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biostatistics
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MGH 2
1
(evidence-based medicine)
P)p(
Citations
MGH 3
Citation
CITATIONS: are footnotes to reference published with a scholarly journal article .
1962ISIInstitute for Scientific InformationScience Citation index (SCI)
Cited reference
Citation Medline) (
SCIMedlineInspec
MGH 4
Impact factor Citation index
Impact factor Citations (impact factor)
(The New England journal of medicine)34.833
(Saudi medical journal)0.306 (American Journal of Preventive Medicine ) 3.256 (respiratory research)4.03
Citations Impact factor
MGH 5
60
(HCR)
5000500
500
MGH 6
MGH 7
MGH 8
Snow
Statistical Analysis
Excel
MGH 9
Data
- CasesObservationsRecords
-
VariablesFields
Values variables
cases
GIS
MGH 10
dependentoutcome independentexposure
MGH 11
Measurement scales
Categorical Nominal
A, B, AB, O
Dichotomous Nominal Yes/No , binary, logical
coding0, 1
MGH 12
Ordinal
1 I, II, III, IV, VIIIIIIIIIIIIIIV
2 I, II, III, IV 3
||||||
10,000||10,00020,000
||20,00040,000||40,000 015||1545||
MGH 13
Continuous
Interval
Ratio
cyclic
variables
506070
(50+60+70) / 3 =60 nominal
21:00,
01:00, 02:00(21+1+2) / 3 = 8
Continuous
165
MGH 14
proportionbinary
23 Rate
5.5
Time to an event
Data Types
Numeric String
Date
Currency Binary
MGH 15
coding
Martial status
* 1 single * 2 divorced * 3 widowed * 4 married
) 1,2,3,4. (
. ( .
MGH 16
MGH 17
scaleordinal
100001200020000
30000100002000020000300003000040000
MGH 18
Descriptive statistics
Inferential Statistics
Inferential statistics
Estimation a parameter within population
Detect Relations between variables.
Predict values: one variable based on others, parameters of the population,.
1
2 2020
MGH 19
there is no other way of representing "meaning" except in terms of relations between some quantities or qualities; either way involves relations between variables
Population and samples
Population) Censussampleinterference
Sampling variation
Population 10
target population
Population
MGH 20
census
Representing sample
students are typical
Observational
Experimental
MGH 21
Confounders
association causation
Confounders
MGH 22
ExcelAccessExcel
ExcelAccess
1 SAS System 1982
SAS
PC Personal computerMain frameWindows,
Unix, Linux, Mac
MGH 23
SAS Specialist
2 SPSS
Graphics
3 STATISTICA SPSSGraphics
SPSS 4 Epi Info
5 RS-Plus
:
MGH 24
- 2 spss
Data view Variable view
SPSS Viewer
Data View
Value Labels
Labels
30
MGH 25
Variable view Variable view
Name
_
Underscore
Label
Measure Scale/, Ordinal, Nominal
MGH 26
TYPE
Numeric Date dollarcustom currency String
Character
Values
ValueValue
Label
MGH 27
Missing Values
SPSS MissingSPSS
MGH 28
ExcelFileOpen
DataExcel . Files of type
MGH 29
3
Reliability - Unbiased
Reliable and unbiased
Reliable = Free of random error. (stochastic error) Unbiased = Free of systematic error.
ReliablePrecision
UnbiasedAccuracy
MGH 30
BiasReliability (a)intra-arterial cannula
(b)sphygmomano-meter
Unreliable
Unreliable Results Cant be used.
