Treatment Spring Late Summer Fall Mean = 1.33 Mean = 4.88 Mean = 3.
|
|
- Kevin Butler
- 4 years ago
- Views:
Transcription
1 The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only two groups t time. Scientists often find tht they need to compre the mens of three or more groups. The sttisticl hypothesis test used to compre the mens of three or more groups is the nlysis of vrince (ANOVA). ANOVA: n exmple ANOVA clcultions re tedious enough tht they re rrely done by hnd, but there is no better wy to relly understnd this prticulr sttisticl test. As n exmple, consider gin the issue of the role of controlled fire in pririe restortions. One prticulrly contentious issue mong restortion ecologists is the timing of pririe burns. Although nturl fires my primrily hve been sprked by lte-summer lightening strikes, most controlled burns re done during the spring or fll. The timing of burning my strongly influence the outcome of pririe restortions becuse burns done t different times of yer cn fvor drmticlly different plnt species. As scientists, you cn collect dt to help resolve such issues. For exmple, you could collect dt to nswer the following question: How does the timing of controlled burns influence the biomss of desirble pririe plnt species? An exmple of the dt you might collect is in Tble 2, below. Tble 2. Totl biomss (g) of Rudbecki hirt (Blck-eyed Susn) growing in ech of 15, 0.5 m 2 plots. One third of the plots were burned in the spring, lte summer, nd fll of 1998, respectively. All plots were smpled during summer Tretment Spring Lte Summer Fll Men = 1.33 Men = 4.88 Men = 3.52 Before we go ny further, we need to stte null nd lterntive hypotheses. For exmple, the null hypothesis could be H 0 : The timing of controlled burning does not influence biomss of Rudbecki hirt. While the lterntive hypothesis could red s follows: H A : The timing of controlled burns influences the biomss of Rudbecki hirt. ANOVA: clcultions To nlyze these dt using n ANOVA, you first need to clculte the grnd men. The grnd men is simply fncy term for the men of ll of your observtions, regrdless of group. The grnd men cn be clculted using the following formul: 46
2 ! 1 n "" n Where is the number of groups, n is the number of observtions within ech group, nd is single observtion. Applying this formul to our pririe burn dt, where = 3 nd n = 5, gives the following grnd men:! 1 $ 0.10 # 0.61#1.91# 2.99 #1.06 # 5.56 #...# 3.53 # 3.85 # 3.01# 2.13# 2.50 # 6.10%! Once you hve clculted the grnd men, you need to clculte the sum of squres mong groups (SS mong ). The SS mong is n estimte of the vrition mong your groups or, more precisely, n estimte of the devition of the group mens from the grnd men. The SS mong cn be clculted using the following formul: SS mong! n " $ & % 2 Where is the number of groups, n is the number of observtions within ech group, nd is the men of ech group. Applying this formul to our pririe burn dt, where = 3 nd n = 5, gives the following SS mong : SS mong! 5$ 3.52& 3.24% 2 # $ 1.33 & 3.24% 2 # $ 4.88 & 3.24% 2 %! The lst thing you need to clculte is the sum of squres within groups (SS within ). The SS within is n estimte of the vrition mong observtions within groups, or, more precisely, n estimte of the devition of the observtions within ech group from the group men. The SS within cn be clculted using the following formul: SS within! "" n $ &% 2 Where is the number of groups, n is the number of observtions within ech group, is n individul observtion, nd is the men of ech group. Applying this formul to our pririe burn dt, where = 3 nd n = 5, gives the following SS within : SS within! $ 0.10 &1.33% 2 # $ 0.61&1.33% 2 #...# (2.50 & 3.52) 2 # $ 6.10 & 3.52% 2! ANOVA: the F-vlue The test sttistic for n ANOVA is clled n F-vlue. The F-vlue for n AVOVA is clculted using the 47
