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樽艾
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1 ~CABLE 2006 ~

2 < > by /10() 8/11() 1 vs. 2 Z () t 3 Z- t- () 4 () () () 3

3 ~CABLE 2006 ~ ()

4 ( 1)

7 (Statistics) vs. (Biostatistics)

9 (Descriptive Statistics) (Inferential Statistics)

10 ( )

12 (variable) Ex.

13 (nominal variable) (ordinal variable) (discrete variable) (interval variable) (ratio variable) (continuous variable)

14 (ex. ) ( ) (frequency)

15 (ex. ) ( ) ( ) ( ) ( )

16 (ex. )

17 0( 0) (ex. )

18 Ex.

19 vs. (1) (continuous variable) ( ) (ex. n ) (discrete variable) ( ) (ex )

20 vs. (2) ( ) ( )(ex. )

21 ( vs. p.14)

23 vs. (Population) (ex. ) (parameter)(ex. N) (Sample) (statistics)(ex. n)

24 (ex. )

25 0 (random) Ex. ( 0) Ex.

26 ( p.29 ) 0~9 ( ) (ex )

27 ( ) / K(K ) K 1 K R R, R+K, R+2K,, R+(n- 1)K

28 ( ) (ex. )

29 (ex. )

30 (1) ex. ( )

31 (2) (Probability Proportional to size, PPS ) ( ) Ex. 7~12

32 (ex. )

33 Ex.

35 ex. ( ) ( )

36 (ex. AIDS )

37 ( 2) (Descriptive Statistics)

39 Check data, clean data (outlier)

40 ) (ex. 0( 0) (ex. )

41 1

42 2 (Mean) ( ) (Median) ( 2) n X X n i i = = 1 N X N i i = = 1 µ

43 3 (Maximum) (Minimun) (range)= ex. A B A B ( )

44 4 (Variance) ( ) 2 X µ 2 X X 2 S = ( n 1) ( ) (Standard Deviation) σ = N ( ) 2 ( ) ( ) 2 X µ X X 2 2 σ = σ = = S = N ( n 1) 2

45 5 (Coefficient of variancec.v.) % σ S µ X %CV ( ) ex.

46 (frequency) (Mode)

47 x ( )y (histogram ) (stem-and-leaf plot) (box plot) (outlier) (bar chart, bar graph) x x

49 (stem) (leaf)

50 outlier 1.5(IQR) IQR= 1.5(IQR)

53 1 (Normal Distribution) or or (Gausian shape, symmetric) 50%

54 2 mean = median = mode

55 1 (positively skewed) mean > median > mode

56 2 (negatively skewed) mean < median < mode

58 3 (bimodal distribution)

59 ( 3) ()

60 ( ) vs. ( ) ( ) ( )

61 ( ) vs. Z-test t-test Paired t-test ANOVA

62 Z-test vs. t-test Z-test Z X µ Z = 0 t-test σ n t ( 2 2 ) X1 X 2 [( n1 1) s1 + ( n2 1) s2 ] t = s = 1 1 n1 + n2 + n n 1 2 t (n-1) t Z n120 tz 2

63 vs. H o ( ) ( ( ( ( ) ) ) ) H ( ) ( ) ( H o ) ( H o ) ( )

66 p-value vs. -value p : H o : H o 0.05 (5%) p p0.05 H o ( ) % %

67 Z Z= Z= 1.96~ %

69 Paired t-test ( ) A B

70 ( ) ( ) ( ) ( ) Ex.

71 vs % (95% Confidence Interval 95% C.I.) 95% Ex. Ho: % C.I. 0 Ho: 1 2 Ho

73 ANOVA 1 Analysis of Variance N-way ANOVA N (ex. ) One-way ANOVA ( ) vs. ( ) Z-testt-test ANOVA

74 ANOVA 2 H o : H 1 : 2 Assumption ANOVA (F-test)

75 ANOVA 3 (TSS=WSS+BSS) WSS( Within Sum of Square) = n-kk BSS( Between Sum of Square) = k-1 TSS( Total Sum of Square) = n-1 =(n-k)+(k-1)

76 F-test F=MBSS/MWSS ANOVA 4 MBSS=BSS/(k-1) ( Mean Between Sum of Square) MWSS=WSS/(n-k) ( Mean Within Sum of Square) p0.05