biased
Validation
MGH 31
Validity Unbiased
Bias ReliableUnbiasedUnvalid
Gold standard
Internal VExternal V
ValidReliableUnbiased
Validation study
-4 -
Descriptive Statistics
Pictorial Numerical summaries
v
MGH 32
Frequency distributions
Frequency Table Frequency
Percent
Valid percent
Cumulative percent
MGH 33
-
100 - ordinal
Frequency Analysis
significant figures
92420420.452497551420
0.452%45.2
MGH 34
2650224,175,9000.00109621560.001090.0011110
100,000
Graphics 1 Bars
. Frequency
MGH 35
2 Pie
SPSS AnalyzeDescriptive Statistics
Frequencies Charts OK
MGH 36
Histogram 512
Grouping140160160180161179
MGH 37
SPSS cm140
cm140cm 1499
Frequency Percent Cumulative frequency
=190 4 0.2 100
MGH 38
histogram
MGH 39
histogram , bars
bars
Histogram
MGH 40
Steam and leaf diagrams histogram
leaves
Frequency Stem & Leaf 3.00 1 . 259 12/15/ 19 4.00 2 . 0224 20/22/22/24 8.00 3 . 01125689 30/31/31/32/35/36/ 7.00 4 . 0002457 40/40/40/42/44/45/47 5.00 5 . 01127 50/51/51/52/57 4.00 6 . 2789 62/67/68/69 2.00 7 . 04 70/74 1.00 8 . 0 80
Stem width: 10.00 Each leaf: 1 case(s) stem * stem width + leaf =X E.g. 1*10+2=12
MGH 41
Frequency Analysis
Crosstabulation
MGH 42
CrosstabulationSPSS AnalyzeDescriptive statisticsCrosstabs
Cells PercentageRowColumn
MGH 43
Clustered bar chart
male ,female
Clustered bar chart
MGH 44
22.2 20.6
77.1 74.2
0.8 1.20 4.30
102030405060708090
Male Female
singlemarrieddivorcedwidowed
Scale scatter plots
MGH 45
Time series
Time series
0
5
10
15
20
25
30
35
1988 1990 1992 1994 1996 1998 2000 2002
Income
0
2
4
6
8
10
12
14
16
0 30 60 90 120 150 180 210 240 270 300 330Times (minutes)
Con
cent
ratio
n (m
g/10
0 m
l)
Healthy not-healthy
MGH 46
Stacked bar chart
3-D graphics
single marrieddivorced widowed
single married divorced widowed
MGH 47
None Win Mac
01020304050607080
`
Mac Win None
n
MacWinNone
McGill
MGH 48
0102030405060708090
Male Female
singlemarrieddivorcedwidowed
Stacked bar chart
Stacked bar chartClustered bar chart
1990
2000
0
20
40
60
80
100
120
Male Female
widoweddiv orcedmarriedsingle
1990 1992 1994 1996 1998 2000
Income
1990 1992 1994 1996 1998 2000
Income
MGH 49
0
50
100
150
200
250
1990 1992 1994 1996 1998 2000
Income
198200202204206208210212214
1990 1992 1994 1996 1998 2000
Income
1980
MGH 50
Rubber-band Scales
MGH 51
MGH 52
11010
100
1970
100
100
10101 1001002 100010003 10010
MGH 53
21
3
1 2 3
- :
.
45 HGM
5
: )tnemirepxe(
) ....( : . )ecaps elpmaS( . )semoctuO( : )tnevE(
. : :
. }6,5,4,3,2,1{ * . 6,5, 4, 3, 2 ,1 semoctuO * 1 *
...) : )elpmiS(
dnuopmoC ()
( . ( {1} ) 1 :
4 2 .. }6,4,2 { 6
B A :(noinU) . B U A
A : (noitcesretnI) . B A B A: )tnemelpmoc(
. A A A :
.
: .
: . A * . B *
.
55 HGM
B U A * .
BA * .
4 321 ) A * (6 .
B ,A : .
:)evisulcxe yllautuM( .
3 1 : * .
a n: . n/a
84 001 : * . 84.0
: (ytilibaborp) .
.
65 HGM
A B
B,A B, A
1 < P > 0 : P
. ) ( 0=P * . ) ( 1=P *
A( B A: . )B U
6/1 1 * 6/2 3 1 6/1 3
)A( : P -1 . 3.0 = 7.0-1 7.0 *
: B A: )B A( P )B(P + )A(P = )B U A( P
( 6 4 2 ) 2 * )6/4( = )6/1( )6/2( + )6/3( = P(6, 3 ) 3
(
B UA * )( .
M 2E N 1E: . M x N
* .
.
