Lecture 8 Topic 5: Multiple Comparisons (means separation)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Lecture 8 Topic 5: Multiple Comparisons (means separation)"

Transcription

1 Lectue 8 Topic 5: Multiple Compaisons (means sepaation) ANOVA: H 0 : µ 1 = µ =... = µ t H 1 : The mean of at least one teatment goup is diffeent If thee ae moe than two teatments in the expeiment, futhe analysis is equied to detemine which means ae significantly diffeent. Thee ae two stategies: 1. Planned, single d.f. F tests (othogonal contasts) Motivated by the teatment stuctue Independent Poweful and pecise Limited to (t 1) compaisons Well-defined method. Multiple compaisons (means sepaation) Motivated by the data Useful when no paticula elationship exists among teatments Up to unlimited compaisons Many, many methods/philosophies to choose fom Eo ates Selection of the most appopiate multiple compaison test is heavily influenced by the eo ate. Recall that a Type I eo occus when one incoectly ejects a tue null hypothesis H 0. The Type I eo ate is the faction of times a Type I eo is made. In a single compaison, this is α. When compaing thee o moe teatment means: 1. Compaison-wise Type I eo ate (CER) The numbe of Type I eos, divided by the total numbe of compaisons.. Expeiment-wise Type I eo ate (EER) The numbe of expeiments in which at least one Type I eo occus, divided by the total numbe of expeiments. 1

2 Example: An expeimente conducts an expeiment with 5 teatments. In such an expeiment, thee ae 10 possible paiwise compaisons that can be made: Total possible paiwise compaisons: p = t( t 1) Suppose that thee ae no tue diffeences among the teatments (i.e. H 0 is tue), but that one Type I eo is made. CER = (1 Type I eo) / (10 compaisons) = 0.1 o 10% EER = (1 expeiments with a Type I eo) / (1 expeiment) = 1 o 100% Things to conside: 1. EER is the pobability of thee being a Type I eo somewhee in the expeiment. As the numbe of teatments inceases, the EER à 100%.. To maintain a low EER, the CER has to be kept vey low. Convesely, a easonable CER will inflate the EER to a potentially unacceptable level. 3. The elative impotance of contolling these two Type I eo ates depends on the objectives of the study: When incoectly ejecting one compaison jeopadizes the entie expeiment o when the consequence of incoectly ejecting one compaison is as seious as incoectly ejecting a numbe of compaisons, EER contol is moe impotant. When one eoneous conclusion will not affect othe infeences in an expeiment, CER contol is moe impotant. 4. Diffeent multiple compaison pocedues have been developed based on diffeent philosophies egading contol of these two kinds of eo.

3 Computing EER So you set CER = α what is EER? The EER is difficult to compute because, fo a given set of data, Type I eos ae not independent. But it is possible to compute an uppe bound fo the EER by assuming that the pobability of a Type I eo fo any single compaison is α and is independent of all othe compaisons. In that case: Uppe bound EER = 1 - (1 - α) p whee p = t( t 1), as befoe Example: Fo 10 teatments and α = 0.05: t( t 1) 10(10 1) p = = = 45 Uppe bound EER = 1 (1 0.05) 45 = 0.90 This fomula may also be used to detemine a value fo α fo some fixed maximum EER. 0.1 = 1 (1 α) 45 (1 α) 45 = 0.9 (1 α) = 0.9 (1/45) α =

4 Patial null hypothesis Suppose thee ae 10 teatments, one of which shows a significant effect while the othe 9 ae appoximately equal: x Y i. x x x x x x x x x Y Teatment numbe ANOVA will pobably eject H 0. Even though one mean is tuly diffeent, thee is still a chance of making a Type I eo in each paiwise compaison among the 9 simila teatments. An uppe bound the EER is computed by setting t = 9 in the above fomula: t( t 1) 9(9 1) p = = = 36 Uppe bound EER = 1 (1 0.05) 36 = 0.84 Intepetation: The expeimente will incoectly conclude that two tuly simila effects ae diffeent 84% of the time. This is called the expeiment-wise eo ate unde a patial null hypothesis. Some teminology: CER = compaison-wise eo ate EERC = expeiment-wise eo ate unde a complete null hypothesis (standad EER) EERP = expeiment-wise eo ate unde a patial null hypothesis MEER = maximum expeiment-wise eo ate unde any complete o patial null hypothesis. 4

5 Multiple compaisons tests Statistical methods fo making two o moe infeences while contolling cumulative Type I eo ates ae called simultaneous infeence methods: 1. Fixed-ange tests: Those which povide confidence intevals and tests of hypotheses. Multiple-ange tests: Those which povide only tests of hypotheses Equal eplications. Results (mg shoot dy weight) of an expeiment (CRD) to detemine the effect of seed teatment by diffeent acids on the ealy gowth of ice seedlings. Teatment Replications Mean Contol HCl Popionic Butyic t = 4, = 5, oveall mean = 3.86 Souce df SS MS F Total Teatment Eo Unequal eplications. Results (lbs/animal day) of an expeiment (CRD) to detemine the effect of diffeent foage genotypes on animal weight gain. Teatment Replications (Animals) Mean Contol Foage-A Foage-B Foage-C t = 4, = vaiable, oveall mean = Souce df SS MS F Total Teatment Eo