77 ANOVA ( ) Scheffe s( )Bonferroni LSD( Least Significant Difference method) ( k 1) F k 1, n k, 1 α Scheffe s: t Bonferroni: LSD: tt * α α = k C 2 α n k,1 2

78 ( 4) ()

79 (binomial variable) (proportional variable) (ex. ) 1(p+q=1=100%) AB

80 ( ) McNemar s test B (cells) 5 ( RC table) Chi- Square test for trend Fisher s Exact test Chi- Square test Proportional Z-test

81 Proportional Z-test 1 p~ p B 17% B p~ p ~ H 0 : p 1 =p 0 p p ~ 0 p p0 Z = = σ ~ p p0 q0 n 50% t pq σ p ~ σ p ~

82 Proportional Z-test 2 ~ p 1, ~ p 2 ( p 1 -p 2 ) B 17%30% B 95% ~ p 1, ~ p 2 (p 1 p 2 ) ( ~ p1 ~ p2 ) µ ( p1 p2 ) H 0 : p 1 =p 2 =p 0 Z = σ ~ ~ ( p p ) 1 2 B 17%30% B

83 Chi-Square test 1 ( ) (association) A B ex.

84 Chi-Square test 2 H 0 : X 1 X 2 2 χ ( O E) = E 2 (Observed O ) (Expected E ) 10 (26.67) 90 (73.33) Total 70 (53.33) 130 (146.67) Total E11 = 100 = E12 = 100 = /

85 Fisher s Exact test OE ( ) OE ( )( ) (146.67) 5 (4.08) Total (53.33) 2 (2.92) Total ( ) ( )!!!!! )! )!( )!( )!( ( )! )!( (!!!!!!! ),,, ( d c b a n d b c a d c b a d b c a n d c d c b a b a C C C P n c a d c c b a a d c b a = = = O c+d d c n=a+b+c+d b+d a+c Total a+b b a X 2 Total X 1

86 McNemar s test bc ad H 0 : p=1/2 E 12 =E 21 =(b+c)/2 X 2 a c X 1 b d Total a+b c+d 2 χ ( ) b + c 2 ( b + c) Total a+c b+d n=a+b+c+d b c 1 = ( b + c) Ex. vs. A B vs. ( 1/2 by chance) = b

87 Chi-Square test for trend Ex. ( ) vs. ( ) ( 2k table)

88 ( 5) ()

89 (pearson correlation) (simple linear regression)

90 (pearson correlation) x 1 x 2 (simple linear regression) x y x y (Scatter plot)

92 yˆ = 1 β + β x y i = β + β x + ε i β 0 β ε 1 i

93 1 () x y ( r ) x -1~1 y 0 r

94 2

95 ~ ~

96 ~CABLE 2006 ~ ()

97 ( 1) ()

98 (multiple linear regression)

99 xy2

100 assumption (y) () (mean=0variance= 2 ) 1 >1

101 y ŷ k ˆ y = β + β x + β x + β x β k x k y y = x k k β + β x + β x + β x β + ε ŷ 100% y

102 (x) x y (dummy variable) (reference group) y k k-1 ( SAS ) xb(cd ) A y (ex. 0 x y )

103 Reference Ex. ( ) 3 X 11 X 12 1(0 ) Contrast (Effect) SAS default X

104 1 ( ) x x 1 y )... 0 ( )... 1 ( ˆ ˆ ) ( y y... ˆ... ˆ... ˆ β β β β β β β β β β β β β β β β β β β β β β β β β β = = = = = k k k k k k k k k k x x x x x x y y x x x x x y x x x x y x x x x y

105 (Full Model) (Model selection) (Backward selection) (Forward selection) (Stepwise selection)

106 (r 2 R 2 ) -1r1 0r 2 1 y % x ( ) x r 2 =

107

108

109 (transformation)

110 ( 2) ()

111 (logistic regression, logit model) (multicategory logistic regression, polytomous logistic regression, polychotomous logit model) (proportional odds logit model)

112 assumption (y) ABP(A)+P(B)=1

113 )... ( exp 1 1 ) logit ( log ) 1 log(... ) log( k x k x x x y y y y k k y y P P odds P P x x x x P P β β β β β β β β β β = = = = = = + = = = = = y