75 HGM
01 5 *= 01 x 01 x 01 x 01 x 5 = M x N x....... :
00005
sddO . . : )ssol( ytilibaborp / )niw( ytilibaborP= )P-1( / P = sddO
)sddO+1( / sddO = P
) P : sddo
.( P > sddO . sddO P )1.0< P( P : . 1 = sddO ) 5.0=P( :
ytilibaborP lanoitidnoC
A B A . B
: )3,2,1( : A * )4,3,2( : B * ) B = 6/3 A *
A 4,3,2( . 3/2
. )B|A(P : . )B( P / ) B A( P = )B|A( P : ) 6/2 B A )BA( P
. 3/2 = )6|3( / )6|2( = )B|A( P : ( 3 2
stneve tnednepednI
B A .
.
85 HGM
. 1 A : . 3 B
( 3 ) B .6/1
. )B(P = )A|B(P )A(P = )B|A( P :
: B A )B(P * )A(P = )BA( P
: . = *
.
: 001 *
001 (0103 *.172)
4 . ) (
001 *
.
...... ( ** ) ) ( . .
: Ai :
)iA|B(P * ) iA(P = )B( P :
)B( P / )iA|B(P * )iA(P = )B|iA( P
. B %06 A :
. : %05 %03 %04
.
95 HGM
) ( * .
* * . : ) (
00001 0083
%83 0081 0083 :
. %4.74 0083/0081 0024 0026 :
%7.76 0026/0024 .
%1 %5 %99
. *
*
.
06 HGM
99 495 * 495/99
. %7.61 6049 *
5049 . %989.99
. %1
%5 %99 *
. . *
.
yticificepS ytivitisneS
:: )PT( *
. evitisoP eurT( ) PT
.
16 HGM
: )PF( * ( evitisoP eslaF )
) ( . evitageN eslaF :)NF( * ( .) evitageN eurT :)NT( * . NF + PT: )tneitaP( * : . )yhtlaeh( * . : )tset +( * . : )tset ( * : . )lla( *
: ytivitisneS *
. : / PT *
tneitap / PT = ytivitisneS yticificepS:
*
* :
. yhtlaeh / NT = yticificepS
: VPP eulav evitciderp evitisoP : *
)tset +( / PT = VPP : VPN eulav evitciderp evitageN
: * )tset - ( / NT = VPN
:
.
26 HGM
*
. *
.
: )( %59 *
)( %09 ) %01
( . ) (
. 00001 *
. 0001 0009 %01 * %59 *
059 59.0 * 0001 0001 . 05
0009 %09 * . 009 0018 9.0 * 0009
. *
: * %59 = 0001 / 059 = tneitap / PT = ytivitisneS *
: : * % 4.15 = 0581 / 059 = )tset+( / PT = VPP *
.
36 HGM
: * %4.99 = 0518 / 0018 = )tset-( / NT = VPN *
( %09 %59 )
. %01 %1
59 099 5801 5 0198 5198
001 0099
%8.8 = 5801 / 59 = VPP : . %8.8 * :
%49.99 = 5198 / 0198 = VPN . *
.
VPN
VPP
:
.
: ) ( .
0
02
04
06
08
001
21 01 8 6 4 2 0
VPPVPN
.
46 HGM
setar ytilatroM
001
0203
040506
0708
001 09 08 07 06 05 04 03 02 01 0sititapeH %
%
yspoib lacidem yregruS
.
gnikaM-noisiceD lacinilC
05 . esatahpsohp enilaklA TPGS
: : (sititapeh cilohocla ) E
)(. ( sitignalohc) E
. . %5 :
. % 5 : : .1 : : ) ( .2
. %05 : 0 . %01 : 0
: : ) ( .3 . %52 : 0 . %57 : 0
) ( ) ( .
1
2
3
.
56 HGM
( : 1 ) * .
: ( :2 ) * .
: ( :3 ) *
. %5 *
%89 %05 .
. .
: %5 %01
. %05 .1 .2 .3
.4 .5 . ) (
%05 .1 .
%52= 0001/052 = .2= 0009/052 = .3
%68.2
.
66 HGM
= 000,01/052 = .4 %5.2
= 000,01/057,8 = .5 %5.78
.
- %01
.
: : =
x x
. :)detceffanu|reirraC( P :
)detceffanU( P , 2/1 = )detceffanu dna reirraC( P 4/3 =
)detceffanu( P / )detceffanu dna reirraC( P = )detceffanu|reirraC( P 76.0 = )4/3( / )2/1(=
: %01 760.0 = 1.0 * 76.0 = P
%52 :
)% 7.1( 57610.0 = 52.0 * 760.0 = P
: dlihc 000,01/52 = )%52.0( 5200.0 = 52.0 * 1.0 * 1.0= P
.
