/.+)0')"#1&%'
G"(%'
I=%.E=,'
!"#$%&'(%)'*+,$-,"'."#$%&'
@J-=#"'*=.K"E#'.='
#+FL.K"E(-"+$4'
(%$F1=$4'.E"(.*"%.'
>/!2!B''
/!2!'3"%141,,1%'
2&"'>GHB'
5
<=)0'4=*-=#1$=%'>?@A2BC'
6
D14E=F1=*"'#(*-,"#C'
!
7
!
8:'
!
89'
!
95'
!
!
9:'
!
;5'
!
!
"#$%$
!
M=E*=%"',"N",#C'
O+"#$=%#'
•! 2E"'-E"41#"'#.(."*"%.#'.K(.'(E"'(*"%(F,"'.='
F"1%&'-E=N"%'T(,#"'+#1%&')(.(U'
•! V+,,'K0-=.K"#1#C'('-E=-=#1$=%'.K(.'4=EE"#-=%)#'
.=')"T(+,.'-=#1$=%U'>WV=.K1%&'#-"41(,'1#'
K(--"%1%&XB'
•! 2,."E%($N"'K0-=.K"#1#C'('-E=-=#1$=%'.K(.'
)"#4E1F"#'('%=%')"T(+,.'=+.4=*"'>W/=*".K1%&'1#'
&=1%&'=%XB'
•! !K"'1%T"E"%4"'1#'=F.(1%")'F0'E"Y"4$%&'.K"'V+,,'
K0-=.K"#1#U'V+,,'K0-=.K"#1#'4(%'%"N"E'F"'
4=%ZE*")'F0'.K"')(.(['
@J(*-,"'=T'K0-=.K"#"#'
•! QT'.K"'V+,,'M0-=.K"#1#'G(#'1%'T(4.'.E+"'('-.'/-/,'+#")'.='-"ET=E*'
.K"'."#.'G=+,)'T=,,=G'('4"E.(1%')1#.E1F+$=%C'%+,,')1#.E1F+$=%U'
•! 3LN(,+"'1#'.K"'.(1,'-E=F(F1,1.0'+%)"E'.K"'%+,,')1#.E1F+$=%U'
0.3
density
0.0
0.1
0.2
0.1
density
0.3
0.4
One!tail p!value
0.4
Two!tail p!value
0.0
•! \"%"E(,']+"#$=%C'2E"'(%0'.(J('(##=41(.")'G1.K'(%$F1=$4'
.E"(.*"%.P'
•! ^%1N(E1(."'K0-=.K"#1#']+"#$=%C'Q#'.(J=%'!'(##=41(.")'G1.K'(%$F1=$4'
.E"(.*"%.P'
•! V+,,'K0-=.K"#1#C'(F+%)(%4"'=T'.(J=%'!'T=,,=G'.K"'#(*"')1#.E1F+$=%'
1%'.E"(.")'(%)'4=%.E=,'&E=+-#U'
•! 2,."E%($N"'K0-=.K"#1#'8C'(F+%)(%4"'=T'.(J=%'!'T=,,=G')1#.E1F+$=%'
=T')1R"E"%.'!"#$%1%'.K"'.G='&E=+-#U'
•! 2,."E%($N"'K0-=.K"#1#'9C'(F+%)(%4"'=T'.(J=%'!'T=,,=G'.K"'#(*"'
T=E*'=T')1#.E1F+$=%'F+.'G1.K')1R"E"%.'$&'(%F".G""%'&E=+-#U'
•! 2,."E%($N"'K0-=.K"#1#';C'(F+%)(%4"'=T'.(J=%'!'T=,,=G'.K"'#(*"'
T=E*'=T')1#.E1F+$=%'F+.'G1.K')1R"E"%.'$&)*'(%F".G""%'&E=+-#U'
•! 2,."E%($N"'K0-=.K"#1#'6C'(F+%)(%4"'=T'.(J=%'!'T=,,=G'.K"'#(*"'
T=E*'=T')1#.E1F+$=%'F+.'G1.K')1R"E"%.'+'#*'(,&%F".G""%'&E=+-#U'
3LN(,+"#'
0.2