6 Fixed-ange tests These tests povide a single ange fo testing all diffeences in balanced designs and can povide confidence intevals. LSD à Dunnett à Tukey à Scheffe Less consevative à Moe consevative Moe likely to declae diffeences à Less likely to declae diffeences Highe Type I eo ates à Lowe Type I eo ates Highe powe à Lowe powe Least significant diffeence (LSD), the epeated t test One of the oldest, simplest, and most widely misused multiple paiwise compaison tests. The LSD test declaes the diffeence between means significant when: Y i Y i and Y j > LSD, whee 1 1 LSD = t + α fo unequal, df 1 LSD = tα fo equal, df Y j of teatments T i and T j to be Seed teatment data: = and df = 16. LSD = t α, df = = So, if Y i Y j > 0.143, they ae declaed significantly diffeent. Contol 4.19 HCl 3.87 Popionic 3.73 Butyic

7 Teatment Mean LSD Contol 4.19 a HCl 3.87 b Popionic 3.73 c Butyic 3.64 c All acids educed shoot gowth. The eduction was moe sevee with butyic and popionic acid than with HC1. We do not have evidence to conclude that popionic acid is diffeent in its effect than butyic acid. When teatments ae equally eplicated, only one LSD value is equied to test all possible compaisons. Foage data: = and df =. In cases of unequal eplication, diffeent LSD values must be calculated fo each compaison involving diffeent numbes of eplications. The 5% LSD fo compaing the contol with Feed B: LSD = t α, df 1 Cont 1 + =.074 B = A vs. Contol = A vs. B = A vs. C = B vs. C = C vs. Contol = Teatment Mean LSD Feed B 1.45 a Feed A 1.36 b Feed C 1.33 b Contol 1.0 c At the 5% level, we conclude all feeds cause significantly geate weight gain than the contol. Feed B causes the highest weight gain; Feeds A and C ae equally effective. 7

8 Confidence intevals The (1 α) confidence limits of the quantity (µ A - µ B ) ae given by: (1 α) CI fo (µ A - µ B ) = ( YA Y ) ± LSD B Geneal consideations fo LSD The LSD test is much safe when the means to be compaed ae selected in advance of the expeiment (i.e. befoe looking at the data). The LSD test is the only test fo which CER equals α. This is often egaded as too libeal. It has been suggested that the EEER can be maintained at α by pefoming the oveall ANOVA test at the α level and making futhe compaisons if and only if the F test is significant (Fishe's Potected LSD test). Howeve, it was then demonstated that this assetion is false if thee ae moe than thee means: A peliminay F test contols only the EERC, not the EERP. Bonfeoni to the escue... Again conside the case of 5 teatments and thus 5*4/ = 10 paiwise compaisons (i.e. hypotheses): α = 0.05 α Bon = 0.05/10 = Uppe bound EER = 1 ( ) 10 =

9 Dunnett's Test Paiwise compaison of a contol to all othe teatment means, while holding MEER α. This test uses the t* statistic (Table A-9b), a modified t statistic based on the numbe of compaisons to be made (p = numbe of teatment means, excluding the contol). DLSD = t * 1 α, p, df fo unequal ( 0 i ) * DLSD = t fo equal ( α 0 = i ) p, df, Seed teatment data: = , df = 16, and p = 3. DLSD = t * α, p, df = = (DLSD = > LSD = 0.143) The smallest diffeence between the contol and any acid teatment is: Contol - HC1 = = 0.3 > All othe diffeences, being lage, ae also significant. The 95% simultaneous confidence intevals fo all thee diffeences take the fom: (1 α) CI fo (µ 0 - µ i ) = ( Y0 Yi ) ± DLSD Contol Butyic = 0.3 ± 0.15 Contol HC1 = 0.46 ± 0.15 Contol Popionic = 0.55 ± 0.15 We have 95% confidence that the 3 tue diffeences fall simultaneously within the above anges. 9

10 Animal foage data: = 0.004, df =, and p = 3. When teatments ae not equally eplicated, thee ae diffeent DLSD values fo each of the compaisons. The 5% DSLS to compae the contol with Feed-C: DLSD = t * α, p, df = = Since Y0 YC = 0.15 > , the diffeence is significant. All othe diffeences with the contol, being lage than this, ae also significant. 10

11 Tukey's w pocedue All possible paiwise compaisons, while holding MEER α. Sometimes called the "honestly significant diffeence" (HSD) test, Tukey's contols the MEER when the sample sizes ae equal. Instead of t o t*, it uses the statistic q α, p, df that is obtained fom Table A-8: YMAX YMIN qα, p, df = s The citical diffeence in this method is labeled w: 1 1 w = q + α, p, df fo unequal 1 w = q fo equal α,p,df We do not multiply by a facto of because Table A-8 (class website) aleady includes the facto in its values: Fo p =, df =, and α= 5%, the citical value is.77 = 1.96 * Y Tukey citical values ae lage than those of Dunnett because the Tukey family of contasts is lage (all pais of means). Seed teatment data: = , df = 16, and p = 4. w = q α , p, df = 4.05 = (w = > DLSD = > LSD = 0.143) Teatment Mean w Contol 4.19 a HCl 3.87 b Popionic 3.73 b c Butyic 3.64 c 11