76 HGM
-6-\
elbairav modnaR : . :
* . 01 0
. *
. ( )
. :
. :
.
: . X * : *
4 3 2 1 0 : X 5 52651.0 5213.0 5213.0 52651.0 52130.0 : P 52130.0 57869.0 5218.0 5.0 5781.0 52130.0 :cP 1
: cP P :: X : *
: . X : . P .
.Pc
.
86 HGM
laimoniB : noitubirtsid laimoniB
. N *
. * . * . p * ) ( *
: ,01=n) 01 *
(5.0=p ,8=n) 8 4 *
(761.0=p 01 *
.(10.0=p ,01=n) 10.0 : SSPS
n ) ( )p ,n ,X (moniB.FDP =P .1. p
. X .)p ,n ,X( moniB.FDC =cP .2
. X
.
96 HGM
: X : X : )p ,n ,1-X( moniB.FDC -1=cP-1
: 761.0=6/1=p 6=n ) 6 * 5 *
8350. = )761.0 ,6 ,3 (moniB.FDP =P 2 1 0 ) 5 *
( 45 3 32199.0 = )761.0 ,6 ,3( moniB.FDC=P
5 4 3 ) 5 * ( 6
6260.0 = )761.0 ,6 ,2( moniB.FDC -1=P ) ( *
433. = )761.0 ,6 ,0 (moniB.FDP = P
noitroporP . . 02 %01 :
3 * 91.0 = )1.0 ,02 ,3(moniB.FDP =P
5 * 40.0 = )1.0,02,4( moniB .FDC 1 = P
... * 21.0 = )1.0 ,02 ,0(moniB.FDP = P
nossioP
. :
. * . * . *
:
. : SSPS
.
07 HGM
),X( nossioP.FDP=P : .1 .
: ),X( nossioP.FDC=cP .2 :
x 3 * 3) )3( nossioP
(.3= : *
6 5 4 3 2 1 0 : X 101.0 861.0 4202.0 422.0 941.0 050.0 :P 7 220.0 050.0 669.0 619.0 518.0 746.0 324.0 991.0 050.0 :cP
889.0
: *
422.0 = )3,3( nossioP.FDP=P
746.0 = )3,3( nossioP.FDC=P
775.0 = )3,2( nossioP.FDC-1=P
x 3 :
X : )3,X(nossioP.FDC E (.) 91324.0 = )3,2(nossioP.FDC : E
( 1 0 ) : 8675.0 = 91324.0-1 E
. ....( 543 )( 102 ) E
. :
* 5
.
17 HGM
04 . 04
3 32-E 5.7 = )5,04( nossioP * .
.
etaR :
000,001 01 E 6 000,02
000,001 01 ) E : (4 000,02
01.0 = )4,6( nossioP.FDP= P 5
E .
E .
: . p : 0 : 0
.
) ( )
( 261 )x(F )x(f
. ...... : :
051 041 . )041(F )051(F
.
27 HGM
=P )071(F 071 =P )071(F -1 071
: :
) ... (
.
.
.
.
37 HGM
: ) ( E (evitagen ) ( evitisop ) E
. ladom . U
: E
.
.
47 HGM
E .
: E
( ) ) (
- - - : -
.
77 HGM
- 7-
ecnairav & ycnednet lartneC
ycnednet lartneC : , :
: naeM ) / (
. eulav detcepxe . : edoM : )(
E sdohtem lacirtemarap
-non . sdohtem lacirtemarap
: naideM E .
: :(1) E 581 771 071 851 541 431
391 661 = 7 / )391++541+431( = naeM ( . 071 ) naideM 7 naideM . edoM :(2) E
001 001 001 001 001 001 001 001 001 0001
. 001 = naidem , 091 = naeM
.
.
87 HGM
elbailer
. naideM naeM
)( . edoM > naideM > naeM :
. )(
/ :
.
. ) ( :
. )
(. .
sreiltuO ) ( .
04 054 021-08
.
