 29.429 4.571 1 559 28.367 5.6339 585 33 1 29.429 3.571 1 585 31.614 1.38610 614 33 1 29.429 3.571 1 614 35.235 -2.23511 645 39 1 29.429 9.571 1 645 39.105 -.10512 675 43 1 29.429 13.571 1 675 42.851 .14913 711 50 1 29.429 20.571 1 711 47.346 2.65414 719 47 1 29.429 17.571 1 719 48.345 -1.345

Algebraic Algebraic AlgebraicSum = 7945 412 Sum = 412.0004 .000 Sum = 412.000543 -.001Sum of Sum of Sum of Squares =4618597.000 14056.000 Squares = 12124.595 1931.429 Squares = 13836.582 219.450Average = 567.500 29.429 Average = 29.429 .000 Average = 29.429 .000

Total Sum of Squares = 14056.024 Total Sum of Squares = 14056.032

WHAT DO THESE TWO MODELS HAVE IN COMMON? SUMOF SQUARES OF THE PREDICTED (ESTIMATED) VALUES + SUM OF SQUARES OF THE ERRORS (RESIDUALS) = SUM OF SQUARES OF THE OBSERVED RESPONSE (DEPENDENT) VALUES



PUMOPredict MANATEES Killed Knowing NUMBER OF BOATS

Is there a "significant" difference between the predicted number of MANATEES

Killed for different number of BOATS?

Hypothesis 1: There is NO DIFFERENCE between the predicted number of MANATEESKilled for different number of BOATS.

ASSUMED MODEL: (Model #2) Y = c12*U + c22*BOATS + E2 Y = -41.430*U + .125*BOATS + E2

RESTRICTED MODEL: (Model #1) Y = c11*U + E1Y = 29.429*U + E1


WHERE --

1931.429 = SSERESTR = SUM OF SQUARES OF ERRORS IN THE RESTRICTED MODEL 219.450 = SSEASSUM = SUM OF SQUARES OF ERRORS IN THE ASSUMED MODEL 2 = PREDASSU = NUMBER OF PREDICTORS IN THE ASSUMED MODEL 1 = PREDREST = NUMBER OF PREDICTORS IN THE RESTRICTED MODEL 14 = NUMCASES = NUMBER OF CASES (OBSERVATIONS)


(PREDASSU - PREDREST) = NUMERATOR DEGREES OF FREEDOM = (2 -1) = 1

(SSERESTR - SSEASSUM) / (PREDASSU - PREDREST) = 1711.979/1



F = (1711.979/1) = 1711.979 = 93.615 (219.450/12) 18.2875



PUMO

COMPUTE MODELS FOR MANATEE STUDY USING SIMPLE REGRESSION USING DATA ON PAGE 674 OF MOORE & MCCABE RESULTS ARE ON PAGE 674. *************************************************************** MODEL #1 MGLH MODEL MANATEES = U (This model gives the AVERAGE NUMBER OF MANATEES KILLED)


DEP VAR:MANATEES N: 14 MULTIPLE R: 0.929 SQUARED MULTIPLE R: 0.863 ADJUSTED SQUARED MULTIPLE R .863 STANDARD ERROR OF ESTIMATE: 12.189


U 29.429 3.258 0.929 1.000 9.034 0.000




******************************************************************** ESTIMATE RESIDUAL MANATEES U

CASE 1 29.429 -16.429 13.000 1.000 CASE 2 29.429 -8.429 21.000 1.000 CASE 3 29.429 -5.429 24.000 1.000 CASE 4 29.429 -13.429 16.000 1.000 CASE 5 29.429 -5.429 24.000 1.000 CASE 6 29.429 -9.429 20.000 1.000 CASE 7 29.429 -14.429 15.000 1.000 CASE 8 29.429 4.571 34.000 1.000 CASE 9 29.429 3.571 33.000 1.000 CASE 10 29.429 3.571 33.000 1.000 CASE 11 29.429 9.571 39.000 1.000 CASE 12 29.429 13.571 43.000 1.000 CASE 13 29.429 20.571 50.000 1.000 CASE 14 29.429 17.571 47.000 1.000


