Study design and the statistical basics
Originality Accuracy Objectivity Verifiability Readability perfect Interdisciplinary Sciences Health Science 2014.12.25 2
1. 7 2. 7 3. Bias8 4. random sampling8 5. 9 6. 9 7. 9 8. 10 9. 10 10. 10 11. 11 12. 12 13. 12 14. 13 15. 13 16. normal distribution 13 17. 16 18. 17 19. 19 20. 19 21. Skewness 19 22. Kurtosis 20 23. Excel 20 24. 21 25. 22 26. 22 27. 23 28. 24 29. 4 24 3
30. quartile deviation25 31. 25 32. 26 33. 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 34. 3 (One-way analysis of variance:)38 35. two-way analysis variance 40 36. 1 40 1) 2) 37. 2 41 1) 2) 38. 2 41 1) 2) 39. Post hoc comparison test42 40. repeated measure ANOVA 42 41. 43 42. p 44 43. t p 44 44. 45 45.! 2 : Chi-square 45 4
1) 1 2 46. 2 47 1) 2) 3) Covariance, Cov 4) 47. Correlation coefficient; r 48 1) Pearson r 2) r 3) r 4) r, p 48. Spearman 50 49. 51 1) 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 coefficient52 51. regression analysis53 52. 53 53 55 54. 56 55.multicollinearlity 56 56coefficient of variation, CV57 57.Research 57 58.validityreliability58 59.error 59 1) random error 5
2) systematic error 60bias59 1) selection bias 2) information bias 3) 61 60 1) 2) 62cross-sectional studylongitudinal study60 1) 2) 3) cohort 63Odds Ratio/OR62 64 62 65. 63 66 63 1) 2) 6
1. (population) )(sample) sampling (sample survey) 2. 7
3. Bias selection bias(measurement bias) 4. (random sampling) 8
5. 6. 7. 0.0001mg, 2mg. 0.1kg 9
8. 2 3 2.5 153.0cm 154cm 9..,.. 10., 2, 211/250., 1234 566. 1 611/616.7.. 10
. 11.!118,148,128,141,139,120,125,123,134,144 10 1!. 110180mmHg! 11
1. 2.10 12. 1, 0 13. scale ABO AB0, 1, 2, 3, 4 12
-1012 14. frequency (class). (range),. (frequency distribution),,. 15. 16. (normal distribution) 13
1 68.27%, 22 95.45%, 33 99.73%,., 50. 180, 155, 164, 157, 166, 163, 161, 154, 146, 157 147, 137, 161, 175, 156, 187, 163, 165, 166, 162, 168, 179, 166, 166, 170, 176, 180, 171, 179, 173 187, 168, 160, 165, 180, 158, 159, 169, 163, 141 166, 173, 160, 153, 177, 172, 197, 165, 150, 152 14
. 1). (..) 2). 3). 4)(). 5). cm 130 140 130-139 1 140 150 140-149 3 150 160 150-159 10 160 170 160-169 20 170 180 170-179 10 180 190 180-189 5 190 200 190-200 1.,, = () / 2. 15
, %, % 130 140 130-139 1 2.0 1 2.0 140 150 140-149 3 6.0 4 8.0 150 160 150-159 10 20.0 14 28.0 160 170 160-169 20 40.0 34 68.0 170 180 170-179 10 20.0 44 88.0 180 190 180-189 5 10.0 49 98.0 190 200 190-200 1 2.0 50 100.0 1) 2,. 2),. 17., %.., (%). 150cm 150cm 2.0+6.0=8.0 8% 16
18. (65+53+44+78+50)/5=58 (78-44)=34, 0 65-58=7, 53-58=-5, 44-58=-14, 78-58=20, 50-58=-8, 7+(-5)+(-14)+20+(-8)=0, (7+5+14+20+8)/5=10.8 22 2 2 146.8 ="146.8=12.1. 17
S2 V), s 2 =S/(n-1) s="s/(n-1) 50180,155,,152. =180155152/ 50 = 165.3cm = (( ) 2 )) 1) =((180-165.3) 2 +(155-165.3) 2 ++(152-165.3) 2 )) / 50 1 = 140.8 nn-1 (n-1) (n) 140.8 = 11.9 100 3030170cm100 170cm 100 18
n X = (x 1 + X 2 +X n n # 2 /n 19. 0 1 Z n X = (X 1 + X 2 ++X n) / n # 2 /n n X - µ/ (# - "n ) 0 1 20. 0 21(skewness) 0 0 19
22. (Kurtosis) 510 SKEWKURT 23. Excel 1 fxsum( fx return key 2 20
fx = AVERAGE fx return key 3 fx = STDEVP fx return key 4 fx VAR fx return key 24. 1 1mode 2 1 2median 3)mean 21
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
