Microsoft Word - 研究デザインと統計学.doc
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1 Study design and the statistical basics
2 Originality Accuracy Objectivity Verifiability Readability perfect Interdisciplinary Sciences Health Science
3 Bias8 4. random sampling normal distribution Skewness Kurtosis Excel
4 30. quartile deviation testing statistical phypothesis 30 1) 2) 3) 4) 5) t- 6) t- t- 7) 8) p p value; probability value 9) significance level; level of significance; critical p value (One-way analysis of variance:) two-way analysis variance ) 2) ) 2) ) 2) 39. Post hoc comparison test repeated measure ANOVA p t p ! 2 : Chi-square 45 4
5 1) ) 2) 3) Covariance, Cov 4) 47. Correlation coefficient; r 48 1) Pearson r 2) r 3) r 4) r, p 48. Spearman ) 1= x, X 2= y = rxi, X = ryi 2) rxi ryi di 2 = di 2 3) Spearman rs 4) Spearman n=14 p<0.05 p<0.01 rs 50partial correlation coefficient regression analysis multicollinearlity 56 56coefficient of variation, CV57 57.Research validityreliability58 59.error 59 1) random error 5
6 2) systematic error 60bias59 1) selection bias 2) information bias 3) ) 2) 62cross-sectional studylongitudinal study60 1) 2) 3) cohort 63Odds Ratio/OR ) 2) 6
7 1. (population) )(sample) sampling (sample survey) 2. 7
8 3. Bias selection bias(measurement bias) 4. (random sampling) 8
9 mg, 2mg. 0.1kg 9
10 cm 154cm 9..,.. 10., 2, 211/250., /
11 . 11.!118,148,128,141,139,120,125,123,134, ! mmHg! 11
12 , scale ABO AB0, 1, 2, 3, 4 12
13 frequency (class). (range),. (frequency distribution),, (normal distribution) 13
14 %, %, %,., , 155, 164, 157, 166, 163, 161, 154, 146, , 137, 161, 175, 156, 187, 163, 165, 166, 162, 168, 179, 166, 166, 170, 176, 180, 171, 179, , 168, 160, 165, 180, 158, 159, 169, 163, , 173, 160, 153, 177, 172, 197, 165, 150,
15 . 1). (..) 2). 3). 4)(). 5). cm ,, = () / 2. 15
16 , %, % ) 2,. 2),. 17., %.., (%). 150cm 150cm =8.0 8% 16
17 18. ( )/5=58 (78-44)=34, =7, 53-58=-5, 44-58=-14, 78-58=20, 50-58=-8, 7+(-5)+(-14)+20+(-8)=0, ( )/5= ="146.8=
18 S2 V), s 2 =S/(n-1) s="s/(n-1) 50180,155,,152. = / 50 = 165.3cm = (( ) 2 )) 1) =(( ) 2 +( ) 2 ++( ) 2 )) / 50 1 = nn-1 (n-1) (n) = cm cm
19 n X = (x 1 + X 2 +X n n # 2 /n Z n X = (X 1 + X 2 ++X n) / n # 2 /n n X - µ/ (# - "n ) (skewness)
20 22. (Kurtosis) 510 SKEWKURT 23. Excel 1 fxsum( fx return key 2 20
21 fx = AVERAGE fx return key 3 fx = STDEVP fx return key 4 fx VAR fx return key mode 2 1 2median 3)mean 21
22 4). 25. n x 1,x 2 x n n n"x 1!X 2!Xn X 1, X 2 Xn 26 2 a,b,, 22
23 a b 1/a + 1/b[ 1 /1 / a + 1/b] m = 2ab /(a + b) 80km, 20km 80km a, 20km b. = ( )/2= 50km. = 2ab / (a + b) = 2 (80 $ 20 ) / ( ) = 32km., 20km 50km 32km 27. (outlier) 2#3# 23
24 28. median) ( 5 + 1) / 2 = (range) (quartile)1/4 2/423/
