Chapter 2 Organizing and Summarizing Data. Chapter 3 Numerically Summarizing Data. Chapter 4 Describing the Relation between Two Variables

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1 Copyright 013 Peron Eduction, Inc. Tble nd Formul for Sullivn, Sttitic: Informed Deciion Uing Dt 013 Peron Eduction, Inc Chpter Orgnizing nd Summrizing Dt Reltive frequency = frequency um of ll frequencie Cl midpoint: The um of conecutive lower cl limit divided by. Chpter 3 Numericlly Summrizing Dt Popultion Men: m = gx i N Smple Men: x = gx i n Rnge = Lrget Dt Vlue - Smllet Dt Vlue Popultion Stndrd Devition: g(x = i - m) gx (gx i ) i - N = B N R N Smple Stndrd Devition = B g(x i - x) n - 1 (gx gx i ) i - n = R n - 1 Popultion Stndrd Devition: Smple Stndrd Devition: Empiricl Rule: If the hpe of the ditribution i bellhped, then Approximtely 68% of the dt lie within 1 tndrd devition of the men Approximtely 95% of the dt lie within tndrd devition of the men Approximtely 99.7% of the dt lie within 3 tndrd devition of the men Popultion Men from Grouped Dt: m = gx i f i Smple Men from Grouped Dt: x = gx i f i Weighted Men: x w = gw i x i gw i Popultion Stndrd Devition from Grouped Dt: = B g(x i - m) f i = R gx i f i - (gx i f i ) Smple Stndrd Devition from Grouped Dt: (gx g(x i - m) gx i f i ) i f f i - i gf = = i B ( ) - 1 R - 1 Popultion z-core: z = x - m Smple z-core: z = x - x Interqurtile Rnge: IQR = Q 3 - Q 1 Lower nd Upper Fence: Lower fence = Q 1-1.5(IQR) Upper fence = Q (IQR) Five-Number Summry Minimum, Q 1, M, Q 3, Mximum Chpter 4 Decribing the Reltion between Two Vrible x i - x x b y i - y b y Correltion Coefficient: r = n - 1 The eqution of the let-qure regreion line i yn = b 1 x + b 0, where yn i the predicted vlue, b 1 = r # y x i the lope, nd b 0 = y - b 1 x i the intercept. Reidul = oberved y - predicted y = y - yn R = r for the let-qure regreion model yn = b 1 x + b 0 The coefficient of determintion, R, meure the proportion of totl vrition in the repone vrible tht i explined by the let-qure regreion line. Chpter 5 Probbility Empiricl Probbility frequency of E P(E) number of tril of experiment Clicl Probbility number of wy tht E cn occur P(E) = number of poible outcome = N(E) N(S) Addition Rule for Dijoint Event P(E or F ) = P(E) + P(F ) Addition Rule for n Dijoint Event P(E or F or G or g) = P(E) + P(F ) + P(G) + g Generl Addition Rule P(E or F ) = P(E) + P(F ) - P(E nd F )

2 Copyright 013 Peron Eduction, Inc. Tble nd Formul for Sullivn, Sttitic: Informed Deciion Uing Dt 013 Peron Eduction, Inc Complement Rule P(E c ) = 1 - P(E) Multipliction Rule for Independent Event P(E nd F ) = P(E) # P(F ) Multipliction Rule for n Independent Event P(E nd F nd G g ) = P(E) # P(F) # P(G) # g Conditionl Probbility Rule P(F E) = P(E nd F ) P(E) Generl Multipliction Rule = N(E nd F ) N(E) Fctoril n! = n # (n - 1) # (n - ) # g# 3 # # 1 Permuttion of n object tken r t time: n P r = Combintion of n object tken r t time: n! nc r = r!(n - r)! Permuttion with Repetition: n! n 1! # n! # g # n k! n! (n - r)! P(E nd F) = P(E) # P(F E) Chpter 6 Dicrete Probbility Ditribution Men (Expected Vlue) of Dicrete Rndom Vrible m X = gx # P(x) Stndrd Devition of Dicrete Rndom Vrible X = 3g(x - m) # P(x) = 3gx P(x) - m X Binomil Probbility Ditribution Function P(x) = n C x p x (1 - p) n-x Men nd Stndrd Devition of Binomil Rndom Vrible m X = np X = np(1 - p) Poion Probbility Ditribution Function P(x) = (lt)x x! e -lt x = 0, 1,, p Men nd Stndrd Devition of Poion Rndom Vrible m X = lt X = lt Chpter 7 The Norml Ditribution Stndrdizing Norml Rndom Vrible z = x - m Finding the Score: x = m + z Chpter 8 Smpling Ditribution Men nd Stndrd Devition of the Smpling Ditribution of x m x = m nd x = n Men nd Stndrd Devition of the Smpling Ditribution of pn m np = p nd np = B p(1 - p) n Smple Proportion: pn = x n Chpter 9 Etimting the Vlue of Prmeter Confidence Intervl A (1 - ) # 100% confidence intervl bout p i pn(1 - pn) pn { z / #. B n A (1 - ) # 100% confidence intervl bout m i x { t/ # 1n. Note: t / i computed uing n - 1 degree of freedom. A (1 - ) # 100% confidence intervl bout i (n - 1) (n - 1) 6 6. B B x / x 1-/ Smple Size To etimte the popultion proportion with mrgin of error E t (1 - ) # 100% level of confidence: n = pn(1 - pn) z / E b rounded up to the next integer, where pn i prior etimte of the popultion proportion, or n = 0.5 z / E b rounded up to the next integer when no prior etimte of p i vilble. To etimte the popultion men with mrgin of error E t (1 - ) # 100% level of confidence: n = z / # E b rounded up to the next integer.