a b 1/a + 1/b[ 1 /1 / a + 1/b] m = 2ab /(a + b) 80km, 20km 80km a, 20km b. = (80 + 20)/2= 50km. = 2ab / (a + b) = 2 (80 $ 20 ) / (80 + 20 ) = 32km., 20km 50km 32km 27. (outlier) 2#3# 23
28. median) 2 +12 4 + 1 22.5 2.52113 1311 + 13212 12 5 1 2 3 4 1 2 3 4 5 ( 5 + 1) / 2 = 3 313 29. (range) (quartile)1/4 2/423/4 3123 24
(quartile range) 31 30. (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)/212 2 8(1,5, 7,10)( 14, 18, 20, 24)2 (57)/2611820)/219 3 3119%6 13. /213/26.5 31. 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
32. 1)(bar chart) 2)(Line chart) 26
3)pie chartcircle graph 4) (bar graph) 5) (histogram) 27
6) (radar chart) 7)(scatter plot) 2 2,,.,.,,. 28
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
33. (testing statistical hypothesis) 1) 2) A B, A B 5%(p<0.05) 30
3)(null hypothesis) 2 1) (2) #/"n 3 31
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
= & t2 t t (p<0.05) t F 0 = (A) / (B) df =A-1, df = B-1 F 0, A > B. F 0 1.0. 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
A B AB CCA2 7)., 10014 %100 No No 1 5.5 7.7 1 5.5 7.7 2 8.2 9.3 2 8.2 9.3 3 7.3 8.8 3 7.3 8.8 4 9.9 14 4 9.9 14 5 11.5 12.4 5 11.5 12.4 6 8.6 15.6 6 8.6 15.6 7 10.5 11.4 7 10.5 11.4 8 10.1 13.3 8 10.1 13.3 9 12.2 14.4 9 12.2 14.4 10 12.9 16.6 10 12.9 16.6 11 14 17.4 11 14 17.4 12 16.6 17.3 12 16.6 17.3 13 15.7 14.4 13 15.7 14.4 14 14.9 17.7 14 14.9 17.7 34
11.28 13.59 11.28 13.59 10.90 10.93 10.90 10.93 t -1.85 t -1.85 (14+14-2)=26 (14+14-2)=26 26 2.5%(-2.06)2.5%(+2.06) 26 5%-1.71-1.85< -1.71 5% -2.06<-1.85<2.06 5% 2.5% t- t 35
No 1 178.2 170.1 2 180.3 163.5 3 179.2 180.2 4 169.0 160.3 5 177.5 177.2 6 190.3 170.3 7 169.6 162.2 8 185.2 159.3 9 174.2 178.6 10 177.7 172.3 11 193.6 168.2 12 184.2 180.2 12 12 179.9 170.2 51.2 54.5 7.15 7.38 55.8 59.4 7.15 7.71 11 11 t- p t (0,05/2) -3.1355 0.0048 2.0739 p<0.025 1)AVERAGE(B2:B13) 2)VARP(B2:B13) 3)STDEVP(B2:B13) 36
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), 1001. P,. p. TTEST12 1 2 12 122 23 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
., 12, t-. =179.9, SD=7.155=170.2. 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 21.0 23.5 2 22.7 24.2 25.2 3 24.9 26.5 4 25.5 23.6 22.3 5 27.0 28.4 6 27.4 24.5 24.75 24.93 24.63 24.76 38
(two-way ANOVA)b2:2 b A B C 10.6 11.3 11.7 12.7 15 13.8 13.6 14.7 14 15.8 15.4 14.7 D 20 21.5 21.3 22.2 22.8 11.1 13.8 24.7 24.2 25.3 25.3 26.1 t- 1 2 t- 2 1 1 2 2 2 2 t-, (parametric 39
,., one-way ANOVA,, t-. 3,,.,. ANOVA.,, 4Steps Statcel 2. 35. (two-way analysis of variance) 3 3 1 F 36.1 1 2 40
3 372 21 1) 2) 3443 382 2 1) 2) 41
39. Post hoc comparison test 3 2 (A priori comparisons) ANOVA (Post hoc comparisons) ANOVA p 40(repeated measures AN0VA) ANOVA ANOVA ANOVA 42
2 41. 3 1 cm cm cm 12 two-way ANOVA!!cm!!cm!!cm ''cm ''cm ''cm 1 3. 2 33 43
42p p p 5 %5 % 95% p 1%p<0.015% (p<0.05) t p 10 010100% -2+2 0.055% 43. t p t -p- tp t-p- t-p- 10%(p<0.10)5%p<0.05 1%p<0.01 44
44. 1) (parametric) t F 2) (non-parametric) 45. " 2 (Chi-square test " 2 45
1)1 81 325=38 =1881 25 27 38 27 18 27 81 81 81 3 = 27) " 2 2 / } 25-27) 2 /27}+{38-27) 2 /27}+{18-27) 2 /27}=7.630 " 2 7.63! 2 p<0.025=7.38, 5% p<0.05. 2) 2 7 13 20 11 8 19 18 21 39 1821 = / 9.23 10.76 20 8.76 10.23 19 18 21 39 46