12 Animal foage data: = 0.004, df =, and p = 4. The 5% w fo the contast between the Contol and Feed-C: w = q α ,, 3.93 = p df + = + Cont C 6 7 Since Y Y = 0.15 > , it is significant. As in the LSD, the only paiwise Cont C compaison that is not significant is that between Feed C ( Y C = ) and Feed A ( Y =1.361). A Scheffe's F test Compatible with the oveall ANOVA F test: Scheffe's neve declaes a contast significant if the oveall F test is nonsignificant. Scheffe's test contols the MEER fo ANY set of contasts. This includes all possible paiwise and goup compaisons. Since this pocedue allows a lage numbe of compaisons, it is less sensitive than othe multiple compaison pocedues. Fo paiwise compaisons, the Scheffe citical diffeence (SCD) has a simila stuctue as that descibed fo pevious tests: SCD = 1 1 df F +,, fo unequal Tt α df Tt df 1 SCD = dftt F df Tt df fo equal α,, Seed teatment data: = , df Tt = 3, df = 16: SCD = df 3(3.4) Tt Fα, df Tt, df = = (SCD = > w = > DLSD = > LSD = 0.143) 1

13 The table of means sepaations: Teatment Mean F s Contol 4.19 a HCl 3.87 b Popionic 3.73 b c Butyic 3.64 c Animal foage data: = 0.004, df Tt = 3, df =. The 5% SCD fo the contast between the Contol and Feed-C: SCD = df = (3.05) F,, = Tt α df Tt df Since Y Y = 0.15 > , it is significant. Cont C Scheffe's pocedue is also eadily used fo inteval estimation: (1 α) CI fo (µ 0 - µ i ) = ( Y0 Yi ) ± SCD The esulting intevals ae simultaneous in that the pobability is at least (1 α) that all of them ae tue simultaneously. Scheffe's F test fo goup compaisons The most impotant use of Scheffe's test is fo abitay compaisons among goups of means. To make compaisons among goups of means, you fist define a contast, as in Topic 4: Q = t i= 1 t c i Y i, with the constaint that c i = 0 (o ic i = 0fo unequal ) i= 1 We eject the null hypothesis (H 0 ) that the contast Q = 0 if the absolute value of Q is lage than some citical value F S : t i= 1 13

14 Citical value F S = df Tt F α, df Tt, df t i= 1 c i i (The pevious paiwise expessions ae fo the paticula contast 1 vs. -1.) Example: If we wish to compae the contol to the aveage of the thee acid teatments, the contast coefficients ae (+3, 1, 1, 1). In this case: Q = c i Y i t i= 1 = 4.190(3) ( 1) ( 1) ( 1) = The citical F s value fo this contast is: F S c = dftt F 3 3(3.4) ( 1) + ( 1) 5 + ( 1) t i α, df, df = = Tt i= 1 i Since Q = > = F s, we eject H 0. The aveage of the contol (4.190 mg) is significantly lage than the aveage of the thee acid teatments (3.745 mg). 14

15 Multiple-stage tests (MSTs) / Multiple-ange tests Allow simultaneous hypothesis tests of geate powe by fofeiting the ability to constuct simultaneous confidence intevals. Duncan à Student-Newman-Keuls (SNK) à REGWQ All thee use the Studentized ange statistic (qα), and all thee ae esult-guided. With means aanged in ode, an MST povides citical distances o anges that become smalle as the paiwise means to be compaed become close togethe in the aay. Such a stategy allows the eseache to allocate test sensitivity whee it is most needed, in disciminating neighboing means. The geneal stategy: µ 1 α 4 µ α 4 α 3 α α 1 α α 3 α 3 µ 3 µ 4 µ 5 α 4 α 4 α 1 < α < α 3 < < α t-1 "Confidence" is eplaced by the concept of "potection levels" So if a diffeence is detected at one level of the test, the eseache is justified in sepaating means at a fine esolution with less potection (i.e. with a highe α). 15

16 Duncan's multiple ange test As the test pogesses, Duncan's method uses a vaiable significance level (α p-1 ) depending on the numbe of means involved: α p-1 = 1 - (1 - α) p-1 Despite the level of potection offeed at each stage, MEER is uncontolled. The highe powe of Duncan's method compaed to Tukey's is due to its highe Type I eo ate. Duncan citical anges (R p ): R = q α p p, df p 1, Fo the seed teatment data: p 3 4 α p 1, p, R p q Identical to LSD fo adjacent means (LSD = 0.14). Duncan's used to be the most popula method of means sepaation, but many jounals no longe accept it. It is not ecommended. The Student-Newman-Keuls (SNK) test As the test pogesses, SNK uses a fixed significance level (α), which is always less than o equal to Duncan's vaiable significance level: α SNK = α 1 - (1 - α) p-1 Moe consevative than Duncan's, holding EERC α. Accepted by some jounals that eject Duncan's. Poo behavio in tems of EERP and MEER. Not ecommended. 16

17 Assume the following patial null hypothesis: µ 1 µ µ 3 µ 4 µ 5 µ 6 µ 7 µ 8 µ 9 µ 10 The SNK method educes to five independent tests, one fo each pai, by LSD. The pobability of at least one false ejection is: 1 (1 α) 5 = 0.3 As the numbe of means inceases, MEER à 1. To find the SNK citical ange (W p ) at each level of the analysis: W = q p α, p, df Fo the seed teatment data: p 3 4 q 0.05, p, R p Again, identical to LSD fo adjacent means (LSD = 0.14). The Ryan, Einot, Gabiel, and Welsh (REGWQ) method Not as well known as the othes, REGWQ method appeas to be among the most poweful step-down multiple ange tests and is ecommended by some softwae packages (e.g. SAS) fo equal eplication (i.e. balanced designs). Contols MEER by setting: α p-1 = 1 - (1 - α) p/t fo p < (t 1) and α p-1 = α fo p (t 1) 17