•! 2E"'(%0'.(J('(##=41(.")'G1.K'(%$F1=$4'
.E"(.*"%.P'
•! Q#'.K"E"')1R"E"%4"'1%'*14E=F1=*"'4=*-=#1$=%'
=N"E'$*"'>G1.K1%SF".G""%'.E"(.*"%.#BP'
•! Q#'.K"E"'4=EE",($=%'F".G""%'(F+%)(%4"'=T'
(%0'.(J('(%)'*".(F=,14'-K"%=.0-"#P'
•! 2E"'.K"E"'(%0'-(1EG1#"'4=EE",($=%#'F".G""%'
.(J(P'
M0-=.K"#"#''
!3
!2
!1
0
statistic
1
2
3
!3
!2
!1
0
statistic
1
2
3
?1#.E1F+$=%'=T'_!^'(F+%)(%4"')(.('
•! 01-/2'34&%)1#.E1F+$=%'(##+*-$=%#'=`"%'(,,=G'T=E'F"a"E'
#.($#$4(,'."#.#'
•! 3E=-"E$"#'=T'_!^'(F+%)(%4"')(.(C'
–! I=EE",(.")C'/+*#'.='8b'K"%4"'.='1%4E"(#"'#=*".K1%&b'#=*".K1%&'
",#"'K(#'.=')"4E"(#"'
–! c(E1(F,"'(4E=##'#+FY"4.#'
•! I(%'5"--*346%F"'*=)",")'.KE=+&K'4=*-=+%)'?1E14K,".L
D+,$%=*1(,')1#.E1F+$=%d'K=G"N"Eb'+#"T+,'*(E&1%(,'
+%1N(E1(."'."#.#'K(N"'%=.'0".'F""%')"E1N")C'
–! Ka-CSSGGGU(*#.(.U=E&S*""$%&#SY#*S9588S=%,1%"-E=&E(*S
2F#.E(4.?".(1,#U4T*P(F#.E(4$)e;59;;6'
•! M(N"'.='E",0'=%'%=%L-(E(*".E14'>)1#.E1F+$=%'TE""B'."#.#b'
-=##1F,0'(.'.K"'4=#.'=T')"4E"(#1%&'.K"'-=G"E'=T'.K"'."#.#'
kE+#H(,Lf(,,1#'=%"LG(0'(%(,0#1#'=T'N(E1(%4"'
>*=E"'.K(%'.G='#(*-,"#S&E=+-#B'
D(%%LfK1.%"0'^'=E'f1,4=J=%'E(%HL#+*'
.G=L#(*-,"'."#.'
•! 2##+*-$=%#C'
–! Q%)"-"%)"%.'=F#"EN($=%#'
–! _F#"EN($=%#'4(%'F"'=E)"E")'G1.K'E"#-"4.'.='"(4K'=.K"E'
•! V+,,'K0-=.K"#1#C'!K"')1#.E1F+$=%'1%'.G='#(*-,"#'1#'.K"'
#(*"U'QT'=%"'E(%)=*,0')E(G#'=%"'=F#"EN($=%'TE=*'"(4K'
#(*-,"'Ab'gd'.K"%'3E>AhgB'e'3E>ghAB'
•! !G=L#1)")'(,."E%($N"'K0-=.K"#1#C'3E>AhgB'i'3E>ghAB'
•! Q%."E-E".($=%C'T=E'4=%$%+=+#'=F#"EN($=%#b'#1&%1Z4(%.'
."#.#'1%)14(."'4K(%&"'1%'.K"'*")1(%'
•! @J(*-,"C'Q#'.K"'(F+%)(%4"'=T'('.(J=%')1R"E"%.'F".G""%'
/!2!'(%)'I=%.E=,P'
•! Q%'jC'wilcox.test!
I=EE",($=%'4="m41"%.#b'E(%H'
4=EE",($=%#'
4e+08
2e+08
0e+00
!
!
!
!
!
0.0
0.5
1.0
1.5
2.0
2.5
x
1e+08
3"(E#=%'4=EE",($=%'4="m41"%.C'5U::'>%=.'
#1&%1Z4(%.b'-e5U8nB'
!
!
!