3 following formul: F! '( SS mong *( )( &1 +( '( SS within *( )( (n &1) +( Where is the number of groups nd n is the number of observtions within ech group. Applying this formul to our pririe burn dt, where = 3 nd n = 5, gives the following F-vlue: F! $ % $ %! If you look t the formul for the F-vlue, you cn see tht it is essentilly the rtio of the vrition mong groups to the vrition within groups. If the vrition mong groups is reltively lrge compred to the vrition within groups, then the F-vlue will be reltively lrge. A reltively lrge F-vlue suggests tht the vrition mong groups is lrgely cused by given vrible or experimentl mnipultion (in our exmple, the timing of burning), rther thn chnce vrition. If the vrition mong groups is similr to the vrition within groups, the F-vlue will be reltively smll. A reltively smll F- vlue suggests tht the difference mong groups is lrgely due to chnce nturl vrition nd mesurement error, rther thn to given vrible or mnipultion. This interprettion of n F-vlue should sound fmilir to you, becuse it is very similr to the interprettion of t-sttistic discussed bove. ANOVA: EXCEL output For dt set of ny size, n ANOVA is extremely tedious to clculte by hnd. As such, you will be using EXCEL to do ANOVAs (see below). The EXCEL ANOVA output for our pririe burn study is inserted below: ANOVA Source of SS Df MS F P-vlue F crit Vrition Between Groups Within Groups Totl By custom, the results of n ANOVA re expressed in the bove formt, which not surprisingly is clled n ANOVA tble. As you cn see, this tble contins the (now fmilir to you) estimtes of the SS mong, SS within, nd F-vlue (the vlues in this tble re not identicl to the vlues clculted erlier in this hndout becuse of rounding error in the hnd clcultions). It lso contins the ssocited P-vlue. To review, P-vlue rnges from 0 to 1, nd is the probbility of clculting given test sttistic ssuming tht the mens of your groups re identicl. The lrger the test sttistic is, the lower the chnce (P) tht tht n observed difference mong groups is due to chnce environmentl vrition, nd the greter the chnce tht difference hs biologicl custion. With smple size of 15 observtions, the probbility tht the differences we see mong spring, lte summer, nd fll burns re due to chnce lone is This vlue is bolded in the EXCEL output. Tht is, the p-vlue equls We cn therefore reject the null hypothesis tht burning seson hs no effect on R. hirt biomss, nd ccept the lterntive 48
4 hypothesis tht it burning seson does ffect R. hirt biomss. If the p-vlue for our F-vlue hd been >0.05, then we would hve ccepted tht null hypothesis. Note tht the ANOVA does not tell you nything bout pirwise differences between groups, only if there re overll differences mong ll groups. There re procedures tht cn be done fter n ANOVA tht test for pirwise differences between groups, but they re beyond the scope of this hndbook. How to do n ANOVA in EXCEL 1. Enter your dt so tht ech group is in seprte column. Lbel your columns ppropritely. For exmple, in our pririe burn exmple, the columns could be lbeled "spring", "lte summer", nd "fll". How to do n ANOVA in Minitb 1. Enter your dt so tht one lbeled column contins the grouping vrible (e.g., for the pririe burn exmple, the entries in this column could be spring, summer, nd fll ) nd second lbeled column contins the dependent vrible. 2. Click on Tools > Dt nlysis > Anov: single fctor. If the Dt nlysis module is not vilble in the Tools menu, click on Add-ins nd instll the Anlysis ToolPk. 2. Select Stt > ANOVA > generl liner model. 3. In the dilog window, plce the dependent vrible in the response box. The dependent vrible is wht you mesure. In this cse biomss is the dependent vrible. Plce the grouping vrible in the model box. The grouping vrible is the sme s the independent vrible or tretment, so in this exmple it would be seson. 3. Input the rnge of your dt by highlighting ll of your dt (including lbels). Click Lbels, then click OK. The ANOVA output should pper on the screen 4. Click OK to view the ANOVA output. 49
5 Exmple problems Crry out ANOVAs for the following dt sets: 1. Three different methods were used to mesure dissolved oxygen (mg/kg) content of lke wter. (Dt from JH Zr's Biosttisticl Anlysis, 4 th ed.) Method Number of eggs lid per femle per dy for femles from ech of three lines of Drosophili melnogster. The RS nd SS lines were selected for resistnce nd susceptibility to DDT. The NS line is the nonselected control. (Dt from RR Sokl nd FJ Rohlf's Biometry, 3 rd ed.) Line RS SS NS Strontium concentrtions (mg/ml) in three different bodies of wter. (Dt from JH Zr's Biosttisticl Anlysis, 4 th ed.) Gryson's Pond Bever Lke Angler's Cove
Lecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
Helicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
Graphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
SPECIAL PRODUCTS AND FACTORIZATION
MODULE - Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come
DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
Experiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
Unit 29: Inference for Two-Way Tables
Unit 29: Inference for Two-Wy Tbles Prerequisites Unit 13, Two-Wy Tbles is prerequisite for this unit. In ddition, students need some bckground in significnce tests, which ws introduced in Unit 25. Additionl
Or more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
Math 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
c. Values in statements are broken down by fiscal years; many projects are
Lecture 18: Finncil Mngement (Continued)/Csh Flow CEE 498 Construction Project Mngement L Schedules A. Schedule.of Contrcts Completed See Attchment # 1 ll. 1. Revenues Erned 2. Cost of Revenues 3. Gross
Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999
Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,
Basic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE. Skandza, Stockholm ABSTRACT
COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE Skndz, Stockholm ABSTRACT Three methods for fitting multiplictive models to observed, cross-clssified
Binary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse- rel number to its binry representtion,. convert binry number to n equivlent bse- number. In everydy
Reasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
Operations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
Section 7-4 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
and thus, they are similar. If k = 3 then the Jordan form of both matrices is
Homework ssignment 11 Section 7. pp. 249-25 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If
Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:
Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you
Distributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
Physics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x
PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
Factoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
Project Recovery. . It Can Be Done
Project Recovery. It Cn Be Done IPM Conference Wshington, D.C. Nov 4-7, 200 Wlt Lipke Oklhom City Air Logistics Center Tinker AFB, OK Overview Mngement Reserve Project Sttus Indictors Performnce Correction
Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
Contextualizing NSSE Effect Sizes: Empirical Analysis and Interpretation of Benchmark Comparisons
Contextulizing NSSE Effect Sizes: Empiricl Anlysis nd Interprettion of Benchmrk Comprisons NSSE stff re frequently sked to help interpret effect sizes. Is.3 smll effect size? Is.5 relly lrge effect size?
Small Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
2013 Flax Weed Control Trial
2013 Flx Weed Control Tril Dr. Hether Drby, UVM Extension Agronomist Susn Monhn, Conner Burke, Eric Cummings, nd Hnnh Hrwood UVM Extension Crops nd Soils Technicins 802-524-6501 Visit us on the web: http://www.uvm.edu/extension/cropsoil
Rotating DC Motors Part II
Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors
Integration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
Small Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
Why is the NSW prison population falling?
NSW Bureu of Crime Sttistics nd Reserch Bureu Brief Issue pper no. 80 September 2012 Why is the NSW prison popultion flling? Jcqueline Fitzgerld & Simon Corben 1 Aim: After stedily incresing for more thn
Integration by Substitution
Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is
Basically, logarithmic transformations ask, a number, to what power equals another number?
