Applied Statistics Using SPSS, STATISTICA, MATLAB and R

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5.2 Contingency Tables 197 first categorise the SCORE variable into four categories. These can be classified as: “Poor” corresponding to a final examination score below 10; “Fair” corresponding to a score between 10 and 13; “Good” corresponding to a score between 14 and 16; “Very Good” corresponding to a score above 16. Let us call PERF (performance) this new categorised variable. The 3×4 contingency table, using variables PROG and PERF, is shown in Table 5.13. Only two (16.7%) cells have expected counts below 5; therefore, the recommended conditions, mentioned in the previous section, for using the asymptotic distribution of T, are met. The value of T is 43.044. The asymptotic chi-square distribution of T has (3 – 1)(4 – 1) = 6 degrees of freedom. At a 5% level, the critical region is above 12.59 and therefore the null hypothesis is rejected at that level. As a matter of fact, the observed significance of T is p ≈ 0. Table 5.13. The 3×4 contingency table obtained with SPSS for the independence test of Example 5.12. PERF Total Poor Fair Good Very Good PROG 0 Count 76 78 16 7 177 Expected Count 63.4 73.8 21.6 18.3 177.0 1 Count 19 29 10 13 71 Expected Count 25.4 29.6 8.6 7.3 71.0 2 Count 2 6 7 8 23 Expected Count 8.2 9.6 2.8 2.4 23.0 Total Count 97 113 33 28 271 Expected Count 97.0 113.0 33.0 28.0 271.0 The chi-square test of independence can also be applied to assess whether two or more groups of data are independent or can be considered as sampled from the same population. For instance, the results obtained for Example 5.7 can also be interpreted as supporting, at a 5% level, that the male and female groups are not independent for variable Q7; they can be considered samples from the same population. 5.2.4 Measures of Association Revisited When analysing contingency tables, it is also convenient to assess the degree of association between the variables, using the ordinal and nominal association measures described in sections 2.3.5 and 2.3.6, respectively. As in 4.4.1, the
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Applied Statistics Using SPSS, STAT
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E d itors Prof. Dr. Joaquim P. Marq
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Contents Preface to the Second Edit
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Contents ix 5.2.3 The Chi-Square Te
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Contents xi Appendix A - Short Surv
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Contents xiii E.26 Soil Pollution .
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Preface to the First Edition This b
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Symbols and Abbreviations Sample Se
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|A| determinant of matrix A tr(A) t
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Σ covariance matrix x arithmetic m
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1 Introduction 1.1 Deterministic Da
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18 h 16 14 12 10 8 6 4 2 0 1.1 Dete
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1.2 Population, Sample and Statisti
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Table 1.3 1.2 Population, Sample an
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Table 1.4 1.3 Random Variables 9 Da
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1.4 Probabilities and Distributions
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1.5 Beyond a Reasonable Doubt... 13
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1.5 Beyond a Reasonable Doubt... 15
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1.6 Statistical Significance and Ot
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1.8 Software Tools 19 book we will
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1.8 Software Tools 21 In the follow
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1.8 Software Tools 23 illustrates t
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1.8 Software Tools 25 On-line help
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1.8 Software Tools 27 Figure 1.12.
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2 Presenting and Summarising the Da
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2.1 Preliminaries 31 The data can t
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» meteo=[ 181 143 36 39 37 % Pasti
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2.1 Preliminaries 35 are interested
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2.1 Preliminaries 37 Besides the in
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2.2 Presenting the Data 39 Sorting
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2.2 Presenting the Data 41 In Table
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2.2 Presenting the Data 43 With SPS
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2.2 Presenting the Data 45 Figure 2
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2.2 Presenting the Data 47 Figure 2
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2.2 Presenting the Data 49 Let X de
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2.2 Presenting the Data 51 Commands
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2.2 Presenting the Data 53 A: The c
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2.2 Presenting the Data 55 The s, c
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2.2 Presenting the Data 57 histogra
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2.3 Summarising the Data 59 type da
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2.3 Summarising the Data 61 delimit
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2.3 Summarising the Data 63 The sam
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Note that: 2.3 Summarising the Data
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where sXY, the sample covariance of
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2.3 Summarising the Data 69 STATIST
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2.3 Summarising the Data 71 A: The
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2.3.6 Measures of Association for N
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2.3 Summarising the Data 75 with th
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Exercises 77 A: We use the N, S and
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Exercises 79 2.13 Determine the box
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3 Estimating Data Parameters Making
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3.1 Point Estimation and Interval E
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3.2 Estimating a Mean 85 In Chapter
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3.2 Estimating a Mean 87 There are
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3.2 Estimating a Mean 89 A: Using M
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3.2 Estimating a Mean 91 Figure 3.5
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3.3 Estimating a Proportion 93 esti
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3.4 Estimating a Variance 95 is to
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3.5 Estimating a Variance Ratio 97
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3.6 Bootstrap Estimation 99 i. F df
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3.6 Bootstrap Estimation 101 about
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3.6 Bootstrap Estimation 103 The bi
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3.6 Bootstrap Estimation 105 In the
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Exercises 107 In order to obtain bo
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Exercises 109 3.14 Consider the CTG
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112 4 Parametric Tests of Hypothese
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Page 378: 5 Non-Parametric Tests of Hypothese
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Page 390: s = npq = 224× 0. 75× 0. 25 = 6.4
Page 394: 5.1.3 The Chi-Square Goodness of Fi
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Page 426: 5.2 Contingency Tables 195 male and
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222 5 Non-Parametric Tests of Hypot
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224 6 Statistical Classification (c
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226 6 Statistical Classification Eq
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228 6 Statistical Classification
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230 6 Statistical Classification li
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232 6 Statistical Classification It
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234 6 Statistical Classification ve
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236 6 Statistical Classification Fi
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238 6 Statistical Classification ω
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240 6 Statistical Classification ω
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242 6 Statistical Classification th
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244 6 Statistical Classification Fi
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246 6 Statistical Classification Bo
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248 6 Statistical Classification We
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250 6 Statistical Classification Th
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252 6 Statistical Classification si
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254 6 Statistical Classification In
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256 6 Statistical Classification St
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258 6 Statistical Classification St
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260 6 Statistical Classification At
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262 6 Statistical Classification pe
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264 6 Statistical Classification i(
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266 6 Statistical Classification ap
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268 6 Statistical Classification Co
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270 6 Statistical Classification 6.
