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Course: STAT 217, Fall 2009School: Washington
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statistical What tests should you include in Should you your portfolio assignment? include SPSS output? Single-sample tests z-test for means No t-test for means* Yes z-test for proportions No t-test for correlations No z-test for correlations No 2 test for a variance No Two-sample tests Independent groups z-test for means No Independent groups t-test for means Yes Correlated groups t-test for means Yes...
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statistical What tests should you include in Should you your portfolio assignment? include SPSS output? Single-sample tests z-test for means No t-test for means* Yes z-test for proportions No t-test for correlations No z-test for correlations No 2 test for a variance No Two-sample tests Independent groups z-test for means No Independent groups t-test for means Yes Correlated groups t-test for means Yes Independent groups z-test for proportions No Multiple groups Omnibus ANOVA Yes Multiple comparison procedures Bonferroni adjustment Partial* Tukey's HSD Yes Scheffe' procedure Partial* Repeated measures ANOVA (RB design)** Yes Completely randomized ANOVA** Yes Chi-Square For Tests*** independence No For goodness of fit No For equality of proportions No
Should you construct a confidence Interval? Yes Yes Yes Yes Yes No Yes Yes Yes No No No No No No No No No No
*Partial SPSS output means that SPSS provides some, but not all, relevant output needed for you to draw a conclusion. **For these tests, you just need to include your homework for Chapter 15. You do...
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Washington - STAT - 217
Psych 218 (W 2001): Portfolio Assignment Q. Why? A. The importance of developing a mastery of the various statistical techniques you've learned in class and of learning the appropriate circumstances in which to apply these techniques cannot be ove
Washington - STAT - 217
Sample Portfolio Entry: One-sample t-test for means This test is used when the standard deviation of the population is not known. The standard error of the t statistic is based on an estimate of the population standard deviation. Example (Equity the
Washington - STAT - 217
Source table for a oneway ANOVA. Group1 5.82 26 0.59 Group2 5.41 19 0.50The formulas for the ANOVA table are in the cells. Group3 5.70 23 0.65 Group4 5.23 16 0.51Mean n SDN number of grps Overall Mean84 4 5.58Computed Anova Summary Table So
Washington - STAT - 217
Psych 218 Third SPSS Tutorial Multiple ComparisonsYou are researching treatments for substance abuse, and your main outcome of interest is the number of days in which participants use substances (per month). You randomly assign 40 participants to 4
Washington - STAT - 217
The formulas for the ANOVA table are in the cells. Enter the appropriate values in the RED cells Mean n SD contrast A c contrast B c contrast C c contrast D c Total number of contrasts Total N number of grps Overall Mean Group1 19.40 10 3.8064 0 Grou
Old Dominion - INTS - 4465
HIV/AIDS and the Natural Environmentby Lori M. HunterThe global HIV/AIDS pandemic poses challenges in multiple arenas, as evidenced by the wide-ranging topics covered at the 2006 HIV/AIDS conference held in Toronto. The Toronto meeting, with over 2
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Animal Science 425 Gamete Physiology and Fertilization Fall, 2007 (www.ansci.cornell.edu/courses/as425) Date August 23 August 30 September 6 September 13 September 20 September 27 October 4 Topic Introduction and course policies Primordial germ cell
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Animal Science 2140 Captive Raptor Management and Propagation Course Policies Summer Session, 2008http:/www.ansci.cornell.edu/courses/as2140/ Instructor: Dr. John E. ParksOffice:201 Morrison Hall Telephone: 607-255-2865 or 607-229-3573 email: Text
Calvin - M - 162
MATH 162: Calculus IIFramework for Mon., Jan. 29 Review of Differentiation and IntegrationDifferentiationDefinition of derivative f (x): f (x + h) - f (x) h0 h lim Differentiation rules: 1. Sum/Difference rule: If f , g are differentiable at x0 ,
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MATH 162: Calculus IIFramework for Tues., Jan. 30 Integration by PartsIntegration by parts formula: u dv = uv - Remarks Counterpart to product rule for differentiation Applicable for definite integrals as well:b b bv duu dv = uva a-av
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MATH 162: Calculus IIFramework for Wed., Jan. 31 Trigonometric IntegralsTypes we handle and relevant trig. identities:integral type sinm x cosn x dx, sinm x cosn x dx, m or n odd m, n eventrig. identity sin2 + cos2 = 11 1 sin2 = 2 [1 - cos(