1e+04
1/(exp(!x))^8 (log!scale)
•! V+,,'K0-=.K"#1#C'!K"',=4($=%'>*")1(%B'=T'(,,'.K"'&E=+-#'
1#'.K"'#(*"U'
•! 2,."E%($N"'K0-=.K"#1#C'l=4($=%'T=E'(.',"(#.'=%"'&E=+-'
1#')1R"E"%.'TE=*',=4($=%'=T'(.',"(#.'=%"'=.K"E'&E=+-'
•! @J(*-,"C'Q#'.K"'(+%)(%4"'=T'('.(J=%')1R"E"%.'1%'/!2!S
4=%.E=,'=N"E';'#(*-,")'$*"'-=1%.#P'
•! Q%'jC'kruskal.test!
!
!
1e+00
–! Q%)"-"%)"%.'=F#"EN($=%#'.K(.'T=,,=G')1#.E1F+$=%'G1.K'.K"'
#(*"'#K(-"'(%)'#4(,"'
–! _F#"EN($=%#'4(%'F"'=E)"E")'G1.K'E"#-"4.'.='"(4K'=.K"E'
•! l1%"(E'4=EE",($=%'
4="m41"%.'>3"(E#=%B'
(##+*"#',1%"(E')"-"%)"%4"'
F".G""%'.G='N(E1(F,"#'
•! j(%H'4=EE",($=%'4="m41"%.'
*"(#+E"'.K"'"J."%.'=T'
*=%=.=%141.0'F".G""%'.G='
N(E1(F,"#'
•! V+,,'K0-=.K"#1#'T=E'
4=EE",($=%'."#$%&C'
4=EE",($=%'4="m41"%.'1#'
"]+(,'.='5U'
1/(exp(!x))^8
!
•! 2##+*-$=%#C'
!
0.0
0.5
1.0
1.5
2.0
2.5
x
?1(4=%1#b'3U'>8o77Bb'\E=+-'j"-E"#"%.($=%#'1%'3E=F(F1,1.0'(%)'/.($#$4#b'l"4.+E"'V=."#LD=%=&E(-K'
/"E1"#b'M(0G(E)b'I2C'Q%#$.+."'=T'D(.K"*($4(,'/.($#$4#b'Q/<V'5Lo65:55L86Ln'
j(%H'4=EE",($=%'4="m41"%.#'
•! /-"(E*(%p#'qC'j(%H'4=EE",($=%'*"(#+E"')"Z%")'(#'.K"'
3"(E#=%'4=EE",($=%'=T'.K"'.G='N(E1(F,"#'(`"E'
4=%N"E#1=%'.='E(%H#'
•! k"%)(,,p#'rC'j(%H'4=EE",($=%'*"(#+E"'F(#")'=%'
4=+%$%&'4=%4=E)(%.'-(1E#U's>J8b08B'(%)'>J9b09B'(E"'
4=%4=E)(%.'1T'J8hJ9'GK"%'08h09t'
•! @J(*-,"C'Q#'.K"E"'4=EE",($=%'F".G""%'(%0'&1N"%'.G='
.(J(P'Q#'.K"E"'4=EE",($=%'F".G""%'('&1N"%'*".(F=,14'
N(E1(F,"'(%)'('&1N"%'.(J=%P'
•! Q%'jC''
–! cor.test(x, y, method=‘spearman’) !
–! cor.test(x, y, method=‘kendall’)!
3E=F,"*#'G1.K'."#$%&'*(%0'
K0-=.K"#"#'#1*+,.(%"=+#,0'
•! f"'K(N"'*(%0'_!^#'.K(.'G"'G=+,)',1H"'.='(--,0'
.K"'."#.'.=U'
•! QT'.K"'."#.'1#'(--,1")'(.'#-"41Z")'#1&%1Z4(%4"',"N",'
>-E=F(F1,1.0'=T'T(,#",0'E"Y"4$%&'.K"'%+,,b'GK"%'1.'1#'
.E+"Bb'G"'4(%%=.'&+(E(%.""'.K(.'4=*F1%")'E"#+,.'
1#'(.'.K"'#1&%1Z4(%4"',"N",'=E1&1%(,,0'#-"41Z")U'
•! @J-"4.")'%+*F"E'=T'E"Y"4$=%#'F0'*"E"'4K(%4"'
*uv'
•! M=G')='G"'4=%.E=,'#1&%1Z4(%4"'T=E'*+,$-,"'."#.#P'
wf@jC'w(*1,0G1#"'"EE=E'E(."'