18 Assuming the sample means have been aanged in descending ode fom Y 1 to Y t, the homogeneity of means Y,..., Y, with i < j, is ejected by REGWQ if: i j Y Yj > qα p i 1, p, df Fo the seed teatment data: p 3 4 α p q 0.05, p, R p >SNK =SNK =SNK <Tukey =Tukey Tukey w = The diffeence between the HCl and Popionic teatments is declaed significant with SNK but not with REGWQ ( < 0.145). Teatment Mean REGWQ Contol 4.19 a HCl 3.87 b Popionic 3.73 b c Butyic 3.64 c Some suggested ules of thumb: 1. When in doubt, use Tukey.. Use Dunnett's (moe poweful than Tukey's) if you only wish to compae each teatment level to a contol. 3. Use Scheffe's if you wish to "mine" you data. 18

19 One final point to note is that seveely unbalanced designs can yield vey stange esults: Teatment Data Mean A B C D * NS Data fom ST&D page

The Type I error rate is the fraction of times a Type I error is made. Comparison-wise type I error rate CER. Experiment-wise type I error rate EER

The Type I error rate is the fraction of times a Type I error is made. Comparison-wise type I error rate CER. Experiment-wise type I error rate EER Topic 5. Mean separation: Multiple comparisons [S&T Ch.8 except 8.3] 5. 1. Basic concepts If there are more than treatments the problem is to determine which means are significantly different. This process

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

More information

LATIN SQUARE DESIGN (LS) -With the Latin Square design you are able to control variation in two directions.

LATIN SQUARE DESIGN (LS) -With the Latin Square design you are able to control variation in two directions. Facts about the LS Design LATIN SQUARE DESIGN (LS) -With the Latin Squae design you ae able to contol vaiation in two diections. -Teatments ae aanged in ows and columns -Each ow contains evey teatment.

More information

Semipartial (Part) and Partial Correlation

Semipartial (Part) and Partial Correlation Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

LAL Update. Letter From the President. Dear LAL User:

LAL Update. Letter From the President. Dear LAL User: LAL Update ASSOCIATES OF CAPE COD, INCORPORATED OCTOBER 00 VOLUME 0, NO. Lette Fom the Pesident Dea LAL Use: This Update will claify some of the statistics used with tubidimetic and chomogenic LAL tests.

More information

Financing Terms in the EOQ Model

Financing Terms in the EOQ Model Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad

More information

An Introduction to Omega

An Introduction to Omega An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

More information

Single Particle State A A

Single Particle State A A LECTURE 3 Maxwell Boltzmann, Femi, and Bose Statistics Suppose we have a gas of N identical point paticles in a box of volume V. When we say gas, we mean that the paticles ae not inteacting with one anothe.

More information

VISCOSITY OF BIO-DIESEL FUELS

VISCOSITY OF BIO-DIESEL FUELS VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use

More information

The Binomial Distribution

The Binomial Distribution The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between

More information

UNIVERSITY OF CANTABRIA

UNIVERSITY OF CANTABRIA Failue Assessment Diagam - Cack Diving Foce Diagam COMPATIBILITY UNIVERSITY OF CANTABRIA Novembe 1997 J. Ruiz Ocejo F. Gutiéez-Solana M.A. González-Posada I. Goochategui Depatamento de Ciencia e Ingenieía

More information

Infinite-dimensional Bäcklund transformations between isotropic and anisotropic plasma equilibria.

Infinite-dimensional Bäcklund transformations between isotropic and anisotropic plasma equilibria. Infinite-dimensional äcklund tansfomations between isotopic and anisotopic plasma equilibia. Infinite symmeties of anisotopic plasma equilibia. Alexei F. Cheviakov Queen s Univesity at Kingston, 00. Reseach

More information

Database Management Systems

Database Management Systems Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012

More information

SIMULATION OF GAS TURBINES OPERATING IN OFF-DESIGN CONDITION

SIMULATION OF GAS TURBINES OPERATING IN OFF-DESIGN CONDITION SIMULAION OF GAS URBINES OPERAING IN OFF-DESIGN CONDIION Analdo Walte: awalte@fem.unicamp.b Univesity of Campinas Dept. of Enegy DE/FEM/Unicamp P.O. Box 6122 - ZIP code 13083-970 - Bazil Abstact. In many

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance the availability

More information

Lab #7: Energy Conservation

Lab #7: Energy Conservation Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 1-4 Intoduction: Pehaps one of the most unusual

More information

The transport performance evaluation system building of logistics enterprises

The transport performance evaluation system building of logistics enterprises Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics

More information

Power and Sample Size Calculations for the 2-Sample Z-Statistic

Power and Sample Size Calculations for the 2-Sample Z-Statistic Powe and Sample Size Calculations fo the -Sample Z-Statistic James H. Steige ovembe 4, 004 Topics fo this Module. Reviewing Results fo the -Sample Z (a) Powe and Sample Size in Tems of a oncentality Paamete.