Calvin - M - 162
MATH 162: Calculus IIFramework for Fri., Feb. 2 Trigonometric SubstitutionsTrigonometric substitution a technique used in integration useful most often when integrands involve (a2 + x2 )m , (a2 - x2 )m or (x2 - a2 )m , where a and m are constants
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MATH 162: Calculus IIFramework for Mon., Feb. 5 Integrals using Partial Fraction ExpansionDefinition: A rational function is a function that is the ratio of polynomials. Examples: 2x 2+6 x x2 - 1 (x2 + 3x + 1)(x - 2)2 1 x+7Definition: A quadrati
Calvin - M - 162
MATH 162: Calculus IIFramework for Wed., Feb. 7 Numerical IntegrationNumerical approximations to definite integrals Riemann (rectangle) sums already give us approximations Main types: left-hand, right-hand and midpoint rules Question: Why rectan
Calvin - M - 162
MATH 162: Calculus IIFramework for Fri., Feb. 9 Improper IntegralsbThus far in MATH 161/162, definite integralsaf (x) dx have: been over regions of integration which were finite in length (i.e., a = - and b = ) involved integrands f which a
Calvin - M - 162
MATH 162: Calculus IIFramework for Tues., Feb. 13 Introduction to SeriesExample: Application of the direct comparison test Suppose g(x) = x-p , with p > 0 (so g has the general shape of the blue curve for x > 0), and f is the step function pictured
Calvin - M - 162
MATH 162: Calculus IIFramework for Thurs., Feb. 15 Geometric Series and Series IntroductionGeometric Series Form of series under this classificationa + ar + ar + + ar + =n=02narn ,a, r nonzero constants Zeno's paradox about cro
Calvin - M - 162
MATH 162: Calculus IIFramework for Fri., Feb. 16 Absolute and Conditional Convergencep-Series Results Revisited Results we have shown: The series whose terms are all positiven-p = 1 + 2-p + 3-p + 4-p + n=1(1)converges for p > 1, and div
Calvin - M - 162
MATH 162: Calculus IIFramework for Mon., Feb. 19 The Ratio TestSeveral Ideas Coming Together Power fns.: ones of form x-p . Identification. The base x varies, while the exponent (-p) remains fixed. These fns. grow without bound as x when p < 0
Calvin - M - 162
MATH 162: Calculus IIFramework for Tues., Feb. 20 Introduction to Power SeriesDefinition: A function of x which takes the series formcn (x - a)n = c0 + c1 (x - a) + c2 (x - a)2 + c3 (x - a)3 + n=0(1)is called a power series about x = a. T
Calvin - M - 162
MATH 162: Calculus IIFramework for Wed., Feb. 21 Differentiation and Integration of Power SeriesWhile power series are allowed to have nonzero numbers as centers, for today's results we will assume all power series we discuss are centered about x =
Calvin - M - 162
MATH 162: Calculus IIFramework for Fri., Feb. 23 Taylor SeriesIn the section on power series, we seemed to be interested in finding power series expressions for various functions f , but able to find such series only when the function f , or some
Calvin - M - 162
MATH 162: Calculus IIFramework for Mon., Feb. 26 Convergence of Taylor SeriesToday's Goal: To determine if a function equals its power series. In a remark from the last class, it was stated that, while a certain function f may allow the constructio
Calvin - M - 162
MATH 162: Calculus IIFramework for Wed., Feb. 28 Limits and ContinuityToday's Goal: To understand the meaning of limits and continuity of functions of 2 and 3 variables.Geometry of the Domain SpaceDefinition: (Distance in R3 ): Suppose that (x1
Calvin - M - 162
MATH 162: Calculus IIFramework for Thurs., Mar. 1 Partial DerivativesToday's Goal: To understand what is meant by a partial derivative. In the framework that introduced multivariate functions, we indicated that one can always turn a function of n v
Calvin - M - 162
MATH 162: Calculus IIFramework for Tues., Mar. 6 DifferentiabilityToday's Goal: To understand the relationship between partial derivatives and continuity.The Mixed Partial DerivativesWe have learned that the partial derivative fx at (x0 , y0 ) m
Calvin - M - 162
MATH 162: Calculus IIFramework for Thurs., Mar. 8 Chain RulesToday's Goal: To extend the chain rule to functions of multiple variables.Chain rule, single (independent) variable caseSetting: y is a function of x, while x is a function of t. More
Calvin - M - 162
MATH 162: Calculus IIFramework for Fri., Mar. 9 VectorsToday's Goal: To understand vectors and be able to manipulate them.Vectors in 2 and 3 DimensionsDefinition: A vector is a directed line segment. If P and Q are points in R2 or R3 , then - t
Calvin - M - 162