97 HGM
) .... (
: . ) / (. )
(.
selitnecreP & selitrauQ : .
%05 naideM
rewoL %52 elitrauQ
reppU %57 litrauQ
elitnecrep-n n
. . 001 : 431 = muminiM : 1 391 = mumixaM : 001 05 = naideM : 05 =elitrauq rewoL : 52
851 771 = elitrauq reppU: 57
5ht 541 = elitnecrep : 5 59ht =elitnecrep: 59
581
-ixaMmum
ht59-necrepelit
reppUnaidemelitrauq
rewoLelitrauq
ht5-necrepelit
-iniMmum
1552055759001
431541851071771581091
-ixaMmum
ht59-necrepelit
reppUnaidemelitrauq
rewoLelitrauq
ht5-necrepelit
-iniMmum
1552055759001
431541851071771581091
.
08 HGM
: : STRAHC
: (ni, mc )
. .
( )
52 : 52 . 57
5 . 59
ecnairaV fO serusaeM :
.
: egnaR .1 mumixaM = egnaR :
muminiM: ytilibailernU :
.
.
18 HGM
: (RQI) egnaR elitrauqretnI .2 rewoL elitrauQ reppU = RQI :
elitrauQ
.
: ecnairaV .3-N( / )naeM X( muS :ecnairaV :
)1 1 /
0 N 1-N
) 1-N 0 (naem
) ( . desaibnU 1-N N ) (
. 1-N . :
.
:) ( noitairaV: V lacigoloiB eurT
. snoitavresbo gnikaM
: snoitidnoc tnereffid rednu ) ( citametsyS
.
.
28 HGM
: V tnemerusaeM .
. ) (: :
: noitairav tcejbus-nihtiW .
: stcejbus neewteb noitairaV .
: noitaiveD dradnatS .4 )ecnairaV( RQS =DS : . ) :
(. ecnairaV DS naeM DS*N
: noitairav fO tneiciffeoC .5 naeM / DS = noitairav fO tneiciffeoC : :
(. )
.
. ) = +
(. . . 2 051 %1 :
( Hp lC K aN) %01 .%04-01
: .6 :
:)ssenwekS( .
(. ) : )sisotruK( . .
.
.
38 HGM
noitubirtsiD lamroN ) , ,X (lamroN.FDP = )x(f :
:
)( . ) ( . )( . + - . 1
.
48 HGM
: ,-( )+
6286.0 ,2-( )2+
4459.0 ,3-( )3+ 3
4799.0
. 01 061 . 071 .1
071 ) ( . 1.071 9.961
. 071 051 .2-)01,061,071(LAMRON.FDC =P
386.0 = )01,061,051(LAMRON.FDC
: 051 .3 6851. = )01,061,051( lamroN.FDC=P
571 .4
.
58 HGM
8660. = )01 ,061 ,571( lamroN.FDC -1 =P
2 .5 176130000. = )01 ,061 ,002( lamroN.FDC -1 = P
)nollim/23(
051 ,X( lamroN.FDC
)01, = 071 051 X
. 051 071 1 = 071
. 071
% 01
. : ) (
)1.0-1(=)01,051,X( lamroN.FDC :
), , p( lamroN.FDI =X 8.271 = )01 ,051 ,9.0( lamroN.FDI = X
: : noitcnuF ytisneD ytilibaborP E
), ,X(lamroN.FDP=P SSPS .
noitcnuF noitubirtsiD evitalumuC E
), ,X(lamroN.FDC =P SSPS snoitcnuF noitubirtsiD esrevnI E
: SSPS ), ,p(lamroN.FDI=X
: :
.
68 HGM
:) ...( .1 .
. ) ...(. .2 (. FDI,FDC ,FDP ) .3 . .4
. Z 1 0 x:
. /)-x(=z (elbairaV dezidradnatS ) z
. 061 01 051 :
1 1=01/051-061 .
.
.
. %99 ]3+,3-[ Z
. . 3+>Z 3-
.
78 HGM
. (nX ,3X 2X ,1X ) : :
.
naeM . )n( rqS/
. )n( rqS/ naem eht fo rorrE dradnatS DS
:
noitubirtsiD lamroN . . :
. ) (
. kcabdeeF :
. )( . :
: .
.