Wht i logrithm? To nwer thi, firt try to nwer the following: wht i x in thi eqution? 9 = 3 x wht i x in thi eqution? 8 = 2 x Biclly, logrithmic trnformtion k, number, to wht power equl nother number? In
J4.12 REGIONAL HYDROLOGICAL CYCLE AND WEATHER AND CLIMATE IN THE CONTIGUOUS UNITED STATES
J4.12 REGIONAL HYDROLOGICAL CYCLE AND WEATHER AND CLIMATE IN THE CONTIGUOUS UNITED STATES 1. INTRODUCTION i Hu 1 nd Song Feng Climte nd Bio-Atmospheric Sciences rogrm School of Nturl Resource Sciences
Regular Sets and Expressions
Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite
Small Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
2 DIODE CLIPPING and CLAMPING CIRCUITS
2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of
Small Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
Value Function Approximation using Multiple Aggregation for Multiattribute Resource Management
Journl of Mchine Lerning Reserch 9 (2008) 2079-2 Submitted 8/08; Published 0/08 Vlue Function Approximtion using Multiple Aggregtion for Multittribute Resource Mngement Abrhm George Wrren B. Powell Deprtment
persons withdrawing from addiction is given by summarizing over individuals with different ages and numbers of years of addiction remaining:
COST- BENEFIT ANALYSIS OF NARCOTIC ADDICTION TREATMENT PROGRAMS with Specil Reference to Age Irving Leveson,l New York City Plnning Commission Introduction Efforts to del with consequences of poverty,
Lecture 5. Inner Product
Lecture 5 Inner Product Let us strt with the following problem. Given point P R nd line L R, how cn we find the point on the line closest to P? Answer: Drw line segment from P meeting the line in right
9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes
The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is so-clled becuse when the sclr product of two vectors
The Velocity Factor of an Insulated Two-Wire Transmission Line
The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the
An Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process
An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct
15.6. The mean value and the root-mean-square value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style
The men vlue nd the root-men-squre vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time
How To Find Out How A Worker'S Work Ethic Is Related To The Ability To Get A Job
RtSWD Reserch Notes Reserch Note No. 11 Previously relesed s RtSWD Working Pper No. 15 Popultion Aging nd Trends in the Provision of Continued Eduction Regin T. Riphhn, Prvti Trübswetter 2007 Reserch Notes
How To Network A Smll Business
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine so-clled volumes of
Econ 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
COMPONENTS: COMBINED LOADING
LECTURE COMPONENTS: COMBINED LOADING Third Edition A. J. Clrk School of Engineering Deprtment of Civil nd Environmentl Engineering 24 Chpter 8.4 by Dr. Ibrhim A. Asskkf SPRING 2003 ENES 220 Mechnics of
Warm-up for Differential Calculus
Summer Assignment Wrm-up for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
How To Study The Effects Of Music Composition On Children
C-crcs Cognitive - Counselling Reserch & Conference Services (eissn: 2301-2358) Volume I Effects of Music Composition Intervention on Elementry School Children b M. Hogenes, B. Vn Oers, R. F. W. Diekstr,
Example A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.
5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous rel-vlued
Algebra Review. How well do you remember your algebra?
Algebr Review How well do you remember your lgebr? 1 The Order of Opertions Wht do we men when we write + 4? If we multiply we get 6 nd dding 4 gives 10. But, if we dd + 4 = 7 first, then multiply by then
Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the
STATUS OF LAND-BASED WIND ENERGY DEVELOPMENT IN GERMANY
Yer STATUS OF LAND-BASED WIND ENERGY Deutsche WindGurd GmbH - Oldenburger Strße 65-26316 Vrel - Germny +49 (4451)/9515 - info@windgurd.de - www.windgurd.com Annul Added Cpcity [MW] Cumultive Cpcity [MW]
Estimating Exchange Rate Exposures:
Estimting Exchnge Rte Exposures: Issues in Model Structure * Gordon M. Bodnr ** Pul H. Nitze School of Advnced Interntionl Studies, The Johns Hopkins University 1740 Msschusetts Avenue NW Wshington, DC
MATH 150 HOMEWORK 4 SOLUTIONS
MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive
n Using the formula we get a confidence interval of 80±1.64
9.52 The professor of sttistics oticed tht the rks i his course re orlly distributed. He hs lso oticed tht his orig clss verge is 73% with stdrd devitio of 12% o their fil exs. His fteroo clsses verge
2015 EDITION. AVMA Report on Veterinary Compensation
2015 EDITION AVMA Report on Veterinry Compenstion AVMA Report on Veterinry Compenstion 2015 EDITION Copyright 2015 by the All rights reserved. ISBN-13: 978-1-882691-31-9 AVMA Report on Veterinry Compenstion
Small Businesses Decisions to Offer Health Insurance to Employees
Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employer-sponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults
19. The Fermat-Euler Prime Number Theorem
19. The Fermt-Euler Prime Number Theorem Every prime number of the form 4n 1 cn be written s sum of two squres in only one wy (side from the order of the summnds). This fmous theorem ws discovered bout
PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS
PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,
RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS
RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS Known for over 500 yers is the fct tht the sum of the squres of the legs of right tringle equls the squre of the hypotenuse. Tht is +b c. A simple proof is
NQF Level: 2 US No: 7480
NQF Level: 2 US No: 7480 Assessment Guide Primry Agriculture Rtionl nd irrtionl numers nd numer systems Assessor:.......................................... Workplce / Compny:.................................