3 Copyright 013 Peron Eduction, Inc. Tble nd Formul for Sullivn, Sttitic: Informed Deciion Uing Dt 013 Peron Eduction, Inc Chpter 10 Hypothei Tet Regrding Prmeter Tet Sttitic z 0 = pn - p 0 p 0 (1 - p 0 ) C n t 0 = x - m 0 1n (n - x 1) 0 = 0 Chpter 11 Inference on Two Smple Tet Sttitic Compring Two Popultion Proportion (Independent Smple) z 0 = pn 1 - pn - (p 1 - p ) pn(1 - pn) B 1 n n where pn = x 1 + x n 1 + n. Confidence Intervl for the Difference of Two Proportion (Independent Smple) pn 1 (1 - pn 1 ) (pn 1 - pn ) { z / + pn (1 - pn ) C n 1 n Tet Sttitic Compring Two Proportion (Dependent Smple) z 0 = 0 f 1 - f f 1 + f 1 Tet Sttitic for Mtched-Pir Dt t 0 = d - m d d 1n where d i the men nd d i the tndrd devition of the differenced dt. Confidence Intervl for Mtched-Pir Dt d { t / # d 1n Note: t / i found uing n - 1 degree of freedom. Tet Sttitic Compring Two Men (Independent Smpling) t 0 = (x 1 - x ) - (m 1 - m ) 1 + Cn 1 Confidence Intervl for the Difference of Two Men (Independent Smple) 1 (x 1 - x ) { t / + Cn 1 n Note: t / i found uing the mller of n 1-1 or n - 1 degree of freedom. Tet Sttitic for Compring Two Popultion Stndrd Devition F 0 = 1 n Finding Criticl F for the Left Til 1 F 1-,n1-1,n -1 = F,n -1,n 1-1 Chpter 1 Inference on Ctegoricl Dt Expected Count (when teting for goodne of fit) E i = m i = np i for i = 1,, p, k Expected Frequencie (when teting for independence or homogeneity of proportion) (row totl)(column totl) Expected frequency = tble totl Chi-Squre Tet Sttitic x 0 = (oberved - expected) expected i = 1,, p, k = (O i - E i ) E i All E i Ú 1 nd no more thn 0% le thn 5. Chpter 13 Compring Three or More Men Tet Sttitic for One-Wy ANOVA where Men qure due to tretment F = Men qure due to error = MST MSE MST = n 1(x 1 - x) + n (x - x) + g + n k (x k - x) k - 1 MSE = (n 1-1) 1 + (n - 1) + g + (n k - 1) k n - k Tet Sttitic for Tukey Tet fter One-Wy ANOVA q = (x - x 1 ) - (m - m 1 ) = # b B n 1 n x - x 1 # b B n 1 n