88 HGM
: kcabdeeF
.
.
.
.
SSPS
: : SSPS
. sevitpircseD scitsitatS evitpircseD ezylanA . mumixam ) snoitpO
.)....... ecnairav ,egnar, muminim, . , KO
:
.
98 HGM
: SSPS . erolpxE scitsitatS evitpircseD - ezylanA . elbairav tnednepeD evitpircseD ) scitsitatS
sreiltuO ...( elitnecreP
.( tlopxoB ,faeL dna metS, margotsiH) stolP
.
09 HGM
)(
:
.
19 HGM
tolpxoB
.
.
29 HGM
. naideM ( ) .
.
.
erolpxE erolpxE
. scitsitatS evitpircseD ezylanA : :
. erolpxE . elbairav tnednepeD . tsil rotcaF
.
39 HGM
:
) : ( .
sreiltuO
. sreiltuO
.
49 HGM
)(: : : lacirtemaraP .I
2 > |Z| = reiltuO laitnetoP
3 > |Z| = reiltuO dekraM
. %5.0 %5 6>Z Z 01 BD
) (. . . tolP P-P margotsiH
: lacirtemarap-noN .II egnaR elitrauqretnI *5.1 edistuO = reiltuO laitnetoP egnaR elitrauqretnI*3 edistuO = reiltuO dekraM
: . (RQI*3) . RQI( *3) RQI( *5.1)
: sreiltuo dna tolpxoB
QLMQU
123456789011121314151
621031051051051551651061061261461461561081781
QLMQU
123456789011121314151
621031051051051551651061061261461461561081781
051= QL : E )( .
061= : M E ) (
461= QU : E . )(
: RQI E
41 = 051-461 = RQI
: E
.
59 HGM
00.
51.
1.5
2.2.
5rF
qeeu
cny
08 06 04 02 0)syaD( yatS fo htgneL
2= ) 5.1 *41( :RQI *5.1 581 = 12 + 461 921 = 12 051
laitnetoP 921 581 0
. : E
24 = ) 3 * 41( :RQI *3 801 = 24 051
602 = 24 + 461
dekraM 801 602 0 .
. : (1)
8.02
0.41 [ 82.84, 96.6-] %59
. [05, 3 ] %59 .
( :2 )
. 1.5
4.6 ,4.7-[ %59 . ]6.71
. , 5 = Z( 5=4.6/1.5-73 = Z : 73
. ( )noillim/3.0=P
.
69 HGM
%59 73
:
. naideM naeM : .ssenwekS .)( : sisotruK : ) margotsiH fael dna metS
(. tolP xoB : tolp ytilibaborP lamroN
.
) D vorogomloK kliW-oripahS . (
. sisotruK ssenwekS
.
79 HGM
) (. .
.001 . liaT yvaeH
noitubirtsid laitnenopxE: .1
) (
. sselyromeM
. . PXE.FDP SSPS
::
) ( 3= . 3/1
. :
. . . sselyromeM
) ( .
-
.
: .2
.
89 HGM
: (.A.)
: (.B)
: (.C) .
(.D).
.
: ammaG .3
.
. . AMMAG.FDP
: mrofinU .4 )
. ( .
.
SSPS . MROFINU.FDP
.
.
99 HGM
.5
. U
:
=6/3 75 =6/3 . : : 85 . : NT : 16
: .
.
101 HGM
8
ataD lacitsitatS
. : 0 : susneC 0
. 002 001 stcart susnec
) ... ( ) ....(
: . .1 ..( ) .2 . .3
.
: gnilpmaS 0
. :
. : noitalupoP
. etinifnI etiniF 4002
. 4002
. .: elpmaS
81 0
evitatneserper .
sdohteM gnilpmaS
.
201 HGM
: gnilpmaS :gnilpmaS modnaR
. : gnilpmas modnar-noN
.
: gnilpmaS modnaR elpmiS .1
. : ) :
( ) (. :
.
: gnilpmaS deifitartS .2( )
) ( ) ( . . atartS
.
: gnilpmaS retsulC .3. retsulC
. . . .
.
retsulC deifitarts
.
301 HGM
)
(
)
(
.
.
.
: gnilpmas egats-itluM .4
.
.
.
: gnilpmaS citametsyS
) ( . .