PUMO

MODEL # 2 MGLH MODEL MANATEES = CONSTANT + BOATS

DEP VAR:MANATEES N: 14 MULTIPLE R: 0.941 SQUARED MULTIPLE R: 0.886 ADJUSTED SQUARED MULTIPLE R: .877 STANDARD ERROR OF ESTIMATE: 4.276


CONSTANT -41.430 7.412 0.000 . -5.589 0.000 BOATS 0.125 0.013 0.941 1.000 9.675 0.000




************************************************************************ ESTIMATE RESIDUAL MANATEES BOATS

CASE 1 14.383 -1.383 13.000 447.000 CASE 2 16.006 4.994 21.000 460.000 CASE 3 18.628 5.372 24.000 481.000 CASE 4 20.751 -4.751 16.000 498.000 CASE 5 22.624 1.376 24.000 513.000 CASE 6 22.499 -2.499 20.000 512.000 CASE 7 24.247 -9.247 15.000 526.000 CASE 8 28.367 5.633 34.000 559.000 CASE 9 31.614 1.386 33.000 585.000 CASE 10 35.235 -2.235 33.000 614.000 CASE 11 39.105 -0.105 39.000 645.000 CASE 12 42.851 0.149 43.000 675.000 CASE 13 47.346 2.654 50.000 711.000 CASE 14 48.345 -1.345 47.000 719.000 ***************************************************************

END of the MANATEE problem from Moore & McCabe


PUMO

See the results of this analysis in Section 9.1 Exercises, pp. 674-675 inMoore and McCabe


by W.H. Freeman


PUMO

ANNOUNCING: VOLUNTEER STATISTICIANS ARE AVAILABLE TO ASSIST STUDENTS WITH STATISTICAL DESIGN AND DATA ANALYSIS FOR SCIENCE AND ENGINEERING RESEARCH PROJECTS

Students who have received advice in statistical design and data analysis BEFORE STARTING science fair projects have been recognized not onlyfor SPECIAL AWARDS IN STATISTICS, but also have placed very high in their special science fair category. In the 1997 International Scienceand Engineering Fair (ISEF) in Louisville, KY, the project that received the FIRST PLACE award in STATISTICS also won the FIRST GRANDPRIZE in BEHAVIORAL AND SOCIAL SCIENCES. The ISEF SECOND PLACE winner in STATISTICS also received FOURTH GRANDPRIZE in BEHAVIORAL AND SOCIAL SCIENCES. Of special interest is that the ISEF SECOND PLACE winner in STATISTICS received theFIRST PLACE special award in STATISTICS at the Alamo Regional Science and Engineering Fair in 1997.

Members of the San Antonio Chapter of the American Statistical Association have volunteered to assist students in the San Antonio area with thestatistical aspects of there science projects. IT IS HIGHLY DESIRABLE TO ASK THESE VOLUNTEER STATISTICIANS FOR ASSISTANCEVERY EARLY IN THE RESEARCH PROJECT.

Students and teachers should contact ARASE board member Dr. Joe Ward to locate statisticians who are available to provide assistance.

Call (210) 433-6575 or email to [email protected].****************************************************************************************************

ANNOUNCING: A STUDENT & TEACHER COLLABORATIVE PROJECT IN PROBLEM SOLVING USING DATA ANALYSIS

(STCP98)June 1 through June 12, 1998

Health Careers High School 4646 Hamilton Wolfe

San Antonio, TX 78229

From: Joe Ward 167 East Arrowhead Dr., San Antonio, TX 78228-2402 (210) 433-6575 FAX: (210) 617-5423 email: [email protected]

** Have you ever had students enter research projects into competition and -- be marked down because of -- insufficient data? -- student's inability to explain the data analysis?

** Have you had students doing research projects come to you with a "pile" of -- data and not know what to do with it?

** Have you had a problem finding statistical computer programs to support -- data analysis for research projects?

** Have you had a problem locating someone to help with the statistical -- aspects of student research projects?

If you answered yes to any of the above, then :this project may be for you and your students.!It provides an unusual opportunity for teachers (and their students) to acquire capabilities for data analysis using statistical software not availableelsewhere.