More information

Uncertainty Associated with Microbiological Analysis

Uncertainty Associated with Microbiological Analysis Appendix J STWG Pat 3 Uncetainty 7-8-06 Page 1 of 31 Uncetainty Associated with Micobiological Analysis 1. Intoduction 1.1. Thee ae only two absolute cetainties in life: death and taxes! Whateve task we

More information

Economics 212 Microeconomic Theory I Final Exam. June Faculty of Arts and Sciences Queen s University Answer Key

Economics 212 Microeconomic Theory I Final Exam. June Faculty of Arts and Sciences Queen s University Answer Key Instuctions Economics 1 Micoeconomic Theoy I Final Exam June 008 Faculty of Ats and Sciences ueen s Univesity Anse Key The exam is thee hous in length. The exam consists of to sections: Section A has five

More information

Experiment 6: Centripetal Force

Experiment 6: Centripetal Force Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee

More information

A framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods

A framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com

More information

(3) Bipolar Transistor Current Sources

(3) Bipolar Transistor Current Sources B73 lectonics Analysis & Design (3) Bipola Tansisto Cuent Souces Leaning utcome Able to descibe and: Analyze and design a simple twotansisto BJT cuent-souce cicuit to poduce a given bias cuent. Analyze

More information

On Factoring Arbitrary Integers with Known Bits

On Factoring Arbitrary Integers with Known Bits On Factoing Abitay Integes with Known Bits Mathias Hemann, Alexande May Faculty of Compute Science, TU Damstadt, 689 Damstadt, Gemany hemann@bg.infomatik.tu-damstadt.de, may@infomatik.tu-damstadt.de Abstact:

More information

BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS

BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR John R. Gaham Adapted fom S. Viswanathan FUQUA SCHOOL OF BUSINESS DUKE UNIVERSITY 1 In this lectue we conside the effect of govenment

More information

Determining solar characteristics using planetary data

Determining solar characteristics using planetary data Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation

More information

A study modeling of 15 days cumulative rainfall at Purajaya Region, Bandar Lampung, Indonesia

A study modeling of 15 days cumulative rainfall at Purajaya Region, Bandar Lampung, Indonesia A study modeling of 15 days cumulative ainfall at Puajaya Region, Banda Lampung, Indonesia Ahmad Zakaia* Abstact Aim of this eseach is to study peiodic modeling of 15 days cumulative ainfall time seies.

More information

Chapter 3: Vectors and Coordinate Systems

Chapter 3: Vectors and Coordinate Systems Coodinate Systems Chapte 3: Vectos and Coodinate Systems Used to descibe the position of a point in space Coodinate system consists of a fied efeence point called the oigin specific aes with scales and

More information

The Capital Asset Pricing Model. Chapter 9

The Capital Asset Pricing Model. Chapter 9 The Capital Asset Picing odel Chapte 9 Capital Asset Picing odel CAP centepiece of moden finance gives the elationship that should be obseved between isk and etun of an asset it allows fo the evaluation

More information

Learning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds.

Learning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds. Lectue #0 Chapte Atomic Bonding Leaning Objectives Descibe ionic, covalent, and metallic, hydogen, and van de Waals bonds. Which mateials exhibit each of these bonding types? What is coulombic foce of

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance

More information

The Role of Gravity in Orbital Motion

The Role of Gravity in Orbital Motion ! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

More information

How to create RAID 1 mirroring with a hard disk that already has data or an operating system on it

How to create RAID 1 mirroring with a hard disk that already has data or an operating system on it AnswesThatWok TM How to set up a RAID1 mio with a dive which aleady has Windows installed How to ceate RAID 1 mioing with a had disk that aleady has data o an opeating system on it Date Company PC / Seve

More information

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in

More information

Chapter 6. Gradually-Varied Flow in Open Channels

Chapter 6. Gradually-Varied Flow in Open Channels Chapte 6 Gadually-Vaied Flow in Open Channels 6.. Intoduction A stea non-unifom flow in a pismatic channel with gadual changes in its watesuface elevation is named as gadually-vaied flow (GVF). The backwate

More information

A posteriori multiple comparison tests

A posteriori multiple comparison tests A posteriori multiple comparison tests 09/30/12 1 Recall the Lakes experiment Source of variation SS DF MS F P Lakes 48.933 2 24.467 5.872 0.017 Error 50.000 12 4.167 Total 98.933 14 The ANOVA tells us

More information

The Grating Spectrometer and Atomic Spectra

The Grating Spectrometer and Atomic Spectra PHY 19 Gating Spectomete 1 The Gating Spectomete and Atomic Specta Intoduction In the pevious expeiment diffaction and intefeence wee discussed and at the end a diffaction gating was intoduced. In this

More information

Chapter For the deep-groove 02-series ball bearing with R = 0.90, the design life x D, in multiples of rating life, is ( ) 1.

Chapter For the deep-groove 02-series ball bearing with R = 0.90, the design life x D, in multiples of rating life, is ( ) 1. hapte 11 11-1 Fo the deep-goove 02-seies ball beaing with = 0.90, the design life, in multiples of ating life, is L 0 0( 25000) 350 n = 525 Ans. L = L L = = The design adial load is F = 1..5 = 3.0 kn Eq.