The Definite Integral
Chpter 4 The Definite Integrl 4. Determining distnce trveled from velocity Motivting Questions In this section, we strive to understnd the ides generted by the following importnt questions: If we know
Applications to Physics and Engineering
Section 7.5 Applictions to Physics nd Engineering Applictions to Physics nd Engineering Work The term work is used in everydy lnguge to men the totl mount of effort required to perform tsk. In physics
Radius of the Earth - Radii Used in Geodesy James R. Clynch February 2006
dius of the Erth - dii Used in Geodesy Jmes. Clynch Februry 006 I. Erth dii Uses There is only one rdius of sphere. The erth is pproximtely sphere nd therefore, for some cses, this pproximtion is dequte.
QUANTITATIVE METHODS IN PSYCHOLOGY A Power Primer
QUANTITATIE METHODS IN PSYCHOLOGY A Power Primer Jcob Cohen New \brk University One possible reson for the continued neglect of sttisticl power nlysis in reserch in the behviorl sciences is the inccessibility
How To Set Up A Network For Your Business
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
I I I I I I I I I 1 I I I 1 I I. Regional Economic Multipliers. A Consumer s Guide to. Cletus C. Coughlin and Thomas B. Mandelbaum
1 19 1 1 Cletus C. Coughlin nd Thoms B. Mndelbum Cletus C. Coughlin is reserch officer nd Thoms B. Mndelbum is n economist t the Federl Reserve Bnk of St Louis. Thoms A. Pollmnn provided reserch ssistnce.
4.11 Inner Product Spaces
314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces
Prepared for. U.S. Department of the Interior Bureau of Land Management Wyoming State Office, Cheyenne, and Rawlins and Rock Springs Field Offices
MAPPING ACCURACY, ACTIVITY, AND BURROW DENSITY OF WHITE-TAILED PRAIRIE DOG COMPLEXES COMPRISING POTENTIAL HABITAT FOR BLACK-FOOTED FERRETS IN THE CONTINENTAL DIVIDE/WAMSUTTER II PROJECT AREA. Prepred for
Examples - What is Ecology? What is Ecology? Systematics Taxonomy. Microbiology. Ecology and Evolution. Physiology. Developmental Biology.