MATH 162: Calculus IIFramework for Mon., Mar. 12 Dot Products and ProjectionsToday's Goal: To define the dot product and learn of some of its properties and usesThe Dot ProductDefinition: For vectors u = u1 , u2 , u3 and v = v1 , v2 , v3 , we de
Calvin - M - 162
MATH 162: Calculus IIFramework for Tues., Mar. 13 Cross ProductsToday's Goal: To define the cross product and learn of some of its properties and usesThe Cross ProductDefinition: For nonzero, non-parallel 3D vectors u and v, we define the cross
Calvin - M - 162
MATH 162: Calculus IIFramework for Thurs., Mar. 15 Vector Functions and Differential CalculusToday's Goal: To understand parametrized curves and their derivatives. In yesterday's lab, we called a set of continuous functions over a common interval I
Calvin - M - 162
MATH 162: Calculus IIFramework for Fri., Mar. 16 Vector Functions and Integral CalculusToday's Goal: To understand how to integrate vector functions.Indefinite integralsRecall: For scalar functions f (t), A function F is called an antiderivativ
Calvin - M - 162
MATH 162: Calculus IIFramework for Mon., Mar. 26 Quadric SurfacesToday's Goal: To review how equations in three variables are graphed, and to identify special graphs known as quadric surfaces. What we already know: A 2nd-order polynomial in x and y
Calvin - M - 162
MATH 162: Calculus IIFramework for Tues., Mar. 27 More about Lines and Planes in SpaceToday's Goal: To review how lines and planes in space are represented, and use these notions to derive some useful formulas and algorithms involving points, lines
Calvin - M - 162
MATH 162: Calculus IIFramework for Thurs., Mar. 29Fri. Mar. 30 The Gradient VectorToday's Goal: To learn about the gradient vector of two or three variables. f and its uses, where f is a functionThe Gradient VectorSuppose f is a differentiable f
Calvin - M - 162
MATH 162: Calculus IIFramework for Wed., Apr. 4 Unconstrained Optimization of Functions of 2 VariablesToday's Goal: To be able to locate and classify local extrema for functions of two variables. Definition: Suppose the domain of f (x, y) includes
Calvin - M - 162
MATH 162: Calculus IIFramework for Mon., Apr. 9 Constrained Optimization of Functions of 2 VariablesToday's Goal: To be able to find absolute extrema for functions of two variables on closed and bounded domains. Definition: A function f of two vari
Calvin - M - 162
MATH 162: Calculus IIFramework for Wed., Apr. 11 Double and Iterated Integrals, Rectangular RegionsToday's Goal: To understand the meaning of double integrals over bounded rectangular regions R of the plane, and to be able to evaluate such integral
Calvin - M - 162
MATH 162: Calculus IIFramework for Fri., Apr. 13 Double Integrals, General RegionsToday's Goal: To understand the meaning of double integrals over more general bounded regions R of the plane, and to be able to evaluate such integrals. Important Not
Calvin - M - 162
MATH 162: Calculus IIFramework for Mon., Apr. 16 Applications of Double IntegralsToday's Goal: To use double integrals meaningfully in solving problems. Important Note: In conjunction with this framework, you should look over Section 13.3 of your t
Calvin - M - 162
MATH 162: Calculus IIFramework for Tues., Apr. 17 Triple Integrals, Rectangular CoordinatesToday's Goal: To be able to set up and evaluate triple integrals. Important Note: In conjunction with this framework, you should look over Section 13.5 of yo
Calvin - M - 162
MATH 162: Calculus IIFramework for Thurs., Apr. 19 Polar CoordinatesToday's Goal: To understand the use of polar coordinates for specifying locations on the plane. Important Note: In conjunction with this framework, you should look over Section 9.1
Calvin - M - 162
MATH 162: Calculus IIFramework for Mon., Apr. 23 Double Integrals in Polar CoordinatesToday's Goal: To learn the mechanics of setting up double integrals in polar coordinates, and learn to recognize situations in double integrals that may be easier
Calvin - M - 162
MATH 162: Calculus IIFramework for Thurs., Apr. 26Fri., Apr. 27 Moments, Centers of MassToday's Goal: To learn to apply the skill of setting up and evaluating triple integrals in the context of finding centers of mass. Important Note: In conjunctio
Calvin - M - 162
MATH 162: Calculus IIFramework for Mon., Apr. 30 Integration in Cylindrical CoordinatesToday's Goal: To develop an understanding of cylindrical and spherical coordinates, and to learn to set up and evaluate triple integrals in cylindrical coordinat
Calvin - M - 162
MATH 162: Calculus IIFramework for Tues., May. 1 Integration in Spherical CoordinatesToday's Goal: To learn to set up and evaluate triple integrals in spherical coordinates. Important Note: In conjunction with this framework, you should look over S
Calvin - M - 162
Calvin - M - 162
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