More information

Research on Risk Assessment of the Transformer Based on Life Cycle Cost

Research on Risk Assessment of the Transformer Based on Life Cycle Cost ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,

More information

Theory and practise of the g-index

Theory and practise of the g-index Theoy and pactise of the g-index by L. Egghe (*), Univesiteit Hasselt (UHasselt), Campus Diepenbeek, Agoalaan, B-3590 Diepenbeek, Belgium Univesiteit Antwepen (UA), Campus Die Eiken, Univesiteitsplein,

More information

Introduction to Stock Valuation. Background

Introduction to Stock Valuation. Background Intoduction to Stock Valuation (Text efeence: Chapte 5 (Sections 5.4-5.9)) Topics backgound dividend discount models paamete estimation gowth oppotunities pice-eanings atios some final points AFM 271 -

More information

MATHEMATICAL SIMULATION OF MASS SPECTRUM

MATHEMATICAL SIMULATION OF MASS SPECTRUM MATHEMATICA SIMUATION OF MASS SPECTUM.Beánek, J.Knížek, Z. Pulpán 3, M. Hubálek 4, V. Novák Univesity of South Bohemia, Ceske Budejovice, Chales Univesity, Hadec Kalove, 3 Univesity of Hadec Kalove, Hadec

More information

Controlling the Money Supply: Bond Purchases in the Open Market

Controlling the Money Supply: Bond Purchases in the Open Market Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises

More information

CRRC-1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer

CRRC-1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer CRRC- Method #: Standad Pactice fo Measuing Sola Reflectance of a Flat, Opaque, and Heteogeneous Suface Using a Potable Sola Reflectomete Scope This standad pactice coves a technique fo estimating the

More information

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request. Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to

More information

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates 9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated

More information

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS ON THE R POLICY IN PRODUCTION-INVENTORY SYSTEMS Saifallah Benjaafa and Joon-Seok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poduction-inventoy

More information

1.4 Phase Line and Bifurcation Diag

1.4 Phase Line and Bifurcation Diag Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes

More information

Ilona V. Tregub, ScD., Professor

Ilona V. Tregub, ScD., Professor Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation

More information

Psychology 282 Lecture #2 Outline. Review of Pearson correlation coefficient:

Psychology 282 Lecture #2 Outline. Review of Pearson correlation coefficient: Psychology 282 Lectue #2 Outline Review of Peason coelation coefficient: z z ( n 1) Measue of linea elationship. Magnitude Stength Sign Diection Bounded by +1.0 and -1.0. Independent of scales of measuement.

More information

Th Po er of th Cir l. Lesson3. Unit UNIT 6 GEOMETRIC FORM AND ITS FUNCTION

Th Po er of th Cir l. Lesson3. Unit UNIT 6 GEOMETRIC FORM AND ITS FUNCTION Lesson3 Th Po e of th Ci l Quadilateals and tiangles ae used to make eveyday things wok. Right tiangles ae the basis fo tigonometic atios elating angle measues to atios of lengths of sides. Anothe family

More information

Exponentially Weighted Moving Average Charts for Monitoring the Process Generalized Variance

Exponentially Weighted Moving Average Charts for Monitoring the Process Generalized Variance Geogia Southen Univesity Digital Commons@Geogia Southen Electonic Theses & Dissetations Jack N Aveitt College of Gaduate Studies COGS Summe 014 Exponentially Weighted Moving Aveage Chats fo Monitoing the

More information

Figure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!

Figure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360! 1. What ae angles? Last time, we looked at how the Geeks intepeted measument of lengths. Howeve, as fascinated as they wee with geomety, thee was a shape that was much moe enticing than any othe : the

More information

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years. 9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,

More information

Problem Set # 9 Solutions

Problem Set # 9 Solutions Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new high-speed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection of Electrons by Electric and Magnetic Fields Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An

More information

Efficient Redundancy Techniques for Latency Reduction in Cloud Systems

Efficient Redundancy Techniques for Latency Reduction in Cloud Systems Efficient Redundancy Techniques fo Latency Reduction in Cloud Systems 1 Gaui Joshi, Emina Soljanin, and Gegoy Wonell Abstact In cloud computing systems, assigning a task to multiple seves and waiting fo

More information

Supplementary Material for EpiDiff

Supplementary Material for EpiDiff Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module

More information

Converting knowledge Into Practice

Converting knowledge Into Practice Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading

More information

Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt

Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB-30 AIRCRAFT - PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado

More information

Economics 326: Input Demands. Ethan Kaplan

Economics 326: Input Demands. Ethan Kaplan Economics 326: Input Demands Ethan Kaplan Octobe 24, 202 Outline. Tems 2. Input Demands Tems Labo Poductivity: Output pe unit of labo. Y (K; L) L What is the labo poductivity of the US? Output is ouhgly

More information

Chris J. Skinner The probability of identification: applying ideas from forensic statistics to disclosure risk assessment

Chris J. Skinner The probability of identification: applying ideas from forensic statistics to disclosure risk assessment Chis J. Skinne The pobability of identification: applying ideas fom foensic statistics to disclosue isk assessment Aticle (Accepted vesion) (Refeeed) Oiginal citation: Skinne, Chis J. (2007) The pobability

More information

Nontrivial lower bounds for the least common multiple of some finite sequences of integers

Nontrivial lower bounds for the least common multiple of some finite sequences of integers J. Numbe Theoy, 15 (007), p. 393-411. Nontivial lowe bounds fo the least common multiple of some finite sequences of integes Bai FARHI bai.fahi@gmail.com Abstact We pesent hee a method which allows to

More information

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero. Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the

More information

Butterfly Network Analysis and The Beneˇ s Network

Butterfly Network Analysis and The Beneˇ s Network 6.895 Theoy of Paallel Systems Lectue 17 Buttefly Netwok Analysis and The Beneˇ s Netwok Lectue: Chales Leiseson Lectue Summay 1. Netwok with N Nodes This section poves pat of the lowe bound on expected