This project is designed to strengthen the skills of students who are already in or about to begin independent science research initiatives. In the past,students who work on science fair or research projects have had a difficult time collecting, sorting, analyzing and interpreting numerical data. Fewstudents or teachers have experienced real-world problem solving using modern computer-based data analysis procedures.

This project will empower students to: (1) Identify and express real-world problems in natural language in preparation for creating formalmathematical/statistical models, (2) Translate the natural language problem statement into a mathematical model appropriate for analysis using astatistical software package, and (3) Interpret and present the results in both written and verbal form appropriate to assist in real-world decisions.


PUMO

Student participants will be selected by their mentor teachers and will be those who have been identified by their teachers as students who arecommitted to conducting a research project to completion. Monitoring and evaluation of the project will consist of testing of skill acquisition during theformal learning sessions; but, of most importance, are the students' performance in the successful conduct and completion of research projects. Thefocus of evaluation in this project is the short-term performance of the students who apply their new skills in research projects. The teachers' successwill be indicated by the quality of their students' research project analysis.

Students who have participated in this program in past years have received special awards in Alamo Regional Science Fairs for the best application ofstatistics in their projects. In 1996, a project submitted by graduates of this program received the special award for the best application of a computer ina research project from the American Statistical Association's national project competition.

The project director is Dr. Joe Ward. Dr. Ward has had much experience in introducing high school students and teachers in the applications ofstatistics and computers in research. He has developed curriculum and taught Problem Solving Through Data Analysis in the San Antonio PREPprogram. He is a past member of the American Statistical Association-National Council of Teachers of Mathematics Joint Committee on theCurriculum in Statistics and Probability. Assistance in the workshop will be provided by Ms. Laura Niland who teaches Advanced Placement Statisticsat MacArthur HS. Ms. Niland has been recognized as a Texas Presidential Awardee in Mathematics. The workshop will be enriched with a specialpresentation from Mr. Paul Foerster, the first Texas Presidential Awardee in Mathematics. Mr. Foerster, who teaches at Alamo Heights HS, is theauthor of several mathematics text books used by many students in the San Antonio area. In addition, visits by several statisticians will provideparticipants with the opportunity to learn more about the activities of practicing statisticians. Phase 1 -- Students and their mentors will meet at HealthCareers High School from (8:30 am to 3:30 pm), 5 days per week, for two weeks beginning Monday, June 1 through Friday, June 12.

Phase 2 -- Progress report meetings will be conducted twice per month (and as needed) prior to project competitions to facilitate quality studentresearch projects. Statisticians from the San Antonio area will be available to assist teachers and students with the design and analysis of theirresearch. The short-term objectives of this project will be active participation by students in one or more competitions such as the Junior Academy ofScience, the Alamo District Science Fair, the National Statistics Project and Poster contests and similar activities.

Each teacher who successfully completes both phases of the project will receive a stipend of $1,000. Each student who successfully completes both phases of theproject will receive $100 for expenses associated with their research projects. One-half of the payments will be made after successful completion of Phase 1 andthe final payment will be made after satisfactory completion of the research projects of Phase 2.******************************************************************************Teacher & Student Application Form

Each teacher should choose 2 students who are committed to the Project objectives.(If you have more than 2 qualified and interested students please call Joe Ward).

Teacher Name:_____________________________________________________________ (Last Name) (First, Name) (MI) Home ______________________________________ Home phone:__________________Address: ______________________________________ Email:_______________________School: ___________________________ Subjects taught: _______________________

Student Applicants:Student Name:_____________________________________________________________ (Last Name) (First, Name) (MI) Home ______________________________________ Home phone:__________________Address: ______________________________________ Email:_______________________School: ___________________________ School grade Sept. 98 __________________

Student Name:_____________________________________________________________ (Last Name) (First, Name) (MI) Home ______________________________________ Home phone:__________________Address: ______________________________________ Email:_______________________School: ___________________________ School grade Sept. 98 __________________

For more information contact Joe Ward. C::ALLWARD\ALLC\G\STCP98\APPLI98A.DOC

1 niland-ward-camt-1998 pumo using calculators and computers in statistics camt98 45th annual...

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