&$'()*
&$
0()12$
+,-,.),/$ +,-,.),/$
x'.E+"'%+,,'
K0-=.K"#"#'
^'
c'
*5'
x'%=%L.E+"'
%+,,'
K0-=.K"#"#'
!'
/'
*L*5'
*Lj'
j'
*'
!=.(,'
wf@j'4=%.E=,'*".K=)#'()Y+#.'
>*=E"'#.E1%&"%.'."#.#'%"")'.='F"'
-"ET=E*")B'.K"'#1&%1Z4(%4"'=T'
"(4K'1%)1N1)+(,'."#.'.='"%#+E"'
=N"E(,,'#1&%1Z4(%4"'(.'&1N"%'vU'
•! /+--=#"'G"'-"ET=E*'*'
."#.#'>"U&U'*'.(J('(E"'."#.")'
T=E'(##=41($=%'G1.K'
(%$F1=$4'.E"(.*"%.B'
•! !K"'%+*F"E'=T'.E+"'%+,,'
K0-=.K"#"#'1#'+%H%=G%'*5'
•! c'1#'T(,#"'-=#1$N"'E(."'>!0-"'
Q'"EE=EB'
•! !'1#'T(,#"'%"&($N"'E(."'>!0-"'
QQ'"EE=EB'
•! f"'=F#"EN"'jb'F+.'/b'!b'^b'c'
(E"'+%=F#"EN")'
•! wf@j'e'3E>cy8B'
w?jC'T(,#"')1#4=N"E0'E(."'
•! D=)1Z"#'.K"'1)"('=T'4=%.E=,,1%&'!0-"'Q'"EE=Eb'.='
1%#."()'4=%.E=,'.K"'E(."'(.'GK14K'.0-"'Q'"EE=E#'
)='=44+E'
•! w?j'1#'.K"'"J-"4.")'N(,+"'=T'cSj'
@J(*-,"C'<=%T"EE=%1'4=EE"4$=%'
•! !='"%#+E"'=N"E(,,'#1&%1Z4(%4"'(.'('&1N"%'vb'=%"'
-"ET=E*#'"(4K'1%)1N1)+(,'."#.'(.'vp'e'vS*'
•! c"E0'#.E1%&"%.b'E"#+,.#'1%',=##'=T'-=G"E'
>1%4E"(#"'1%'!0-"'QQ'"EE=EB'
D".K=)#'T=E'w?j'4=%.E=,'
•! <"%Y(*1%1zM=4KF"E&'
–! 2##+*"#'."#.#'(E"'1%)"-"%)"%.'
•! <"%Y(*1%1zM=4KF"E&zg"H+$",1''
–! 2##+*"#'.K(.'."#.#'(E"'+%1T=E*,0'4=EE",(.")C'
•! 3=#1$N",0'4=EE",(.")C'1T'=%"'."#.'K(#',=G'-LN(,+"b'=.K"E'
."#.#'(E"'$"#&%,1H",0'.='(,#='F"'#1&%1Z4(%.'
•! V"&($N",0'4=EE",(.")C'1T'=%"'."#.'K(#',=G'-LN(,+"b'=.K"E'
."#.#'(E"'4&--',1H",0'.='F"'#1&%1Z4(%.'
w?j'1%'j'
•! w?j'1#'1*-,"*"%.")'1%'j'(#'('-LN(,+"'()Y+#.*"%.'
-E=4")+E"U'
•! Q%-+.C'-LN(,+"#'T=E'('#".'=T'+%1N(E1(."'."#.#'
•! _+.-+.C'-LN(,+"#'.K(.'(E"'()Y+#.")'.='w?j'
•! @U&U'5U5n'()Y+#.")'-LN(,+"'*"(%#'.K(.'"J-"4.")'
E(."'=T'T(,#"'-=#1$N"#'1#'5U5n'T=E'."#.#'#1&%1Z4(%.'
(.'.K(.'()Y+#.")',"N",'
•! p.adjust!
–! D".K=)#C'
•! method = ‘fdr’: <"%Y(*1%1LM=4KF"E&''
•! method = ‘BY’: <"%Y(*1%1LM=4KF"E&Lg"H+$",1!