???? t ??????? ??????

1
CHIDIST(x,df)
0.317311 chidist(1,1)
0.367879 chidist(2,2)
0.391625 chidist(3,3)
0.406006 chidist(4,4)
0.41588 chidist(5,5)
0.440493 chidist(10,10)
0.45793 chidist(20,20)
0.465654 chidist(30,30)
0.470257 chidist(40,40)
0.473398 chidist(50,50)
0.481192 chidist(100,100)
0.484644 chidist(150,150)
0.494053 chidist(1000,1000)
??? ??????? s2 ???? ???? ?-2? ???? ???????? t ???
???? ??? ?? z
2
???? t ??????? ??????(t-test for dependent
samples)
????? ????? z ????? t ???? ???? ???, ?????? ??
????? ????? ?, ??? ?? ?? ????? ?. ???? ???? ?????
?? ?? ????? ?? ????? 1 ???? t ??????? ?????? ?)
???? ???? test-retest ?) ?????? ???????
paired samples ???? ???? ????? ?????? ?????
???? ????? ?????? ???? ???? ???????. ????? ?? ???
?????? ??? ?????????? ?? ???? ???? ??? ??????
????? ?????? ???? ?????? ??????, ??? ?????? ?????
???? ??? ??????? ???? ???? ?-0.
3
???? ?????
????? ???? ??????
????? ???? ??????
?????????
x ?-y ?? ???? ?????? ?????? ?????.
?????????
???? ?-0
??? ???? ???? ????? ?????? ?? ?d
??????? ?????
Var(x?y)Var(x)Var(y) ?2cov(x,y)
4
???? ?-?d ?? ????? ???? ????? ???? ?"? ?????
?????. ?????? ??? ??????? ??? ?? ??????? t ????
???? ???, ?? ?????? ????? ?? ???? x ??? ?????? ??
???? d ??? ?????? ???? 2 ??????. di(?d,?d) ??
n?30 ???
???? ?- ?d ?? ?????, ????? ???? ?"? sd
dfn-1 ???? n ??? ???? ?????? (???? ???????, ????
??? ???? ??? ??????).
5
?????
H0?d0 (?) H1?d?0 (?) ? ????? ???????
?????? ???????? ?? ??????? ?????? t, ?????
?????. (???? ??????? ?????? ???????? ?? ???????
?????? t ???? ??????? ?????? ?????????? ????????
?????? ?? ???? ??? x ???? dx-y ?? ???? ngt30)
????? ????????
????? ??????? ???? ?? EXCEL
??????
?? ???? ???? ????? ???? ????? (???? ?? ????)
????? ???? ???? ???????.
6
????? ????? ????? ???? ???????? ??? ???? ?????
???? ????? ?????? ????? ??? ???? ???? ????? ????
????? ????? ??? ???? ???? ?????. ?? ????? ????
????? ?????? ????? ???? ??????. ????? ??????
????? ???????, ?? ???? ?????? ???? ????? ?? 95?
7
H0?d?0 H1?dlt0
?0.05
????? ????? ???? ????? ??????
????? ??????? ?????? ??? t, ????? ?????
TDIST(2.41,9,1)0.0198
EXCEL
t(9,0.05)1.833 ??-????
????
t(9)2.41, plt.05 (?? tgttc1.833) ??? ???? ?????
?? H0 ????? ???? ????? ?? 95 ?????? "?????
?????? ?????". ??????, ?? ???? ???? ?????? ????
???? ???? ????. ?????? ?????? ??????? ???? ?????
???? ????? ???? ????? ??????.
8
??? ??????, ????? ?? ?? ?????? ?????? ?-EXCEL.
TTEST(Array1, Array2, tails, type)
1??-???? 2??-????
1?????? ??????
9
?????? ??????? (paired samples) ???? ?? ??? ?????
?????? ???? ???? ?????? ????????. (????? ?? ???
??????? ????? ?????? ????????) ???? ??????? ??
??????? ??? ???????? ??????? ????? (???? ??????
?????), ????????? ???? ??? ???? ?????. ??? ????
???? ???? "?????" ????? ???? ???? ??????? (??
????? placebo, ?? ????? ???...). ?????? ?? ???
??? ???? ???? ?"?????", ?????? ?? ????? ???????
??????? ???? t ??????? ?????? ???
??????. ????? ?? ????????? ????? ?? ???, ??
???? ???????? ???? ???? ?? (?? ????? ????). ?????
n ??? ???? ?????? ??? ???? ???????. ???? ???,
???? ?? ?? ????.
10
?????
????????? ???? ??????????? ????? ????? ??? ????
???? ????? ???? ?????? ?? ????? 5 ?????? ?????
???? ??? ??????, ???? ????? ?????? ??????. ?????
????????? ???? ????? ?? ?????? ??????, ???? ??
???? ????? ???? 200 ???????? ??? ????? ?-100
????? ??? ????? ???? ????. ??????? ???? ????? ???
???? ???? ???? ??????? ?????? ?? ????? ??????
????? ???? ??? ?? ????? ?????. ????? ???? ?????
????? ????????, ??? ??? ????? ????? ??????? ????
????? ?? 95, ?? ????? ??????? ???? ??? ???? ???
????? ????? ?? ?
H0?d?5 H1?dgt5
?0.05
TDIST(2,99,1).024
t(99)2, plt.05 ??? ???? ????? ?? H0 ...
11