More information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 3 Savings, Present Value and Ricardian Equivalence Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,

More information

The Supply of Loanable Funds: A Comment on the Misconception and Its Implications

The Supply of Loanable Funds: A Comment on the Misconception and Its Implications JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently Fields-Hat

More information

Reduced Pattern Training Based on Task Decomposition Using Pattern Distributor

Reduced Pattern Training Based on Task Decomposition Using Pattern Distributor > PNN05-P762 < Reduced Patten Taining Based on Task Decomposition Using Patten Distibuto Sheng-Uei Guan, Chunyu Bao, and TseNgee Neo Abstact Task Decomposition with Patten Distibuto (PD) is a new task

More information

Modeling and Verifying a Price Model for Congestion Control in Computer Networks Using PROMELA/SPIN

Modeling and Verifying a Price Model for Congestion Control in Computer Networks Using PROMELA/SPIN Modeling and Veifying a Pice Model fo Congestion Contol in Compute Netwoks Using PROMELA/SPIN Clement Yuen and Wei Tjioe Depatment of Compute Science Univesity of Toonto 1 King s College Road, Toonto,

More information

Evaluating the impact of Blade Server and Virtualization Software Technologies on the RIT Datacenter

Evaluating the impact of Blade Server and Virtualization Software Technologies on the RIT Datacenter Evaluating the impact of and Vitualization Softwae Technologies on the RIT Datacente Chistophe M Butle Vitual Infastuctue Administato Rocheste Institute of Technology s Datacente Contact: chis.butle@it.edu

More information

Fisher's least significant difference (LSD) 2. If outcome is do not reject H, then! stop. Otherwise continue to #3.

Fisher's least significant difference (LSD) 2. If outcome is do not reject H, then! stop. Otherwise continue to #3. Fisher's least significant difference (LSD) Procedure: 1. Perform overall test of H : vs. H a :. Á. Á â Á. " # >. œ. œ â œ.! " # > 2. If outcome is do not reject H, then! stop. Otherwise continue to #3.

More information

LINES AND TANGENTS IN POLAR COORDINATES

LINES AND TANGENTS IN POLAR COORDINATES LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Pola-coodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and

More information

Promised Lead-Time Contracts Under Asymmetric Information

Promised Lead-Time Contracts Under Asymmetric Information OPERATIONS RESEARCH Vol. 56, No. 4, July August 28, pp. 898 915 issn 3-364X eissn 1526-5463 8 564 898 infoms doi 1.1287/ope.18.514 28 INFORMS Pomised Lead-Time Contacts Unde Asymmetic Infomation Holly

More information

An Immunological Approach to Change Detection: Algorithms, Analysis and Implications

An Immunological Approach to Change Detection: Algorithms, Analysis and Implications An Immunological Appoach to Change Detection: Algoithms, Analysis and Implications Patik D haeselee Dept. of Compute Science Univesity of New Mexico Albuqueque, NM, 87131 patik@cs.unm.edu Stephanie Foest

More information

Hubs, Bridges, and Switches

Hubs, Bridges, and Switches Hubs, Bidges, and Switches Used fo extending LANs in tems of geogaphical coveage, numbe of nodes, administation capabilities, etc. Diffe in egads to: m collision domain isolation m laye at which they opeate

More information

Strength Analysis and Optimization Design about the key parts of the Robot

Strength Analysis and Optimization Design about the key parts of the Robot Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Pint): 2320-9356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.25-29 Stength Analysis and Optimization Design

More information

Lesson C3 2. Exploring Genetics. Performance Standard: 2. Discuss the implications of genetic variation.

Lesson C3 2. Exploring Genetics. Performance Standard: 2. Discuss the implications of genetic variation. Lesson C3 2 Exploing Genetics Unit C. Basic Pinciples of Agicultual/Hoticultual Science Poblem Aea 3. Undestanding Cells, Genetics, and Repoduction Lesson 2. Exploing Genetics New Mexico Content Standad:

More information

Uncertainties in Fault Tree Analysis

Uncertainties in Fault Tree Analysis ncetainties in Fault Tee nalysis Yue-Lung Cheng Depatment of Infomation Management Husan Chuang College 48 Husan-Chuang Rd. HsinChu Taiwan R.O.C bstact Fault tee analysis is one kind of the pobilistic

More information

Left- and Right-Brain Preferences Profile

Left- and Right-Brain Preferences Profile Left- and Right-Bain Pefeences Pofile God gave man a total bain, and He expects us to pesent both sides of ou bains back to Him so that He can use them unde the diection of His Holy Spiit as He so desies

More information

Financial Planning and Risk-return profiles

Financial Planning and Risk-return profiles Financial Planning and Risk-etun pofiles Stefan Gaf, Alexande Kling und Jochen Russ Pepint Seies: 2010-16 Fakultät fü Mathematik und Witschaftswissenschaften UNIERSITÄT ULM Financial Planning and Risk-etun

More information

Firstmark Credit Union Commercial Loan Department

Firstmark Credit Union Commercial Loan Department Fistmak Cedit Union Commecial Loan Depatment Thank you fo consideing Fistmak Cedit Union as a tusted souce to meet the needs of you business. Fistmak Cedit Union offes a wide aay of business loans and

