+ All Categories
Home > Documents > Practical Applications of Posterior Predictive Model …Practical Applications of Posterior...

Practical Applications of Posterior Predictive Model …Practical Applications of Posterior...

Date post: 24-Jan-2021
Category:
Upload: others
View: 4 times
Download: 0 times
Share this document with a friend
44
Practical Applications of Posterior Predictive Model Checking for Assessing Fit of Common Item Response Theory Models November 2003 RR-03-33 Research Report Sandip Sinharay Research & Development
Transcript
  • Practical Applications of Posterior Predictive Model Checking for Assessing Fit of Common Item Response Theory Models

    November 2003 RR-03-33

    ResearchReport

    Sandip Sinharay

    Research & Development

  • Practical Applications of Posterior Predictive Model Checking for

    Assessing Fit of Common Item Response Theory Models

    Sandip Sinharay

    ETS, Princeton, NJ

    November 2003

  • Research Reports provide preliminary and limited dissemination of ETS research prior to publication. They are available without charge from:

    Research Publications Office Mail Stop 7-R ETS Princeton, NJ 08541

  • �� �@�!�������

    � ^&KM\���[ QM\�[��&L J�� LOJ L ]S\�d R_\_N�^�J�_\f]_QM\7^�RZT����� V�� L� I�J��MJ�KM\7RZKM\�c�\��O^�N=\�K3I R_\6I�� a�^��MJ�I�J�LOd ^���d ^0KM\� [ QM\�[��&L J�� ]_^0^�� \��0L� ]� LOJD]_QML����\�OK \�c�\7J ��^�R�]SQM\!ZLOd N��O\fd ^&KM\��"7X+JM^�]:]_^#ZN=\7I�� ^�� ]SQ�\R_\�[7\�J"]$� T�$������\�Z]_\7K [7^�d N�� LO[6I#]S\7KPd ^&KM\��"�� V QM\&%('*)�+-,�.0/1'2.3%4.�,$5�/16�+7/98�,;:

  • 5��1+����� � &%/2� &; &�=�!�

    V QM\ I���]_QM^�R�]SQMI�J��V � I ]_]_QM\[ b�^�QMJ�_^�J`X H&QM\�� e"T�� I�e�\7RZd I�J X��-I�� H&]_\7R_J X�a�\7L"����^�RSI�JR7X��:I�JU L���J�^�R7X=b�^�QMJ���^�JM^���Q=��\�X�Y I��R���^����OI�JMK`X�I JMK� Q�I R$�OL \��/\�[ L����^�R9]SQM\�LOR LOJ c I����MI�e��O\ I K�c&LO[7\W� V QM\I���]_QM^�R-I���Z^d[ L"_QM\ ]S^ ]SQ�I J�� i \7L ]_QcT ^�����Q ]S^�J ��^�R�NMR_^!c&LOKML J��$]SQM\EK�I ] Id_\@] ��^�R ]SQM\�e�I�ZLO[ $�"L��"��]S\Z]�� V QM\ I���]_QM^�R3��RSI ]_\�a���"� T)I�[��"JM^*[O� \7K���\�]SQM\�QM\�� N ^��?� ^0[ QM\��� \fH&]_\7RZJ I�JMK i LOd��RZT�\7R [ L ]SQNMRZ^0^���RZ\6I�K�LOJ����

    m m

  • ��� �������

    ������������

    � ^0K�\���[ QM\7[��"LOJR�MX`^�R-I�$Z\�Z_LOJR��]SQM\ �M]�^��BI d ^&KM\� X�L�-I [�R$�M[�L I���N�I�R ] ^�� I J"T ] I ]_L�Z]_LO[7I��I�J�IW� T=_L"�� T \���^�R_\ d I��"LOJ�� I�J T [�^�JM[��"��_L ^�J� ��RZ^�d ]SQM\ I NMN��OL [6I ]_LO^�J ^�� I�Z]SI ]SL"Z]_LO[6IW��d ^0K�\��/]S^ IK�I ]SI�_\@]6X/I�JDL J"c�\� ]SL���I ]S^�R _QM^��R�OK I�Z_\�Z:]SQM\&�M]�^��W]SQM\ d ^0K�\��/]S^5d I���\_Z�MR_\f]_Q�I ]�]_QM\fd ^0KM\�[6I J \0�0N�� I�L J I�KM\��V��I#]S\�� T ]SQ�\ LOd N=^�R ] I�J ] IW_N�\7[�]$ ^���]_QM\ K�I ]SI _\�]�� H0\7RZLO^��R:d L"Z�M] �9�I�L��"�MR_\E^��]SQ�\fd ^&KM\��]_^�\��0N��OI�LOJ L d N�^�R ] I�J ] I�_N�\7[@]�:^��B]_QM\fK�I ]SI ]SQMI ]:I�RZ\f^��WNMR_I�[�]_LO[7I���L J ]S\7RZ\� ] � ZQM^���� KR_\$��� ] L J ]_QM\�RZ\7N��OI�[7\�d \�J"]-^�R�\��&]S\�J�_L ^�J ^�� ]SQM\Ed ^&KM\���X�L"� N=^�Z_L e��O\W� U c�\7JDLf�BI d ^0K�\��+Q�I�-e=\�\7JI�NMN�^�L J"]_\7K I�9]SQM\ ��J�IW�+d ^&KM\�� ��^�R�I�JPI NMN��OL [6I ]_LO^�J X�L ] L"9LOd N=^�RZ] I J"] ]S^ I�$Z\�$-L ]$O��]�]_^ e�\�II[ I�RZ\^���L ]$ �OLOd L ]SI ]SL ^�J�We�\��^�RZ\�d I��"LOJR�$I�J T5LOJR��\�R_\�JM[7\��

    �^�R Z]SI ]SL"Z]_LO[6IW�=d ^0K�\��� ��_\�K LOJ�N� T&[ QM^�d \�]SRZLO[7X�I�JMK5\_N�\7[�L I��"� T LOJ�L ]S\�d RZ\�_N�^�J�Z\�]SQM\�^�RZT���� V�� X([ \��� k \� ] I�eR�OL�ZQM\7Kh ] I ]_L�Z]_LO[7I��`]S\�[ QMJML��V�M\3��^�R�I�Z_\$_L J���d ^0K�\��l�M]�KM^ JM^�]�\��0L� ] \0�0[7\7N0] ��^�R]SQ�\ ZLOd N��O\Z] d ^0K�\��� � c I�J K�\7R �+LOJMKM\�J�� � I�dfeR�O\�]_^�J`XlFIH�HLK0XMN]�3F*J � � V QM\ Z] I JMK�I�RZK���� ]S\� ]�-KM^JM^�] I�NMNR� T_�MJR�O\�Z�]_QM\-JV�Md�e=\�R�^�� L ]_\7dd L"b_d I����7� X-J�I�� T=ZL� ^��`RZ\�_L K���I��"WQ�I6c�\ RZ\7[�\7L c�\7K5^&[7[7I�_L ^�J�I��I ]Z]S\7J ]_LO^�J ��c I�J KM\�J�� ^����O\�J"e=\�R$�MX F*H�Q�g�M � ^��O\7JMI�I�R7X F*H�Q�jRM]� \7L"_\�R7XGFIH�H�J � X�eR��]�]SQ�\fI�NMNR�OLO[7I ]SL ^�J�Q�I6c�\�e�\7\7J �OL d L ]S\�Kl� V QM\�R_\���^�R_\ X�]_QM\7RZ\ \��0L� ]�O_L"��JML"�M[6I�J ]O_[�^�N�\�^W�G�a�MR ]SQM\�R9R_\�Z\6I�RZ[ Q LOJ�]_QML��I�RZ\6IR�

    V QM\ N=^�Z]S\�R_L ^�R�NMRZ\7KML [�]SL c�\fd ^&KM\���[ QM\7[��"LOJR���YWY � � d \�]_QM^&KDL��I�N�^�N��R� I�R T I6T�\�ZL I�Jd ^0KM\�`[ QM\�[��&L J�� ]_^0^��`e=\�[6I��R_\�^�� L ]� ZLOd N��OL [7L ] T�X� ]SRZ^�J��$]SQM\�^�R_\@]SLO[7I��`e�IW_L��X�I�JMK)^�e c&LO^���9L J ]��ML ]SL c�\I�NMN�\6IW�1� V QM\$d \�]SQ�^0K NMRZLOd I�R_L"� T)[7^�JR_L� ]� ^���[7^�d N�I�RZLOJ���]_QM\$^�e�Z\7RZc�\7K /16$\�+-,$55L\�+1\�X0]SQ�^�_\�N�R_\7K�LO[�]_\7K5e T ]SQM\�d ^&KM\���X���ZLOJ��fI�JV�Mdfe�\7R ^�� 5�/�)*6�.�,-%R\�B]6�^&:

  • ]S^!Z�M[7[�\�$-^�� ]S\�J L" I__\�]�^���KML"_[7RZ\7N�I JM[�T d \6I�Z�MR_\9]SQ�I ]�I R_\ QML���Q�� T �OL"��\�� T ]_^$KM\�]_\7[�]�]SQ�\EIW_N�\7[�]$^��B]_QM\fK�I ]SI ]_Q�I ] ]_QM\fd ^0K�\���[6I�JMJ�^�]�\0��NR� I�L JcSI ]_L�g�I�[�]_^�R_L"� T��O4]:L"-N�^�Z_LOeR�O\E]_Q�I ]�I d ^&KM\��KM^&\�JM^�]:I�KM\��V��I#]S\�� T \0��NR� I�L JDI�K�I ]SI�_\�]7X+e���] Z^�d \�KML�Z[7R_\�N�I�JM[@TDd \6I�Z�MR_\�[ L�����KM\@]S\7[@]:]SQM\ d L�g�M][ QML"�O\E_^�d \�[�^�J�� ]I�

    H0LOJMQMI�RSI6T3I�JMK b�^�QMJ�_^�J � g�i�i�j � I�NMN�� LO\� ]SQ�\ N�^�Z]_\7R_L ^�R�NMR_\�KMLO[@]SL c�\ d ^0K�\��W[ QM\7[��"L J��d \�]SQ�^0KD]S^)I�Z_\$ ]SQM\_�M]�^�� ]SQM\$N�^�N����OI�R��� V d ^&KM\��!��Fk X�g kSX/I�JMK j�Y�� d ^0K�\�� � ]SQMRZ^�����Q3I_\�R_L \��^��P_LOd;��� I ]_LO^�Jh ]��MKML \�� V QML�-N�I�N�\7R I�NMN�� LO\� ]SQ�\ YWY � *d \�]_QM^&K`X4[ L ]SQP]_QM\�K�L�_[�R_\�N�I�JM[@Td \6I�Z�MR_\O��^��MJMK ��Z\�a���+L J�]SQM\EZLOd&���OI ]SL ^�J< ]��MK�LO\��XM]S^f]_QMR_\�\�RZ\6I��=K�I ]SI$\0��I�d NR�O\�����JM\E��^ I��=QM\7RZ\L��]S^5KM\�d ^�J�Z]_RSI ]_\�]SQM\;��_\��a���OJM\$ ^��B]_QM\ KML�Z[7RZ\7N�I�J�[�T d \6IW$�MRZ\��L JDKM\�]_\�]SL J���d ^0K�\�� d L�g�M]-LOJR_\7I��+K�I ]SI$I�NMN�� LO[6I#]SLO^�J���

    d N�^�RZ]SI�J ] I�NMNR�OLO[7I ]SL ^�J�-^��W]SQM\$YWY � d \�]_QM^&KDLOJD\7KR�M[6I ]_LO^�JMI��BI�Z_\�Z_d \7J ]�LOJM[���MK�\�O�MeMLOJ I JMK3H&]S\�R_J �gF*H�H�S � X+H0[ QM\7L JM\��X��-^�L�� ]SLOJR��X I�JMK T ^&^�dd_d I �gF*H�H�H � X+b�I�J�$Z\7J`X V �M\7RZ�OL JM[���� X� \���OKM\�R$�X I�J�K ��\!T ^&\7[�� ��g�i�i�i � X ��^�L�� ]_LOJ�� I�JMK � ^�� \7J�I�I Rd�gF*H�H�K � X ��^�L�� ]_LOJ���� g�i�iRF � X � I�R_L"I�JMK � I�RZL�d��g�i�i g � X �^*�DI�JMK�D �OI�d� g i�i�j � X+I�JMK c I�J���JMJMI ��g�i�i�j � � �-^*[�\�c�\7R7X�\6I�[ Q3^�� ]SQM\_\I�NMNR�OLO[7I ]SL ^�J�9L"�ZN=\�[7LOI��OL�7\7K I�JMK)JM^�J�\�^���]SQM^�Z\ ��^&[��R_\�-^�J��� V d ^&KM\���� V QML"-RZ\�_\7I�R_[ Q ] I�� \��Id ^�R_\&��\7JM\�RSI��BI NMNMR_^�I�[ QDLOJ I ]Z]S\�d N�]_LOJ�� ]S^5NMRZ^�c&L KM\ R_\_\6I R_[ QM\�R$E[ L ]_Q I d ^�RZ\�[7^�d NMRZ\7QM\�J�_L c�\]S^&^��"�&L ] ��^�R IW$_\$ZLOJ��d�M]�^��G�� V d ^0KM\���

    H0\7[@]SLO^�J gPKM\�Z[7R_L e=\f]SQM\<Z] I#]SL� ]SL [6I�� d ^&KM\���L J �� V ]SQ�I#] I�RZ\�^���LOJ ]S\�R_\Z] L J

  • ]SQMI ] L"O��L c�\7J ]_^�� LOJMKML c&LOK���IW����? JMKML c&LOK���IW����Q�IW�I!�MJML c I�RZL I ]_\:NMR_^W��[7L \7JM[@T �I�eML"�OL ] T � NMI�RSI�d \�]_\7R��� ]_Q�I ] ]_QM\ I�Z_\$_d \7J ]EI ]Z]S\7d N�]$-]S^ d \7I�$�MRZ\���4]_\7d�� QMI�:I [�^�R_RZ\�_N�^�JMK�LOJ���L ]S\�d NMI�RSI�d \�]_\7Rc�\�[�]_^�R��!X d \6IW$�MRZLOJ�� I�_N�\7[@]��^��B]_QM\�L ]S\�d � L�� \EL ]� K�L� [���� ] T�X�KML�Z[7RZLOd LOJ�I ]_LO^�J N�^*[ \�R7X \@]S[W� �^�R_L d NR�OLO[�L ] T�X"]_QML��N�I�N�\7R9IW$$��d \ ]SQ�I ] \�c�\�RZT5L JMKML c0L K���I���R_\�[7\�L c�\9\6I�[ Q L ]S\7d ��]_QML�?[ L��"�=JM^ ]9R_\Z]SRZLO[@]]SQ�\f[7^�J�[����R_LO^�J� ^��B]_QML�3Z]$�MK�T�X QM^*[ \@c�\7R � ���+\�]���� � KM\7J�^�]S\�]_QM\&Z[7^�RZ\f^�� ]_QM\���k ]SQ L JMKML c0L K���I��+]_^]SQ�\���k4]_QPL ]S\7d � V Q�L� NMI�N=\�R-K�\6I��"�[ L ]SQ)KMLO[ QM^ ]S^�d ^����_[�^�R_\ ^�J�� T�X�]SQMI ]�L�7X�]_QM\;Z[7^�RZ\�L� FEL"� ]_QM\\���I�d LOJ�\7\E��^�]9]_QM\ L ]_\7d [�^�R_RZ\7[�]7X�I�JMK i ^�]SQM\�RZ[ L"_\��

    V QM\fJM\0�0]�Z]S\�NDL� ]S^5IW$$��d \�I NMR_^�e�I�eML"�OL� ]SL [:[7^�d N=^�JM\7J ]�� ����� ��� ������ � � \0�0NMR_\$_L J���]SQ�\NMRZ^�e�I�eML"�OL ] Tf^��`I�[�^�R_RZ\7[�] R_\_N�^�J�_\-^�� ]_QM\���k4]_Q L JMKML c&L K���I���]_^�]_QM\���k ]SQ L ]S\�d LOJ$]S\�R_dd�^W����� I�JMK���2�

    �^�R \���I�d N��O\ X�]SQM\�j2k N�I RSI�d \�]_\7RO�O^���L�Z]_LO[�d ^&KM\�� ��j�Y �YM �+^�R_K X FIH�Q�i � Q�I��]SQMRZ\7\�L ]_\7d N�I�R_I�d \�]S\�R$��^�R \6I [ Q L ]_\7d)X�]SQ�I#] L"7X� �� �"! � �$# � �$% � � X&! � X'# � X�I�JMK(% � RZ\�_N�\7[@]SL c�\�� T)e=\�LOJ��$]SQM\ $� ^�N�\�X�KML)� [��� ] TI�JMK#���M\$_L J�� NMI�RSI�d \�]_\7RZ-^�� L ]S\�d*�(M IW$$��d L J�� ]_Q�I ] ]SQ�\�NMRZ^���[7L \7JM[�LO\����9-I�RZ\U�MJ�LOKML d \�J�_L ^�J�I���X]SQ�\�d ^&KM\��`\0�0NMR_\$_\ ]SQ�\�N�R_^�e�I eML�� L ] T ^�� I [�^�R_RZ\7[�]�RZ\�_N�^�J�Z\�IW