114 (x) x 1 ( ) e 1 (dummy variable) (reference group) y k k-1 xb(cd ) A ( ) e 1 (ex. 0 x y 1 )

115 1 e OR )... 0 ( )... 1 ( ) log ( ) log( 0 1 log 0) log( 1) log( ) ( y y... ) log( β β β β β β β β β β β β β β β β β = = = = = = = = = = = = = = = = = = = = = = = = odds ratio x x x x x x odds ratio odds odds x P P x P P x P P x P P x x x x x P P k k k k x x y y y y y y y y k k y y OR

116

117

118 (Full Model) (Model selection) (Backward selection) (Forward selection) (Stepwise selection)

119 Concordant pairs( ) (%) C ROC curve Hosmer-Lemeshow chi-square test df=2 chi-square distribution (estimated probability) (percentile) 10( ) (discrepancy) Pseudo R 2

120 (y) baseline-category logit model proportional odds model, cumulative logit model

121 baseline-category logit model ( ) ( )x P P P P P P P P x x x x x P P x x x x x P P b a b a y y y y y y y y b b k k y y a a k k y y β β α α β α β β β β β β α β β β β β + = = + = = + = = = = = = = = = = = = = = = log ) log( ) log(... ) log(... ) log( 0,1,2 y y

122

123 proportional odds logit model x x x x x P P x x x x x P P b k k y y a k k y y j j β α β β β β β β α β β β β β π π π π + = = + = = = = > > = > = = = =... ) log(... ) log( 0,1,2 y y log j) P(Y 1 j) P(Y log j) logit P(Y & &

124 P(Y>j) P(Y>1) P(Y>2) P(Y>3)

125

126 ~ ~

127 2002/3

128 (random error)

129 (systemic error)

130

131

132

133 (test-retest reliability) (alternate form reliability)

134 Weakness biologic, psychological and social changes in the respondent or try to be good in the second time Improvement carry out after a long enough period to reduce memory artifacts but promptly enough to reduce the probability of systematic changes. Apply measure instrument at two times for multiple persons compute correlation between the two measures assumes there is no change in the underlying trait between time1 and time2

135 (quantitative data) Pearson Correlation (categorical data) Spearman Rank Correlation (phi coefficient) SPSS Analysis Correlate Bivariate Pearson Spearman

136 (split half reliability) Cronbach s s coefficient alpha (( Kuder-Richardson reliability

137 Weakness They will underestimate reliability if the items within the set are not close replications of each other. Reliability may be overestimated by the internal consistency design if the whole interview is affected by irrelevant global response patterns socially undesirable response biases Improvement The instrument is well design. Apply Includes several items pertaining to a single underlying psychological trait or symptom dimension. The items that relate to the same underlying concept are considered to be replications of each other.

138 SPSS Analysis Scale Reliability Analysis Model : split half Model : alpha Split half Cronbach s

139 Cronbach s α = + α = + cov is the average covariance between items var is the average variance between items r is the average correlation between items ( = Ε ) Ε( ) Ε( ) = =

140 (Intra-rater rater reliability) (Inter-rater rater reliability)

141 Weakness Insofar as respondent s s idiosyncratic response contribute to unreliability, estimates based on a single interview may underestimate the actual. Improvement well training use video tape Supervision in the process of the collecting data Apply are different observers consistent? can establish this outside of your study in a pilot study can look at percent of agreement (especially with category ratings)

142 (quantitative data) Intraclass Correlation Reliability (ICR) (categorical data) Agreement, Kappa, Random Error SPSS Analysis Scale Reliability Analysis Statistics Intraclass Correlation Coefficient (ICC) Analysis Descriptive Statistics Crosstabs Statistics Kappa