More information

Episode 401: Newton s law of universal gravitation

Episode 401: Newton s law of universal gravitation Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation Newton, who extended the concept of inetia to all bodies, ealized that the moon is acceleating and is theefoe subject to a centipetal foce. He guessed that the foce that keeps the

More information

Tracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors

Tracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors Tacking/Fusion and Deghosting with Dopple Fequency fom Two Passive Acoustic Sensos Rong Yang, Gee Wah Ng DSO National Laboatoies 2 Science Pak Dive Singapoe 11823 Emails: yong@dso.og.sg, ngeewah@dso.og.sg

More information

Universal Cycles. Yu She. Wirral Grammar School for Girls. Department of Mathematical Sciences. University of Liverpool

Universal Cycles. Yu She. Wirral Grammar School for Girls. Department of Mathematical Sciences. University of Liverpool Univesal Cycles 2011 Yu She Wial Gamma School fo Gils Depatment of Mathematical Sciences Univesity of Livepool Supeviso: Pofesso P. J. Giblin Contents 1 Intoduction 2 2 De Buijn sequences and Euleian Gaphs

More information

Carter-Penrose diagrams and black holes

Carter-Penrose diagrams and black holes Cate-Penose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example

More information

CONCEPTUAL FRAMEWORK FOR DEVELOPING AND VERIFICATION OF ATTRIBUTION MODELS. ARITHMETIC ATTRIBUTION MODELS

CONCEPTUAL FRAMEWORK FOR DEVELOPING AND VERIFICATION OF ATTRIBUTION MODELS. ARITHMETIC ATTRIBUTION MODELS CONCEPUAL FAMEOK FO DEVELOPING AND VEIFICAION OF AIBUION MODELS. AIHMEIC AIBUION MODELS Yui K. Shestopaloff, is Diecto of eseach & Deelopment at SegmentSoft Inc. He is a Docto of Sciences and has a Ph.D.

More information

Lesson 2 Power Factor Improvement, Harmonic Reduction, Filter

Lesson 2 Power Factor Improvement, Harmonic Reduction, Filter Lesson 2 Powe Facto Impovement, Hamonic Reduction, Filte 1. Powe Facto Impovement Fo phase-contolled opeation in both single phase full wave half and full contolled bidge convetes, the displacement facto

More information

Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques

Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques Loyalty Rewads and Gift Cad Pogams: Basic Actuaial Estimation Techniques Tim A. Gault, ACAS, MAAA, Len Llaguno, FCAS, MAAA and Matin Ménad, FCAS, MAAA Abstact In this pape we establish an actuaial famewok

More information

Alternative Formulas for Rating Prediction Using Collaborative Filtering

Alternative Formulas for Rating Prediction Using Collaborative Filtering Altenative Fomulas fo Rating Pediction Using Collaboative Filteing Ama Saic, Misad Hadziadic, David Wilson College of Computing and Infomatics The Univesity of Noth Caolina at Chalotte, 901 Univesity City

More information

CHAPTER 17 MAGNETIC DIPOLE MOMENT

CHAPTER 17 MAGNETIC DIPOLE MOMENT 1 CHAPTER 17 MAGNETIC DIPOLE MOMENT 17.1 Intoduction A numbe of diffeent units fo expessing magnetic dipole moment (heeafte simply magnetic moment ) ae commonly seen in the liteatue, including, fo example,

More information

Evidence for the exponential distribution of income in the USA

Evidence for the exponential distribution of income in the USA Eu. Phys. J. B 2, 585 589 (21) THE EUROPEAN PHYSICAL JOURNAL B c EDP Sciences Società Italiana di Fisica Spinge-Velag 21 Evidence fo the exponential distibution of income in the USA A. Dăgulescu and V.M.

More information

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.

More information

Trigonometric Functions of Any Angle

Trigonometric Functions of Any Angle Tigonomet Module T2 Tigonometic Functions of An Angle Copight This publication The Nothen Albeta Institute of Technolog 2002. All Rights Reseved. LAST REVISED Decembe, 2008 Tigonometic Functions of An

More information

International Monetary Economics Note 1

International Monetary Economics Note 1 36-632 Intenational Monetay Economics Note Let me biefly ecap on the dynamics of cuent accounts in small open economies. Conside the poblem of a epesentative consume in a county that is pefectly integated

More information

Coordinate Systems L. M. Kalnins, March 2009

Coordinate Systems L. M. Kalnins, March 2009 Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean

More information

Aus: Statnotes: Topics in Multivariate Analysis, by G. David Garson (Zugriff am

Aus: Statnotes: Topics in Multivariate Analysis, by G. David Garson  (Zugriff am Aus: Statnotes: Topics in Multivariate Analysis, by G. David Garson http://faculty.chass.ncsu.edu/garson/pa765/anova.htm (Zugriff am 20.10.2010) Planned multiple comparison t-tests, also just called "multiple

More information

MERGER SIMULATION AS A SCREENING DEVICE: SIMULATING THE EFFECTS OF THE KRAFT/CADBURY TRANSACTION

MERGER SIMULATION AS A SCREENING DEVICE: SIMULATING THE EFFECTS OF THE KRAFT/CADBURY TRANSACTION MERGER SIMULATION AS A SCREENING DEVICE: SIMULATING THE EFFECTS OF THE KRAFT/CADBURY TRANSACTION Enique Andeu, Kisten Edwads, Aleando Requeo 1,2 Novembe 2010 Abstact In this aticle we pesent a method that

More information