Wht is Ecology? The study of the interctions between orgnisms nd their environment. Orgnism plnt, niml, microbe Environment biotic Non-living components soil, wter, nutrients Biotic Interctions with other
Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00
COMP20212 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE Digitl Design Techniques Dte: Fridy 16 th My 2008 Time: 14:00 16:00 Plese nswer ny THREE Questions from the FOUR questions provided
The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O
The Interntionl Assocition for the Properties of Wter nd Stem Lucerne, Sitzerlnd August 7 Relese on the Ioniztion Constnt of H O 7 The Interntionl Assocition for the Properties of Wter nd Stem Publiction
274 Chapter 13. Chapter 13
74 hpter 3 hpter 3 3. () ounts will be obtined from the smples so th problem bout compring proportions. (b) h n observtionl study compring rndom smples selected from two independent popultions. 3. () cores
Trade liberalization and per capita income convergence: a difference-in-differences analysis
Journl of Interntionl Economics 55 (2001) 203 228 www.elsevier.nl/ locte/ econbse Trde liberliztion nd per cpit income convergence: difference-in-differences nlysis Mtthew J. Slughter* Drtmouth College
Unit 6: Exponents and Radicals
Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -
Lump-Sum Distributions at Job Change, p. 2
Jnury 2009 Vol. 30, No. 1 Lump-Sum Distributions t Job Chnge, p. 2 E X E C U T I V E S U M M A R Y Lump-Sum Distributions t Job Chnge GROWING NUMBER OF WORKERS FACED WITH ASSET DECISIONS AT JOB CHANGE:
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
Redistributing the Gains from Trade through Non-linear. Lump-sum Transfers
Redistributing the Gins from Trde through Non-liner Lump-sum Trnsfers Ysukzu Ichino Fculty of Economics, Konn University April 21, 214 Abstrct I exmine lump-sum trnsfer rules to redistribute the gins from
Deployment Strategy for Mobile Robots with Energy and Timing Constraints
Proceedings of the 2005 IEEE Interntionl Conference on Robotics nd Automtion Brcelon, Spin, April 2005 Deployment Strtegy for Mobile Robots with Energy nd Timing Constrints Yongguo Mei, Yung-Hsing Lu,
Health insurance marketplace What to expect in 2014
Helth insurnce mrketplce Wht to expect in 2014 33096VAEENBVA 06/13 The bsics of the mrketplce As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum
Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
FAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University
SYSTEM FAULT AND Hrry G. Kwtny Deprtment of Mechnicl Engineering & Mechnics Drexel University OUTLINE SYSTEM RBD Definition RBDs nd Fult Trees System Structure Structure Functions Pths nd Cutsets Reliility
Performance Prediction of Distributed Load Balancing on Multicomputer Systems
Performnce Prediction of Distributed Lod Blncing on Multicomputer Systems Ishfq Ahmd *, Arif Ghfoor+, nd Kishn Mehrotr * * School of Computer nd Informtion Science, Syrcuse University, Syrcuse, NY 13244
Vectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
1.00/1.001 Introduction to Computers and Engineering Problem Solving Fall 2011 - Final Exam
1./1.1 Introduction to Computers nd Engineering Problem Solving Fll 211 - Finl Exm Nme: MIT Emil: TA: Section: You hve 3 hours to complete this exm. In ll questions, you should ssume tht ll necessry pckges
Space Vector Pulse Width Modulation Based Induction Motor with V/F Control
Interntionl Journl of Science nd Reserch (IJSR) Spce Vector Pulse Width Modultion Bsed Induction Motor with V/F Control Vikrmrjn Jmbulingm Electricl nd Electronics Engineering, VIT University, Indi Abstrct:
Uplift Capacity of K-Series Open Web Steel Joist Seats. Florida, Gainesville, FL 32611; email: psgreen@ce.ufl.edu
Uplift Cpcity of K-Series Open Web Steel Joist Sets Perry S. Green, Ph.D, M.ASCE 1 nd Thoms Sputo, Ph.D., P.E., M.ASCE 2 1 Assistnt Professor, Deprtment of Civil nd Costl Engineering, University of Florid,
FUNCTIONS AND EQUATIONS. xεs. The simplest way to represent a set is by listing its members. We use the notation
FUNCTIONS AND EQUATIONS. SETS AND SUBSETS.. Definition of set. A set is ny collection of objects which re clled its elements. If x is n element of the set S, we sy tht x belongs to S nd write If y does
CUBIC-FOOT VOLUME OF A LOG
CUBIC-FOOT VOLUME OF A LOG Wys to clculte cuic foot volume ) xylometer: tu of wter sumerge tree or log in wter nd find volume of wter displced. ) grphic: exmple: log length = 4 feet, ech section feet in
baby on the way, quit today
for mums-to-be bby on the wy, quit tody WHAT YOU NEED TO KNOW bout smoking nd pregnncy uitting smoking is the best thing you cn do for your bby We know tht it cn be difficult to quit smoking. But we lso