25 (quartile range) (quartile deviation) 312 nanb a) 1, 5, 7, 10, 13, 16, 18, 20, 24 n=9 b) 1, 5, 7, 10, 14, 18, 20, 24 n=8 (n=9)13 2 1) 8 (1,5.7,10)(16,18,20,23)2 57 (57)/26 1 (1820)/219 32) 31 19%613 /2 13/26.5 b) (n=8) (1014)/ (1,5, 7,10)( 14, 18, 20, 24)2 (57)/ )/ %6 13. /213/ log(x 1), log(x 2 ),log(x n ) (1 / n )(( log(x 1 )log(x 2 )log(x n )) = (1 / n) log (X 1 X 2 X n ) = log {( X 1 X 2 X n ) 1/n } 25
26 32. 1)(bar chart) 2)(Line chart) 26
27 3)pie chartcircle graph 4) (bar graph) 5) (histogram) 27
28 6) (radar chart) 7)(scatter plot) 2 2,,.,.,,. 28
29 8)box- and-whisker plot 4 1/41 23/4 3 9)( triangular graph)3 100% X, Y, Z x, y, z x+y+z 29
30 33. (testing statistical hypothesis) 1) 2) A B, A B 5%(p<0.05) 30
31 3)(null hypothesis) 2 1) (2) #/"n 3 31
32 1) 2) 3) 4) 20132(systolic blood pressure; SBP) SBPSBP SBPSBPSBP SBP +20, +4, +10, +2, +10, -10, +4, +24, +10, -6, +14, +10, +16 SBP11, SBP2,, SBP.,, SBP,., SBP 5).t 2 1)146 2) t 2 32
33 = & t2 t t (p<0.05) t F 0 = (A) / (B) df =A-1, df = B-1 F 0, A > B. F t t 0 = (A) - (B) / {(A-1)(A) + (B -1)()} {(1 / A )+(1 / B)}Studentt- df = A+B - 2 t 0 =(A) - (B)/ {(A/A)+ (B/B)} Welcht-,, Welch. 6) tt t(paired t-test) tt2 t(student t-test) t 33
34 A B AB CCA2 7)., %100 No No
35 t t ( )=26 ( )= %(-2.06)2.5%(+2.06) 26 5% < % -2.06<-1.85<2.06 5% 2.5% t- t 35
36 No t- p t (0,05/2) p< )AVERAGE(B2:B13) 2)VARP(B2:B13) 3)STDEVP(B2:B13) 36
37 4)VAR(B2:B13) 5)STDEV(B2:B13) 6)- 2 7)t- t t 0 =ABAABB. 8) p (p value; probability value) p,., p0.01 (p=0.01), P,. p. TTEST B2B13C2C13t- p =TTEST(B2:B13,C2:C13,1,1) 9) (significance level; level of significance; critical p-value) :significance,,.., p.,,,., 5% (0.05), 1% (0.01). 37
38 ., 12, t-. =179.9, SD=7.155= SD=7.382, 9.7cm0.0048, p<0.01. t 34. 3one-way analysis of variance: t-2., 32, 2,, 2,,. 3analysis of variance; ANOVA. t-, a 11, a
39 (two-way ANOVA)b2:2 b A B C D t- 1 2 t t-, (parametric 39
40 ,., one-way ANOVA,, t-. 3,,.,. ANOVA.,, 4Steps Statcel (two-way analysis of variance) F
41 ) 2) ) 2) 41
42 39. Post hoc comparison test 3 2 (A priori comparisons) ANOVA (Post hoc comparisons) ANOVA p 40(repeated measures AN0VA) ANOVA ANOVA ANOVA 42
43 cm cm cm 12 two-way ANOVA!!cm!!cm!!cm ''cm ''cm ''cm
44 42p p p 5 %5 % 95% p 1%p<0.015% (p<0.05) t p % % 43. t p t -p- tp t-p- t-p- 10%(p<0.10)5%p<0.05 1%p<
45 44. 1) (parametric) t F 2) (non-parametric) 45. " 2 (Chi-square test " 2 45
46 1) =38 = = 27) " 2 2 / } 25-27) 2 /27}+{38-27) 2 /27}+{18-27) 2 /27}=7.630 " ! 2 p<0.025=7.38, 5% p< ) = /
47 = (20$18)/39 = 9.23, = (20$21)/39 = = (19$18)/39 = 8.76, = (19$21)/39 = 10.23! 2 2! 2. " 2 2 / } (7-9.23) 2 /9.23+( ) 2 /10.76+( ) 2 /8.76+( ) 2 /10.23 = 2.07! 2 " p. =-1( -1)=1 5% p=3.841, 1% p=6.635! ! 2 <6.635, 5%, 1% ) 2 2 2) 2 2 3) (Covariance, Cov) xyn=5 5 (50,50),(50,70),(80,60),(70,90),(90,100) X = ( )/5 = 68 Y = ( )/5 = 74 47