143 TYPE of RELIABILITY Intraclass Correlation Reliability (ICR) RATERS FEXED or RANDOM VERSION of INTRACLASS CORRELATION PartA Reliability of single rater Nested n subjects rated by k different raters Random ICR(1,1) = BMS - WMS BMS + (k - 1)WMS Subject by rater crossed design Random ICR(2,1) = TMS - EMS TMS + k 1 EMS + k JMS - EMS n (kappa) Subject by rater crossed design Fixed ICR(3,1) = TMS - EMS TMS + (k - 1)EMS (phi or r) PartB Reliability of the average of k ratings Nested: n subjects rated by k different raters Random ICR(1,k) = BMS - WMS BMS Subject by rater cross design Random ICR(2,k) = TMS - EMS TMS + (JMS - EMS) / n Subject by rater crossed design Fixed ICR(3,k) = TMS - EMS TMS α

144 ICR - F Table Source of Variation Sum of Sq. DF Mean Square F Prob. Between People Within People Between Measures Residual Total ICR(1,1)= %

145 rater1 total rater2 a b a+b c d c+d total a+c b+d n

146 Agreement Agreement =(a+d)/n

147 Kappa = σ = + = ( + )( + ) + ( + )( + ) [ ] = = + + ( )

148 weight kappa Weight kappa A weighted K can be used when some notion of the seriousness of the rater s s disagreements is available and where the disagreements can be weighted accordingly. = Σ Σ

149 generalize kappa Generalize kappa A generalization of k to the case where there are more than two diagnostic (nominal) classes and more than two raters. R raters N subjects C classes = = = = =

150 random error Random error The RE coefficient is recommended in which chance is assumed to operate in a purely random way. = + = + = +

151

152

153 (content validity) (face validity)

154 (1) (content validity matrix) A B C (Principal Component)

155 (2) (2)

156 (external) (criterion) (predictive validity)

157 (predictive validity) (concurrent validity) (postdictive validity) (discriminant validity)

158 (correlation analysis) (sensitivity) (specificity) Receiver Operating Characteristic (ROC)

159 Positive Negative Total Criterion Present Absent a b c a+c d b+d Total a+b C+d N Sensitivity=a/(a+c) Positive predictive value=a/(a+b) Specificity=d/(b+d) Negative predictive value=d/(c+d) Prevalence=(a+c a+c)/n

160 ROC SPSS Analysis Graphs ROC curve Coordinate points of the ROC curve Test variable State variable Value of state variable (positive)

161 ROC analysis Cut off Sensitivity 1 Specificity

162 (construct validity)

163

164 1 (Exploratory factor analysis, EFA)

165 2 (Confirmatory factor analysis, CFA)

166 (internal validity) (external validity)

167

168

169 1 vs Paradigm Kuhn Positivism Interpetive Critical v.s 5. ( ) From Neuman1994

170 2

171 vs. ( ) Z-test t-test Fisher s Exact test ANOVA a ANOVA b c

172

173

174

175

176 < > n [6-18 ] < > n (%)

177 <t-test> 95% t p <ANOVA> 95% F p O A B AB

178 < > n (%) X 2 p O A B AB < > 1.00 (p=) 0.86 (p=) 0.43 (p=) 1.00 (p=) 0.89 (p=) 1.00 (p=)

179 < > (se) p ( O ) A B AB ( ) < > OR 95% C.I. p ( O ) A B AB ( )

180 < > Y=1 / Y=0 Y=2 / Y=0 Y=3 / Y=0 OR 95% C.I. OR 95% C.I. OR 95% C.I. ( O ) A B AB ( ) < > 1(Y=1 & 2 / Y=0) OR 95% C.I. p 2(Y=2 / Y=0 & 1) ( O ) A B AB ( )

181 Factor Analysis FA 1. Exploratory Factor Analysis EFAEFA EFA (1) (2)

182 2. Confirmatory Factor Analysis CFA (1) CFA CFA (2) CFA 3 1 factor loading 1 reference indicator variable 1 0 =

183

184 13.4% 7.0% 9.0% 11.5% 14.0% 9.0% 11.5% 14.0% 14.0% 14.0%

185

186

187

188

189

( ) t ( ) ( ) ( ) ( ) ( ) t-

(Statistics). (Descriptive Statistics). (Inferential Statistics) (Inductive Statistics) ( ) t ( ) ( ) ( ) ( ) ( ) t- ( ) ( ) ( )? ( ) ( )? ( ) )?( t ) ( )? ( ) ( ) ( ) ( ) ( ) ( )? ( ) ( ) ( )? ( )?( t