= (20$18)/39 = 9.23, = (20$21)/39 = 10.76 = (19$18)/39 = 8.76, = (19$21)/39 = 10.23! 2 2! 2. " 2 2 / } (7-9.23) 2 /9.23+(13-10.76) 2 /10.76+(11-8.76) 2 /8.76+(8-10.23) 2 /10.23 = 2.07! 2 " 2 2.07 p. =-1( -1)=1 5% p=3.841, 1% p=6.635! 2 3.841! 2 <6.635, 5%, 1%.. 46. 2 1) 2 2 2) 2 2 3) (Covariance, Cov) xyn=5 5 (50,50),(50,70),(80,60),(70,90),(90,100) X = (50+50+80+70+90)/5 = 68 Y = (50+70+60+90+100)/5 = 74 47
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 (432+72-168+32+572) = 188, 188. 4),, 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 1 167 48 (167-172) 2 =25 48-56) 2 =64 2 172 54 (172-172) 2 =0 (54-56) 2 =4 3 175 55 (175-172) 2 =9 (55-56) 2 =1 4 177 67 (177-172) 2 =25 (67-56) 2 =121 5 169 56 (169-172) 2 =9 (56-56) 2 =0 860 280 68 190 172 56 Sxx=13.6 Syy=38 Sxx=3.69 Syy=6.16,Sxy 18.4 rxy = Sxy/(SxxSyy) = 0.809 48
r fx = CORREL( 1, 2 2) r r -1 +1 r 1 0 r = 0 r = 0.5 r = 1.0 3) r 0-0.2 0.2 0.4; 0.4 0.7; 0.7 1.0; r, p, probability. 49
,,.., p<0.05, 0.05, 5%.,, 5%., 1.0%p<0.01. 4) 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, 2. 14 73 14, X 32 U/L 62 U/L. X. U/L, Units/Liter, 1 L. 50
. X X 35 47 25 57 20 62 73 38 63 36 38 44 59 40 56 40 14 58 69 32 44 46 28 54 42 50 46 48 X X 49. 1). = x, X = y, = rxi, X = ryi. 2). rxi ryi = di = di 2 4 5 (4+5)/2=4.5. X x y rxi ryi di di 2 35 47 5 8-3 9 20 62 2 14-12 144 63 36 12 2 10 100 59 40 11 4.5 6.5 42.25 14 58 1 13-12 144 44 46 8 7 1 1 42 50 7 10-3 9 25 57 3 12-9 81 73 38 14 3 11 121 38 44 6 6 0 0 51
56 40 10 4.5 5.5 30.25 69 32 13 1 12 144 28 54 4 11-7 49 46 48 9 9 0 0 (di 2 = 874.5 3). Spearman (rs) rs = 1 (6di 2 / n 3 n) = 1 (6874.5 / 2744-14)-0.922 4). Spearman, n=14, p<0.05 rs 0.539, p<0.01 rs 0.661., r >0.661, X. 50. partial correlation coefficient 2, 3. 1 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 = 0.302 a b y rby.a rby. a = (0.302 (0.870*0.706)) / ((1 0.870 2 )*(1 0.706 2 ) = -0.894 52
, -0.894,, 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) 52. 1 1 2 53
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 10 10 4 5 2 5 2 4 8 4 9 6 7 6 5 2 1 1 3 2 4 7 6 7 8 9 11 8 6 4 54
,,,. fx=correl(y, X )r = 0.696 fx=slope(y, X )a = 0.5893 fx=intercept(y, X ) b = 1.9549 fx=rsq(y, X ) R 2 = 0.484 Y = 0.5893x+1.9549. 53. 111 n #11+#22#nn) y xy #n#n F 55
54. j 1, 2,, n y j 2R 2 55(multicollinearlity) 105R = 0.904, R 2 = 0.818 t p- 31.7603 1.9594 16.208 5.56E-30 6.8229 3.4285 1.990 0.049-3.6448 3.4411-1.059 0.292 56
56coefficient of variationcv 12 standard deviation, S sx coefficient of variation relative variationrelative standard deviation 100 CV(s) x fxstdevpaverage CV 57. Research 1 1 57
3 58.(validity)reliability),,,,,.,,., internal validity external validity. 58
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
AB3C C 61. Intervention Study2 Observational Study 1) 2) (1) (2) 62.cross-sectional study) (longitudinal study) 1) 60
2) 3) cohort) 61
63. Odds Ratio / OR Odds RatioP1P 010001P 1PP /1P 500.5501 0.50.5 /10.5= 1 1 800.820 10.80.8 /10.8= 0.8 / 0.2 = 4 44 750.75 2510.75 0.75/1 0.75) = 0.75/0.25 = 3 25 0.25 75 10.25 0.25/(1 0.25)= 0.25/0.75 = 0.33 3 0.33 9.1 9 64. 62
Rushing into print 65. Originality: Accuracy: Objectivity: Verifiability: Readability: Impartiality: 66. 1) 63
2) 64