48 Cov (X,Y) = n/1(( x - X )( y - Y ) 5 x - X y - Y (50-68)(50-74)=432, (50-68)(70-74)=72, (80-68)(60-74)=-168, (70-68)(90-74)=32, (90-68)(100-74)=572 Cov(X,Y) = 1/5 ( ) = 188, ),, X Y 0, X Y %, X Y, fx = COVAR( 1, 2). 47(Correlation coefficient; r) 1)Pearson (r) r = X Y / X Y n, x, Y x -X 2 y Y ( ) 2 = ) 2 = ( ) 2 =0 (54-56) 2 = ( ) 2 =9 (55-56) 2 = ( ) 2 =25 (67-56) 2 = ( ) 2 =9 (56-56) 2 = Sxx=13.6 Syy=38 Sxx=3.69 Syy=6.16,Sxy 18.4 rxy = Sxy/(SxxSyy) =
49 r fx = CORREL( 1, 2 2) r r r 1 0 r = 0 r = 0.5 r = 1.0 3) r ; ; ; r, p, probability. 49
50 ,,.., p<0.05, 0.05, 5%.,, 5%., 1.0%p< ) r, p CORREL r, x A1 A10 y B1 B10. fx =CORREL(A1:A10,B1:B10) r. r t t = r(n-2) 0.5 / (1-r 2 ) 0.5 n, TDIST p fx = TDIST(t, n-2, 2) 2,. t, t 48. Spearman, 2. Pearson Spearman. Spearman, (, ).,, 2, 2, , X 32 U/L 62 U/L. X. U/L, Units/Liter, 1 L. 50
51 . X X X X 49. 1). = x, X = y, = rxi, X = ryi. 2). rxi ryi = di = di (4+5)/2=4.5. X x y rxi ryi di di
52 (di 2 = ). Spearman (rs) rs = 1 (6di 2 / n 3 n) = 1 ( / ) ). Spearman, n=14, p<0.05 rs 0.539, p<0.01 rs , r >0.661, X. 50. partial correlation coefficient 2, , x,y,zxyrxy, xzrxzyz ryzzrxyz -1r11 rxyz = (rxy ( rxzryz)) / ((1 rxy 2 ) (1 ryz 2 )), 50m,., 50m., 50m. a, b, 50m y, a b 50m y. a b rab = 0.706, a y ray = 0.870, b y rby = a b y rby.a rby. a = (0.302 (0.870*0.706)) / (( )*( ) =
53 , ,, 50m, 50m. 51) (regression analysis) 2 2 x y y = a + bx a b (Y=aX+b) 2 dependent variable independent variable 1 2 (multiple regression analysis)1 (simple linear regression analysis)
54 Y = ax + b., a (slope), b Y (intercept)., ; least squares method. 1 4 [a, b, c, d] 2 aby = ax + b) Y = ax + b. x y
55 ,,,. fx=correl(y, X )r = fx=slope(y, X )a = fx=intercept(y, X ) b = fx=rsq(y, X ) R 2 = Y = x n #11+#22#nn) y xy #n#n F 55
56 54. j 1, 2,, n y j 2R 2 55(multicollinearlity) 105R = 0.904, R 2 = t p E
57 56coefficient of variationcv 12 standard deviation, S sx coefficient of variation relative variationrelative standard deviation 100 CV(s) x fxstdevpaverage CV 57. Research
58 3 58.(validity)reliability),,,,,.,,., internal validity external validity. 58
59 59.error 1) (random error) 2)systematic error bias 60. bias 2 1)selection bias 2)information bias 3) confounding factor confounding factorconfounder. AB 59
60 AB3C C 61. Intervention Study2 Observational Study 1) 2) (1) (2) 62.cross-sectional study) (longitudinal study) 1) 60
61 2) 3) cohort) 61
62 63. Odds Ratio / OR Odds RatioP1P P 1PP /1P /10.5= /10.8= 0.8 / 0.2 = /1 0.75) = 0.75/0.25 = /(1 0.25)= 0.25/0.75 =
63 Rushing into print 65. Originality: Accuracy: Objectivity: Verifiability: Readability: Impartiality: 66. 1) 63
64 2) 64
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