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197045, . -, ., .17/1; . +79119221982
pan287@users.mns.ru
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197045, .-, ., .17/1; . +79312027052
palkinks@mail.

- , The article considers the method of interval estimations of results of implementation of system of a single criterion-referenced strategy oriented test tasks of the closed type with a single correct answer, based on the use of properties of dichotomicity answer trainee
- ; ; ;
criterion-referenced test; the point estimate; interval estimate; confidence interval
, [1]. , , , , [1].
. - ; [1]. , ; [1].
: 1) , ; 2) , ; 3) , , ; 4) , . ( ).
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- - , ( ) [1]. - - , , , . [1].
. [2,3,4,5,6], [7,8,9], ( ) [10,11,12,13,14].
( ). , .

, , [15]; [16] [17].
, (), .

X -
= ^, (1)

: I (I = 1, ) - , - , ( = 0,1) = 1 - , = 0 - .
(1) , .
, , , .
, - ( -, - ..), .

( . 1)
./' (./'...../,) (2)
= 0,1 ( ( = 1 - , = 0 - ). .
1
= 12
4 5 6 9 ./ /11 112
1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 0 1 1 1 1 1 1 1 1 1 1
3 1 1 1 0 1 1 1 1 1 1 1 1
4 1 1 1 1 1 1 1 1 1 1 1
5 1 0 1 0 1 1 1 1 1 1 1 1
6 1 1 1 1 1 1 1 0 1 1 1
7 1 1 1 1 0 1 1 1 1 1 1
8 1 1 1 1 0 1 1 1 0 1 1 1
9 1 1 1 1 0 1 1 1 1 1 1 0
10 1 1 1 1 1 0 1 1 1 1 1 0
, (2), 1 ( /( = 1).
, . 1 6 = (/, ,/2).
: (;../,../..../ ='10,,12). 1

= X / (5=1=). (3)
=!
*.1
(2) :
1) , , ;
2) , (2) .
^ , ()
() = >- = ^~, (4)
!( - )!
: - , = 1- - , - , , - , - - , .
()
() = , (5)
: - , = 1- - , ( = 1, ( - )) - / ,
.
:, ,
()
5=
() = ( ... , ... ) = () +... () +... () = X^ , (6)
5=1

5=
X = - ; (7)
5=1
] = 0
= 1 > . (8)
+1 = 1
, ] , 5 :
1. , (] = 0), 1 , (/ = 1).
(=0) /, .. = 0 :
=1, = .
2) ( /\
/) ( /,
= 0).
, . {) (4)
5=
() = ()() = -+1 , (9)
5=1
= 1 -
5=
(/) = - (1 - )+1 . (10)
5=1
(9,10)
,

= /(/I) = (), (11)
(0,1) (0,1)
() / = (/,......./(.../),
.

-/ \+1 X ' h _ _
(1 -) Ps ^ max,
7=1
p (0,1), = 1, ,
h = 1, ( - ), h = -
(12)
(12) Solve ( ) Microsoft Excel.

, .
12 , . 1. . 2.
2
, 1
s=1
- n hi h2 hs Ah = hmax - hmin p (2) p (12) (10)
1 12 0 12 - - 0 1,0000 0,9600 0,0150
2 12 1 1 10 - 9 0,9167 0,8757 0,0491
3 12 1 3 8 - 5 0,9167 0,8875 0,0443
4 12 1 5 6 - 1 0,9167 0,8917 0,0425
5 12 2 1 1 8 7 0,8333 0,7951 0,1003
6 12 2 2 5 3 3 0,8333 0,8129 0,0846
7 12 2 4 4 2 2 0,8333 0,8141 0,0836
8 12 2 4 3 3 1 0,8333 0,8158 0,0823
9 12 2 4 6 - 1 0,8333 0,8316 0,0403
10 12 2 5 5 - 0 0,8333 0,8333 0,0397
, = /?,
, . 2 : , .
, (12) (2) (4).

5=
= - (1 - )+1
(0) 5=1
p ^ max Cknpn k (1 - p)k+1 phs ^ min .
F(p,n,k,{hs}) = C^(1 -p)k+1 phs . ()
s=1

p, q , n, k = const
^. (4)
hs = var
, (14) max min (13)
s=m
phs ,
s=1 s=m
(7,8). min phs .
h =var s s=1

I
min a = n a
i=1 V i=1
.. , . (7)
j s=m
s=m hs n-k
min phs = mpm s=1 = mp m . (5)
h =var s s=1
s=m
max phs . , (14) (7)
h =var s s=1
s=m
max phs = (m -1)p + pn-k-m+11. (6)
h =var [
h =var s=1

p = arg max c pn-k (1 - p)k+1 ph
s=1
(8) ,
= ~
F(p,n,k, {,}) = -+1 1 = (1- 1+1 7 = 0 ,(17)
s=1
s=m
F(p,n,k,{hs}) = -+1 = Cknpn-k(1-p)k+'(k + 1)pk+1 jn = 1, ()
s=1
.
(4,17,18) :
1. (4):
()_ [- (1 - ) ]
dp dp d [ pn-k (1 - p)k -
dp
l = n - k, g = k, (19)
d [P (1 - P)s -
= G,
= G. (9)
dp
(20),
= G. ^0)
1-1 -1(1 - 1) 1 =
=
1+
I g,
-
= -
(22)
2. (17):
dP( )
- (1 - )+1
'(1 - )
= 0.