4 Copyright 013 Peron Eduction, Inc. Tble nd Formul for Sullivn, Sttitic: Informed Deciion Uing Dt 013 Peron Eduction, Inc Chpter 14 Inference on the Let-Squre Regreion Model nd Multiple Regreion Stndrd Error of the Etimte g(y i - yn i ) e = C n - Stndrd error of b 1 = C g reidul n - b1 = g(x i - x) Tet ttitic for the Slope of the Let-Squre Regreion Line b 1 - b 1 t 0 = = b 1 - b 1 en g(xi - x) b1 Confidence Intervl for the Slope of the Regreion Line b 1 { t / # e g(x i - x) where t / i computed with n - degree of freedom. e Confidence Intervl bout the Men Repone of y, yn yn { t / # 1 (x* - x) e + Cn g(x i - x) where x* i the given vlue of the explntory vrible nd t / i the criticl vlue with n - degree of freedom. Prediction Intervl bout n Individul Repone, yn yn { t / # e C n + (x* - x) g(x i - x) where x* i the given vlue of the explntory vrible nd t / i the criticl vlue with n - degree of freedom. Chpter 15 Nonprmetric Sttitic Tet Sttitic for Run Tet for Rndomne Smll-Smple Ce If n 1 0 nd n 0, the tet ttitic in the run tet for rndomne i r, the number of run. Lrge-Smple Ce If n or n 7 0, the tet ttitic i z 0 = r - m r r where m r = n 1n n + 1 nd r = B n 1 n (n 1 n - n) n (n - 1) Tet Sttitic for One-Smple Sign Tet Smll-Smple Ce (n " 5) Two-Tiled Left-Tiled Right-Tiled H 0 : M = M 0 H 0 : M = M 0 H 0 : M = M 0 H 1 : M M 0 H 1 : M 6 M 0 H 1 : M 7 M 0 The tet ttitic, k, i the mller of the number of minu ign or plu ign. The tet ttitic, k, i the number of plu ign. The tet ttitic, k, i the number of minu ign. Lrge-Smple Ce (n + 5) The tet ttitic, z 0, i (k + 0.5) - n z 0 = 1n where n i the number of minu nd plu ign nd k i obtined decribed in the mll mple ce. Tet Sttitic for the Wilcoxon Mtched-Pir Signed-Rnk Tet Smll-Smple Ce (n " 30) Two-Tiled Left-Tiled Right-Tiled H 0 : M D = 0 H 0 : M D = 0 H 0 : M D = 0 H 1 : M D 0 H 1 : M D 6 0 H 0 : M D 7 0 Tet Sttitic: T i the mller of T + or T - Tet Sttitic: T = T + Tet Sttitic: T = T - Lrge-Smple Ce (n + 30) n(n + 1) T - 4 z 0 = n(n + 1) (n + 1) C 4 where T i the tet ttitic from the mll-mple ce. Tet Sttitic for the Mnn Whitney Tet Smll-Smple Ce (n 1 " 0 nd n " 0) If S i the um of the rnk correponding to the mple from popultion X, then the tet ttitic, T, i given by T = S - n 1(n 1 + 1) Note: The vlue of S i lwy obtined by umming the rnk of the mple dt tht correpond to M X in the hypothei. Lrge-Smple Ce (n 1 + 0) or (n + 0) T - n 1n z 0 = n 1 n (n 1 + n + 1) B 1 Tet Sttitic for Spermn Rnk Correltion Tet 6gd i r = 1 - n(n - 1) where d i = the difference in the rnk of the two obervtion in the i th ordered pir. Tet Sttitic for the Krukl Wlli Tet H = 1 N(N + 1) 1 1 = N(N + 1) J R 1 + R n 1 c R n i - n i (N + 1) i n d + g + R k R - 3(N + 1) n k where R i i the um of the rnk in the ith mple.

5 Copyright 013 Peron Eduction, Inc. Tble nd Formul for Sullivn, Sttitic: Informed Deciion Uing Dt 013 Peron Eduction, Inc TABLE I Rndom Number Column Number Row Number Tble ii Criticl Vlue for Correltion Coefficient n n n n

6 Copyright 013 Peron Eduction, Inc. Tble nd Formul for Sullivn, Sttitic: Informed Deciion Uing Dt 013 Peron Eduction, Inc Are z Tble v TABLE V Stndrd Norml Ditribution z Confidence Intervl Criticl Vlue, z A/ Level of Confidence Criticl Vlue, z A/ 0.90 or 90% or 95% or 98% or 99%.575 Hypothei Teting Criticl Vlue Level of Significnce, A Left-Tiled Right-Tiled Two-Tiled { { {.575

7 Copyright 013 Peron Eduction, Inc. Tble nd Formul for Sullivn, Sttitic: Informed Deciion Uing Dt 013 Peron Eduction, Inc Are in right til t TABLE VI t-ditribution Are in Right Til df z

8 Copyright 013 Peron Eduction, Inc. Tble nd Formul for Sullivn, Sttitic: Informed Deciion Uing Dt 013 Peron Eduction, Inc TABLE VII Degree of Freedom Chi-Squre (X ) Ditribution Are to the Right of Criticl Vlue Right til Left til Are 1 Two til X The re to the right of thi vlue i. X 1 The re to the right of thi vlue i 1. X 1 X The re to the right of thi vlue i. The re to the right of thi vlue i 1.