9
noitamitsE
0 .
)
... ( .
.
401 HGM
05>n
.
naem elpmas a fo rorre dradnatS
. )n(rqs/S
. n S : .
. )
(. .
:
.
501 HGM
. ) (
.
601 HGM
noitamitsE tnioP
.
. 05
. 961 961
noitamitsE lavretnI
. noitamitsE lavretnI P
. .IC lavretnI ecnedifnoC
: 59.0=P ]5.171-5.661[
. %59 :
)naem fo rorrE dradnatS *Z( naeM
)1-N( rqS / noitaiveD dradnatS = naem fo rorrE dradnatS
:
. naeM 0 . rqS N 0 ) ( . Z 0
. ( Z . ) %59 69.1 ) ( :
. (noitaiveD dradnatS ) 0 . 0 ( Z ) 0
.
.
701 HGM
) ( ) .(
) . P(
: E.S * Z P = )P( 0
] n / )p-1( * p [ rqS = )P( .E.S 0
Z E.S * Z P = )P( : IC 0
.( 69.1=Z %59)
: . 51 04 E 573.0 = 04/51 = P : E : %59 E
051.0 573.0 =] 04 / 526.0 * 573.0 [ rqS* 69.1 573 .0
]5.25-5.22[ %59 E) %59
(%5 ]2.75-8.71[ %99 E
. (%1) %99 04) : E
. (
01 gnitseT sisehtopyH
sisehtopyH evitanretlA & lluN
: . %52 . P . 52.0=P : : oH
.
801 HGM
.52.0>P : : aH )
(. :
. .I . .II
.III .
: .
( ) .
, < , > = :
52.0 > P : aH 52.0 = P :oH P )( : sisehtopyh dedis enO
7.0 < P 52.0> P . P : sisehtopyh dedis owT
. 52.0 P :
)(.
}02..,9,8{
oH X 11=X . aH
: . deliaT reppU X: 52.0>P 0 . deliaT rewoL X :7.0P :aH 52.0=P :oH 0
.
901 HGM
: . 0 11=X X }02, ,01 ,9{ 0
. 11
:deliaT rewoL .2
. 52.0
.
011 HGM
oH tcejeRrorrE I epyTrorrE oN
oH tpeccArorrE oNrorrE II epyT
eslaF :oH52.0>P
eurT :oH52.0 = P
oH tcejeRrorrE I epyTrorrE oN
oH tpeccArorrE oNrorrE II epyT
eslaF :oH52.0>P
eurT :oH52.0 = P
I . rorrE ahplA I . oH= I :
( 52.0>P 52.0=P 02) .}02..,9,8{
02 ro .. ro 9 ro 8=X I ( 218101.0= )
. %1.01
II
. - rorrE ateB II . oH = II aH> 052.( 52.0=P : oH : )
. P: . P
P ( P :aH>0 52 , 52=P :oH : ) }02..,9,8{
( .P ) . )p(B , P
p 7.0 6.0 5.0 4.0 3.0 )p(B 100.0 20.0 31.0 24.0 77.0
5.0=P . %31
.
111 HGM
=3R }02,9{=2R }02..,8{= 1R
: }02,,01{
3R410.0259.0557.0214.0821.0710.0
2R40.0788.0695.0252.0750.0500.0
1R201.0277.0614.0231.0120.0100.0
3.04.05.06.07.0 P )P(B
3R410.0259.0557.0214.0821.0710.0
2R40.0788.0695.0252.0750.0500.0
1R201.0277.0614.0231.0120.0100.0
3.04.05.06.07.0 P )P(B
: ) (
.P
( . ) ) .
P (
: ecnacifingiS fo leveL : ,
) 50.0 . ( 59.0
I .
tseT leveL .
50.0 : : 2R . 50.0
.
211 HGM
10.0 50.0
) : . ( 100.0
sorrE ateB dna ahplA
0
2.0
4.0
6.0
8.0
1
2.0 51.0 1.0 50.0 0rorre ahplA
eBat
E rr
ro
052=N 001=N 52=N
.
tseT .
( }02,..,11,01,9{ 2R) 50.0 . rewoP
fo rewoP ) .IIrorrE-1 = )p( )p( ( tset
02.0 50.0 08.0
P: ecnacifingis fo leveL P
( .%5 )
.