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272 7 Data Regression Correlation d
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274 7 Data Regression These propert
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276 7 Data Regression The total var
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278 7 Data Regression Next, we crea
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280 7 Data Regression b 1 = ∑ ( x
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282 7 Data Regression Example 7.5 Q
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284 7 Data Regression The sampling
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286 7 Data Regression From the defi
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288 7 Data Regression * SSLF SSPE M
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290 7 Data Regression where: - y is
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292 7 Data Regression 1.0000 0.9692
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294 7 Data Regression The first lin
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296 7 Data Regression 7.2.5 ANOVA a
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298 7 Data Regression must ask whic
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300 7 Data Regression model. Simila
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302 7 Data Regression The MATLAB po
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304 7 Data Regression the same way
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306 7 Data Regression 7.3.2 Evaluat
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308 7 Data Regression The MATLAB re
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310 7 Data Regression with s 2 =
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312 7 Data Regression the threshold
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314 7 Data Regression 7.11, the lar
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316 7 Data Regression determination
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318 7 Data Regression smaller discr
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320 7 Data Regression Besides its u
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322 7 Data Regression VIF and Mean
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324 7 Data Regression Taking the na
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326 7 Data Regression Example 7.22
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328 7 Data Regression possible to p
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330 8 Data Structure Analysis In Fi
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332 8 Data Structure Analysis of th
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334 8 Data Structure Analysis 2 −
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336 8 Data Structure Analysis using
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338 8 Data Structure Analysis ∑
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340 8 Data Structure Analysis We se
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342 8 Data Structure Analysis p = 0
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344 8 Data Structure Analysis In or
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346 8 Data Structure Analysis A: On
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348 8 Data Structure Analysis ⎡0.
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350 8 Data Structure Analysis 1 0 -
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352 8 Data Structure Analysis 8.9 C
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354 9 Survival Analysis P( t ≤ T
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356 9 Survival Analysis Example 9.2
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358 9 Survival Analysis the Fatigue
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360 9 Survival Analysis “death”
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362 9 Survival Analysis A: The Hear
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364 9 Survival Analysis From Figure
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366 9 Survival Analysis denominator
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368 9 Survival Analysis The exponen
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370 9 Survival Analysis γ This is
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372 9 Survival Analysis the proport
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374 9 Survival Analysis 9.5 Compute
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376 10 Directional Data Example 10.
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380 10 Directional Data The MATLAB
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382 10 Directional Data A: We use t
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384 10 Directional Data For p = 2,
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386 10 Directional Data Thus, the r
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388 10 Directional Data from a unif
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390 10 Directional Data * 2 z = ( 1
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392 10 Directional Data 10.4.3 The
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396 10 Directional Data 10.5.2 Mean
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398 10 Directional Data Similar res
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400 10 Directional Data Exercises 1
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Appendix A - Short Survey on Probab
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A.1 Basic Notions 405 corresponding
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A.2 Conditional Probability and Ind
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A. 4 Bayes ’ Theorem 409 The firs
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A.5 Random Variables and Distributi
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a 0.5 0.4 0.3 0.2 0.1 0 f (x ) a a+
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Example A. 12 A.6 Expectation, Vari
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n [ X ] = ∑ i= 1 A.6 Expectation,
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A.7 The Binomial and Normal Distrib
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A.7 The Binomial and Normal Distrib
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The following results are worth men
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A.8.2 Moments A.8 Multivariate Dist
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For the d-variate case, this genera
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0.25 0.2 0.15 0.1 0.05 p(x) A.8 Mul
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432 Appendix B - Distributions A: T
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436 Appendix B - Distributions For
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440 Appendix B - Distributions Dist
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442 Appendix B - Distributions 0.45
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444 Appendix B - Distributions B.2.
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448 Appendix B - Distributions B.2.
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450 Appendix B - Distributions Dist
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452 Appendix B - Distributions 1 0.
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456 Appendix C - Point Estimation T
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458 Appendix C - Point Estimation
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460 Appendix D - Tables p n k 0.05
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466 Appendix D - Tables D.3 Student
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468 Appendix D - Tables D.5 Critica
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470 Appendix E - Datasets The varia
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472 Appendix E - Datasets E.6 CTG T
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474 Appendix E - Datasets E.9 FHR T
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476 Appendix E - Datasets E.14 Fore
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478 Appendix E - Datasets DATE_REOP
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480 Appendix E - Datasets CG: Conic
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482 Appendix E - Datasets E.26 Soil
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484 Appendix E - Datasets E.29 VCG
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Appendix F - Tools F.1 MATLAB Funct
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Appendix F - Tools 489 r
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References Chapters 1 and 2 Anderso
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References 493 Gardner MJ, Altman D
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References 495 Raudys S, Pikelis V
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References 497 Mardia KV, Jupp PE (
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500 Index 5.9 (two paired samples t
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502 Index H hazard function, 353 ha
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504 Index S sample, 5 mean, 416 siz
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Applied Statistics Using SPSS, STATISTICA, MATLAB and R

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