• ???? t ??????? ?????? ????? ?
• ??? ?????? ?? ???? ?????? ????? ???????
  (test-retest).
• ?????? ?? 2 ?????? ????? (???? ???? ???? ?????)
  ????? ???????.
• ?????? ?? ???? ?????? ??????? ????? ?? ???????
  (matched pairs).

12
????? 2???? t ??????? ???? ??????(t-test for
independent samples)
?? ????? ????? ???? ???? ?????????? ?????? ?????
???? ????? ?-2 ?????? (????? ?????), ??? ?????
???????? ???? ????? ??? ?????????. ???? ???? ??
?????? ????? ?????? ??? ???? ??????? ????? ????
?????? ???????. ?? ??? ???? ??? 2 ??????, ???
????? ????????? ???? ???? ????? ??????? ??????
???? ???? ?-0.
13
????????? ?????????
????????? ????? ?? ???????
??????? ????? ?? ?????? ??? ???????
?? x1 ?- x2 ???? ??????
14
??? ???? ??????? ????? ??, ???? ???? ???? ?? 2
?????? ???????
?? n1 ?- n2 ?????? ?-30 ?? ???????? ???????
??????? ??? z ????? ???????. ?? ?1 ?- ?2 ??
??????, ???? ????? ???? ??????? ???????? t.
df
15
??? ??? ???? ?
???? ?????? ?? ????? ??? ?????? ???????, ??? ???
?????? ??? ???? ??? S1 ???? S2 ??? ????. ??????
???? ????? ?????? ?"???" ???? ????? ?????? ??
??? ????????
16
???? ? ?? x1 ?- x2 ???? ??????, ?????? ??????
???????
?????? ???
17

• ????? ?????.
• ????? ?????? ????????
• ?????? ????? ????? ?? ?????? ??????? ???? ?????
  ?-2 ??????. ????? ??? ????? ????? ????? ??????
  ?????? ????? "???" (placebo). ???? ?????? ??????
  ?? ??? ??????? ??????? ??? ??????? 2 ??????? ?"?
  ???? t ??????? ?"?.
• ????? ?????? ?? ????? ??? ???? ?? ?????? ??? 2
  ???????. ?????? ?????? ??? ????? ?? ????? ?????.
• ???? ??????? ?? ???? ????? ???.
• ?????
• ????? ?????.
• ??????? ????? t ??' ??? ????' ??????? ?? n?30.
• ????? ???? ????? ????/??? (?????????? ???????
  ???).
• ?????? ??????? ??? ??????? ???? ????? ???? (????
  ?? ????? ????? ?????).

18
????? ???? ????? ??? ????? ?? ???? ?????, ????
12 ????? 14, ??? ???? ??? ???? ???? ?????? ???
???????. ??? ??? ????? 10 ??????? ??? ????. ?????
???????? ????? ??????? ??????? ?? ???? ??????
???? ????? ?? 95, ?? ???? ?????? ?????? ???????
?????? ??????? ????? 1 ????? 2
n1n210
H0?x ?y H1?x? ?y
?x- ?y0
????? ??' ??????? ?????? ???????
?0.05
0.62TDIST(0.5,18,2)
t(18)0.5, pgt.05 ??? ?? ???? ????? ?? H0 ?????
????? ???? ??? ???????.
19
?? ?????? ?????? ???????, ???? ???? ?? ??? ?-p
?-EXCEL.
TTEST(Array1, Array2, tails, type)
2?????? ???? ??????
1??-???? 2??-????