311 HGM
lacitirC: seulaV lacitirC
. lavretni ecnedifnoC: IC
.
52.0 :
: 52.0=P : oH : 0 . 52.0> P : aH : 0 0
: : P .1
.
: ) (
: P )
aP 52.0=oP (. 11 7.0=aP 325 3.0=aP
: ) (
) ( : ) ( .2
. P 50.0 : 3.0=P :
10.0 325 . 1821
: .3 ( )
. P 3.0=P
) ( 50.0 .
.
411 HGM
10.0 = 182106126330259.0 =
50.0 = 617498312319.0 =
50.0 = 325079271118.0 =
3.0 =P4.0 =P5.0 =P6.0 =P7.0 =P
10.0 = 182106126330259.0 =
50.0 = 617498312319.0 =
50.0 = 325079271118.0 =
3.0 =P4.0 =P5.0 =P6.0 =P7.0 =P
0 . 59811 %08 %5 62.0=P
2 ^ ] d/ S * ) bZ + aZ( [ = N 0
IC seulav-P :
. IC 0 ) ( eulav-P 0
. : IC ,
: . -P 50.0
.
511 HGM
C000529.8 ot 1.1210.0
B00043.35.8 ot 5.4-45.0
B043358 ot 54-45.0
A00030484 ot 23100.0P) P sisehtopyH lluN
. 50.0
.
251 HGM
tseT-T selpmaS-deriaP
. tseT-T tnednepeD :
0 0
: 0
.
0 . 0
T : tnednepednI ytilamroN
. ecnairaV fo ytienegomoH
: tseT T selpmas deriaP snaem erapmoC ezylanA 0
.
351 HGM
0) / (
.
: ) 0
(.
0 .
0 )
(. .
.
451 HGM
64: 0 . 5
:
.
651 HGM
rehsiF derauqs -ihC
: . 0
: ( ) 0
:
.
751 HGM
: %3.4 %2.5 0
.
. derauqs -ihC 0 scitsitatS noitalubatssorC 0
derauqs-ihC
.
851 HGM
:
erauqS-ihC nosraeP 0 . 833.0
0 %8.33
. : derauqs-ihC
. 0 ( 50.0>P / ) 0
.
50.0
.
951 HGM
%52 5 : 0
. tset tcaxE rehsiF ihC 0
.
dnert rof tset derauqs-ihC :
. 0 0
. . 0
: 000,01) 0
( 00,04 000,04 000,02 000,02 000,01
. ) ( serauqs-ihc
. P noitaicossa raenil yb raeniL
noitalerroC
: . 0
: ( ) 0
. ( )
) ( .
tneiciffeoc noitalerroC .
: . etairaviB etalerroC ezylanA 0 . 0 nosraeP stneiciffeoc noitalerroC 0
. namraepS
.
061 HGM
. KO 0
: : : noitalerroC nosraeP 0
. . ohr s'namraepS cirtemarapnoN 0
: . .
.
161 HGM
: : ]1+,1-[ r
noitanimreted fo erusaem 0 X )( Y)(
: ) 1- r 0 (.
: . r 0 : ) 1 r 0
(.) ecnacifingis
. ( 50.0
: . enifeD elpmiS rettacS hparG 0 . KO Y X 0
.
261 HGM
0
. yB srekram teS redneg
:
: noitalopartxE
.
361 HGM
. R R
. . R : sreiltuO
.
:spuorG suoenegomoh-noN 0
.
.
.
461 HGM
:
) Y X 0
(. . 0 . 0 . sreiltuo 0
J J
: 56 .1
% 5: : : 0) % 5 : :
( .( : 3 ) 0
: . %5
: 07 .2 ( 45 3 2 1 0 : o 3 2 1 0 : o
: 27 .3 5.7* 01-32 5.7 E-32 = )5,04( nossioP E 5.7-32
: 58 .4 )01, 061 ,X( lamroN.FDC )01, 051 ,X( lamroN.FDC
. 52.0 => P : aH _ 52.0 > P : aH : 901 .5
.
561 HGM
. SSPS .6 ( . 3 56+- ) .7 .8
.( ) : : .9
!! .
-
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