= 0 .
(23)
- ( 1 ^
I = - +-= ( - ) I 1 + I, = +1, (23)
^ )
(20). (21) 1^ ,

=
( - ) I 1 + - .
^ ) - -
+ / \ ( 1 - + & ( - ) | 1 + .+ +1
(24)
,
]. ], (24),

(7,8) 5 = 1. , 5 =-------------= -1


------- .

3. (18):
()
- (1 - )+1 ( +1)

'(1 - )
= 0,

= 0 .
__ ( 1
= - + -- = ( - ) | 1 + -
+1 ^ +1 (20). (21) ,
(25)
= +1, (24)
/
-
=
1 +
+ -
1
+ 2
(26)



(26) (22)
- - -
=----------
_1 n2(k + 2) + n
k + 2
(7)
, j = ,. . ,
(26), (7, 8) h = const .
- -
, h =
k rr k
- .
+1 + 1 +1 +1
,
= , = 2, . , = = ( -1) --------- = + 2
' + 1 + \
= ( + 2). , (26),
, - ( + 2) - , ,
3 =-----=---------------= , ..
+1 +1
.
. -3, , (26), = ( + 2) = 15, = 3
= (.../...../ .) (1.1.1..1.1.1..1.1.1..1.1.1) (27)
, (24),
./ = (..,... .) (1.1.1.1.ї.!. 1.1.. (28)
, (27) = 15, =3
= 0,0105
p, Ap =
n (k + 2) + n
(22), (22), , . 3.
3

n h2 hs h4 Ah = hmax - hmin p (,4) p (7) Ap
5 3 9 0,00 0,7690 0,00
5 3 3 4 3 0,00 0,7 0,0
3 5 3 3 3 3 3 0 0,00 0,795 0,005
4 5 3 3 5 4 - 0,00 0,795 0,0015
5 5 3 4 4 4 - 0 0,00 0,000 0,0000
n
. 3 , p (7) (1.4) j = , : n
1) h = 1 , (17), jn = 0;

2) h = , n = ( + 2) (18), j = 1.
, (12) :
1) :
___________( - )_________ ( ~ + 1)F2(n-k+1), 2, 1-/2 ^9)
^ (n ) + ( + 1)^2(+1),2(-),1-s/2 + ( + 1)^2(-+1),2, 1-s/2
n - , - , Ffta -
F fg ;
2)
, n
,
fp-^JVp+^Jv], (30)
V V n
V '/
: _ - (1 - / 2).
, , .
:
1. . . . - .: , 2009. [ ] URL: http://www.ege.ru/dict/dict1.htm ( : 21.03.2014)
2. .., .., .., .. TestMaker ACT-Test // (Educational technology & Society) - 2007. - . 10 - 3.- .336-360. ISSN 1436-4522. URL: http://ifets.ieee.org/russian/periodical/journal.html
3. .., .., .. // (Educational technology & Society) - 2012. - . 15. - 1. - . 537-554. ISSN 1436-4522. URL: http://ifets.ieee.org/russian/periodical/journal.html
4. .., .. TestMaker // (Educational technology & Society). - 2010. - . 13. - 1. - . 281-292. ISSN 14364522. URL: http ://ifets.ieee.org/russian/periodical/j ournal. html
5. .. , . //
(Educational technology & Society) - 20. - . 16. - 2. - . 361-37i. ISSN 4-4522. URL: http://ifets.ieee.org/russian/periodical/journal.html .
6. .. ( ) / .. , .. , .. , .. ; . .. . - : , 2005. - 126.
7. ., A.B. // (Educational technology & Society) -2007. - . 10. - 1. - . 276-28. ISSN 4-4522. URL: http://ifets.ieee.org/russian/periodical/journal.html
8. .., .. . // (Educational technology & Society)- 202. - . 15. - 1. - . 424-435. ISSN 43-4522. URL: http ://ifets.ieee.org/russian/periodical/j ournal. html
9. .., .., A.H. // (Educational technology & Society) - 202. - . 15. - 1. - . 537-554. ISSN 4-4522. URL: http://ifets.ieee.org/russian/periodical/journal.html
10. AX. A // (Educational technology & Society). - 202. - . 15. - 4. - . 457-479. ISSN 43-4522. URL: http ://ifets.ieee.org/russian/periodical/j ournal. html
11. .. // (Educational technology & Society) - 20. - . 16. - 4. - . 361-37i. ISSN 4-4522. URL: http://ifets.ieee.org/russian/periodical/journal.html .
12. A.B. // (Educational technology & Society). - 2007. - . 10. - 1. - . 271-275. ISSN 43-4522. URL: http://ifets.ieee.org/russian/periodical/journal.html .
13. AX., .. - // (Educational technology & Society). - 20. - . 16. - 1. -. 575-585. ISSN 4-4522. URL: http://ifets.ieee.org/russian/periodical/journal.html .
14. A.H., A^., P.P. // (Educational technology & Society). - 20. - . 16. - 4. - . 365-37i. ISSN 4-4522. URL: http://ifets.ieee.org/russian/periodical/journal.html .
15. .. : . - : , 2002. - 432 . [ ] URL: http://www.twirpx.com/file/i0i903/ ( : 21.03.2014)
16. .. : . - : , 2007. - 214 . [ ] URL: http://www.twirpx.com/file/639729/ ( : 21.03.2014)
17. .., B.A. . - , 2000. - 168 .