    � ����� �+� �����,�� �.- � ����� � F � ������/� � % �10 ��F324% � � �O^���L ]�5�6l�"! � �����'24# � �$� � �gF �

    [ QM\�R_\ �O^���L ]�5�6��87 � 9;:=A@CB6"D 9;:=A@CB �X �Od ^� ]�IW���W^�� ]_QM\ N�^�N����OI�R�d ^&KM\��" LOJ��� V d I�� \ ]_QMR_\�\5I�KMKML ]SL ^�J�I��BIW$$��d N�]_LO^�JR��

    V QM\!��R$ ]�L�:]SQ�I#]�I���� L JMKML c0L K���I��":I�RZ\_Z] I#]SL� ]SL [6I��"� T LOJMKM\�N=\�JMKM\�J"]�� V Q�\ Z\7[7^�JMK L" ]_Q�I ] ��L c�\�J]SQ�\�NMR_^W��[7L \7JM[@T3c I�RZL I�e�� \��X�]SQ�\�^�e�Z\7RZc�\7K ^���]_[7^�d \�U��^�R�KMLfe \�R_\�J"]�L ]_\7ddfI�RZ\ LOJ�KM\7N�\7JMK�\7J ]I�V QML"�L��[6IW���O\�K ]_QM\�IW$$��d N�]_LO^�J3^��E>�'*6$\�>b/9B45=,-%(,�B45=,�B]6�,�E V QM\ ]SQ�LOR_K I�$Z�Md N�]SL ^�J L"�]_Q�I ]E^��:

  • V QM\ I�e=^!c�\$]_QMR_\�\ d ^&KM\��:I�RZ\f]SQM\ d ^� ]:N=^�N���� I R�d ^&KM\���L JDN�ZT&[ QM^�d \�]_R_L [��I�JMKD]SQ�\]S\Z]_LOJ�� [7^�d N�I�JML \�-I�R_^��MJMKP]_QM\ [�^�RZ�OKc��Z\E]_QM\�Z\fd ^&KM\�� ^�N�\7RSI#]SLO^�J�I���� T�� �:J�\�^�e �Z\�[�]_L c�\�LOJ ]SQML"N�I�N�\7RO[ L��"�+e=\ ]S^d��JMK ^���]-L"� ]_QM\�Z\�]SQ�R_\7\�d ^0KM\�� [6I J N=\�RZ��^�RZd I�KM\��=�MI ]S\� T ��^�R�R_\7I���I�$Z\�$Zd \�J ]K�I ]SIR�

    X ] I�J�K�I�R_K)JM^�RZd IW� N�^�N����OI ]SL ^�J5KML� ]SRZLOe���]_LO^�J�I�$Z�Md N0]SLO^�J`X

    ��� � � ���� ��i �IF � �3� F � g �������=��R�0\� ]SQ�\UZ[6I�� \�^W��]_QM\ NMR_^�eR�O\7d ��^�R9]SQM\!FkSX�g k X�I JMKPj�Y � d ^&KM\�1�Y JP^ ]SQM\�RO[�^�RZK�7X�]SQ�L�9N�I�N�\7R �M]$]SQ�\�d ^&KM\��b�I� LOJ ��^����OI�JMK`X F*H�H�i�e �

    ������ 6 �

  • �����������

    ����������������������������! "�#������%$'&(��$)�������*�����+��,�-�(�.���/�/$������102���43502&�6879��

    �/\@];: �1< � = � KM\7JM^ ]S\�]SQ�\E�OL�� \�� LOQM^&^0K KML"Z]SRZLOe��0]SLO^�J

  • ��\�JM\7R_I ]S\�K)^�J ]SQM\��4k4]_Q5KMRSII[ X�� F � g ��������� �bX J T<ZL���J�L"��[7I�J ]9KML"e=\7RZ\7JM[�\�e�\�]-[�\7\7J ]SQ�\�^�e�Z\7RZc�\7KKML"_[7RZ\7N�I JM[�T)I�J�K)]_QM\ R_\7NR�OLO[7I ]S\�K5KML�Z[7RZ\7N�I�J�[7LO\-L JMKML [6I ]_\� I N=^�$_L e��O\��I L�����R_\�^���]SQ�\�d ^&KM\��7�

    �RZ^�d ]_QM\ I e=^!c�\ KM\_[7RZLON�]_LO^�J X�L ]�L� [�� \6I�R:]SQMI ] ]SQM\ YWY � d \@]SQM^&K [7^�dfe�LOJM\�c�\7RZT[�\����b[ L ]_Q3]_QM\ � I R$��^!c [ Q�I�LOJ � ^�J ]S\ I�R$� ^ � � � � I��"��^�R_L ]SQMddd�1D:L��"�V7X ��L [ Q�I�R_KR_^�J`X �H0NML \���\�OQ�IW� ]S\�R7X�F*H�H�JRM=D:\�� d I J`X I�RZ�OLOJ X"H&]S\�R_J`X�� ����eMLOJ`X(FIH�H h � � X-J � � I��"��^�R_L ]SQMd ��\�JM\7R_I ]S\KMR_I*[O3��R_^�d ]SQM\EN=^�Z]S\�R_L ^�R KML"Z]_R_LOeR��]SL ^�J ^W� = X4[ QMLO[ QDL"-]_QM\U��RZZ]E ]S\�N L J ]_QM\ YWY � d \�]_QM^&Kl�V QM\EJM\��&]E ]S\7NPLOJ ]SQM\Ed \@]SQM^&KPL"�]_^

  • [7^�J�_L KM\7R�I�J T5RZ\6I�� L��7\�K KML�Z[7R_\�N�I�JM[�LO\��H0LOJMQMI�RSI6T I�JMK b�^�QMJ�Z^�J � g�i�i�j � NMR_^!c&LOK�\�:I d ^�RZ\EK�\�] I L��O\�KPKML"_[��$ZLO^�J ^W� ]SQM\EN=^�Z]S\�R_L ^�R

    NMRZ\7KML [�]SL c�\�[ QM\7[��V� V QM\�T)[�^�c�\7R�L"$Z�M\�3�OL�� \��I � ]SQM\ER_\� I ]_LO^�J�ZQMLON ^�� ]SQM\_\�[ Q�\7[��V�[ L ]_QP[��OI�$ZLO[7I��]S\Z]_LOJ��MXG�e � ]_QM\�\�e \�[�]�^W� NMRZLO^�R�KML� ]SRZLOe���]_LO^�JR9^�JP]SQ�\ERZ\�$�R� ]�-^�� ]_QM\fYWY � d \�]SQ�^0K`X�\�]_[�� X I JMK�[ � NMR_^!c&LOKM\�I__L d NR�O\�\0�MI d N�� \:KM\7d ^�J� ]SR_I ]SL J��f]SQM\�YWY � d \�]SQ�^0Kl�

    � �1��� � � &�����a� ��&(�c7��/��

    V \�[ QMJMLO[7I���� T�X�I�J T �a�MJM[�]_LO^�J ^�� ]_QM\ K�I ] I I�JMK ]SQM\ N�I�R_I�d \@]S\�R$�[6I�J3N�� I6TD]SQ�\ R_^��O\$^��I K�L�_[�R_\�N�I�JM[@T d \6I�Z�MR_\ LOJ3N=^�Z]S\�R_L ^�REN�R_\7K�LO[�]_L c�\ [ QM\�[��V�����^ [�\�c�\7R�XB[ QM^�LO[�\ ^�� KML�Z[7R_\�N�I�JM[@Td \6I�Z�MR_\ L�9c�\7RZT LOd N�^�RZ]SI�J ] [ L ]SQ)]SQM\EYWY � d \@]SQM^&K`X��Z��Z] I� ]SQM\E[ QM^�L [7\�^�� ]S\Z] Z] I#]SL� ]SL [� L�LOd N�^�RZ]SI�J ] LOJ I J"T [��OI�$ZLO[6IW�=]S\Z]_LOJ��$NMRZ^�e��O\�d#� ��LOR ]���IW��� T�X&I����=d ^&KM\��" I�RZ\�[ R_^�JR� I JMK)I&Z] I#]SL� ]SL [6I��d ^0KM\� I�N�N��OL \7KP]_^ I�K�I ] I�Z\�] ��Z��I��"� T \��0N�� I LOJ��[�\7R ] I�L J I�_N�\7[@]� ^��W]SQM\ KMI ] I5I�K�\��V��I ]_\�� T I�JMK_^�d \�^�]SQ�\7R$-LOJ�I KM\��V��I ]_\�� T�� V QM\E[ Q�I��"�O\7JR��\�]_^ I R_\_\6I R_[ QM\�R:I�NMN�� T&LOJ��$]SQM\EYWY � d \@]SQM^&K)]_^�INMRZ^�e��O\�d L�9]S^ \��0N�� ^�R_\EI�JMK \7d N��O^!T5KML"_[�R_\7NMI�JM[�T)d \6I�Z�MR_\-]_Q�I ]�Q�I6c�\�]_QM\�N=^*[�\7R-]_^ K�\�]S\�[�]-]SQM\I�ZN=\�[�]�9^W�+]SQM\�KMI ] I�]_Q�I ] ]_QM\:d ^0KM\�=[7I�JMJM^ ]9\��0N��OI�LOJ SI ]_L�Z�I [�]S^�R_L�� T����L�_[�R_\�N�I�JM[@T�d \6I�Z�MR_\ ]SQ�I#]R_\� I ]_\:]S^!��\6I ]$�MR_\-^���]SQM\�K�I ]SI J�^�] K�LOR_\�[�]$� T I�K�KMR_\$_\�K e T5]SQM\�NMRZ^�e�I�eML"�OL ] T�d ^0KM\�/I�R_\ \0��N�\7[@]S\�K]S^ N=\�RZ��^�RZd e�\�]Z]S\�R_�1D:\�� d I J \@]:I��7� X F*H�H h � � �I L�����R_\:]S^��R_\�]_QM\fI�N�NMR_^�N�R_L I#]S\�KML�Z[7R_\�N�I�JM[@T �I�JMKI�NMNR� T&LOJ�� I�JV�Mdfe�\7R�^��W^ ]SQM\�R�KML�Z[7RZ\7N�I�J�[7LO\7X][ Q�LO[ Q _Q�^ [ JM^ ZL���J ^W�Wd L"Z�M] � d I6T�� \6I�KP]_^ ]SQ�\LOJ�[7^�RZR_\7[@] [7^�J�[����R_LO^�J ]_Q�I ] ]SQ�\�d ^&KM\��]��]�9]SQM\ K�I#] I$I�KM\��=�MI ]S\� T��

    V Q�I ]-KM^0\ JM^ ] d \6I�J ]SQMI ]�I JPLOJ c�\�Z]_L�� I#]S^�R Q�I��]S^ \���I�d LOJM\�LOJ�J=��d \�RSI�e�� \ KML�Z[7R_\�N�I�JM[@Td \6I�Z�MR_\ LOJ I�J T I�NMN�� LO[7I ]SL ^�J$^�� ]_QM\�YWY � d \�]SQ�^0Kl� �^�R�I�NMRSI [�]SL [6I���NMRZ^�e�� \7d)X0I ��^&^0KdZ]_RSI ]_\���TL��]S^5\0�MI d L JM\fI JV�Md�e=\�R�^�� KML�Z[7RZ\7N�I�J�[7LO\�[7^�R_R_\_N�^�JMKML J���]S^�I�_N�\7[@]�:^��WNMR_I�[�]_LO[7I���L J ]S\7RZ\� ]�I�[�\���� I��_^�d \_ ] I�JMKMI�R_KD[ QM\�[��V�^�JD^!c�\�RSI��"� �M]_JM\�Z �1D:\��Od I�J \@]�I��1� XGFIH�H�J � � �^�R \���I�d N��O\ X`L"� IR_\_\7I�R_[ QM\�R�L�O[�^�R_RZLO\7K)]SQ�I#]-]_QM\U��JMLOKML d \�J�_L ^�J�I�� L ] T I�$Z�Md N�]SL ^�JPd I6T5JM^�]-QM^�� K#��^�R�I NMI�RZ]_LO[��R� I�RNMRZ^�e��O\�d X�L ]3[ L��"��e�\;[ L"_\�]_^5\���I�d LOJM\EKML�Z[7R_\�N�I�JM[�LO\7X`Lf�WN=^�Z_L e��O\ X�]_Q�I ]:[7I�JDKM\�]_\7[@]:]SQM\&�OI�[�� ^���MJML KMLOd \7JR_LO^�J�I��OL ] T�� ��]_QM^�Z\ KML"_[�R_\7NMI�JM[7L \� ��I JMK I���\�[ ^�]_QM\7RZ�\0��I�d L JMLOJR�5^�c�\7R_I����G��]SJM\$�^��]SQ�\�d ^0KM\� � NMRZ^!c0L KM\;� L ]Z]��O\:\@c&LOKM\�JM[7\�I�� I�L J�Z] ]SQ�\U�M] ^�� ]_QM\�d ^0K�\�� XM]_QM\7RZ\�L"-\@c�\7R TPRZ\6I�Z^�JP]_^ e�\[7^�JR��KM\�J"]�]SQMI ]9]SQM\ d ^0K�\��`\0��NR� I�L J� ]SQM\�K�I ]SI$I�KM\��V��I#]S\�� T���^�R ]_QM\ N��MR_N�^�Z\�^W� L J"]_\7RZ\�Z]��

    �^�R ]SQM\ N�^�N��R� I�R� ] I ]_L� ]SLO[7I�� d ^&KM\��"�LOJ �� V X`I JV�Md�e=\�R:^�� KML�Z[7R_\�N�I�JM[�LO\�d I6T e�\ ^��LOJ ]_\7R_\Z]7X KM\�N=\�JMKMLOJR�P^�J ]SQM\ [7^�J"]_\��&]f^W� ]SQ�\ NMRZ^�e�� \7d �< J ]S\�R_\� ]fd I6T e=\ LOJD]S\Z]_LOJ�� ��^�R ^�JM\

  • ^�R d ^�R_\$^�� ^�c�\7R_I����Wd ^0KM\�P�M]6X�L ]_\7d ��]6XG��JMLOKML d \�J�_L ^�J�I�� L ] T�Xl_N�\7\�KM\7KMJ�\�$�XBKML"e=\7RZ\7J ]SLOI��BL ]_\7d�a�MJM[@]SL ^�JMLOJR�MX�N=\�R$Z^�J#�M]7X�\�]S[W� X=I�JMK KML"e=\7RZ\7J ]-KML�Z[7R_\�N�I�JM[�LO\ d I!T�e=\�\e=\7[@]SL c�\U��^�R \0�MI d L JMLOJ�� ]_QM\KMLfe \�R_\7J ]�] T&N=\�^��G��]I�OX �"_^MX�L ]�L"�N�^�Z_LOeR�O\ ]S^ \�d NR�O^!T5^!c�\�RSI��"��K�L�_[�R_\�N�I�JM[�LO\�-^�R ]SQM^�Z\�e�IW_\7KP^�JL ]_\7dd7X`L JMKML c0L K���I��"7X+I JMK LOJ ]S\�RSI�[@]SLO^�J��e�\�]-[�\7\7J ]SQM\�d#� V QM\!��� ]_LOd I ]S\U��^ I�� ^W��^��MR�[ ^�R$� L"�]S^$�R����\� ] K�L"e=\7R_\�J ]-K�L�_[�R_\�N�I�JM[@T d \6IW$�MRZ\� ]SQ�I ]-I�RZ\ N=^*[�\7RZ�a�R� ��^�R I�$Z\�$ZLOJ�� ]SQM\�I�ZN=\�[�]��^�� d ^&KM\���M] ]SQMI ]�I�R_\ ��Z��I��"� T ^�� L J"]_\7RZ\�Z] ]_^ NRZT&[ QM^�d \�]_R_LO[�L I�JR��

    � �1��� � � &�����a� ��&(�c7��/�������&��^�����/$

    V QML�EN�I�N�\7REI�NMN�� LO\�EI JV�Md�e=\�R�^��9K�L�_[�R_\�N�I�JM[@T d \6I�Z�MR_\7XBIW���W^�� [ QML [ Q I�RZ\ e�IW_\7K^�J K�I ]SIW< ^�JR� T �I�JMK JM^ NMI�RSI�d \�]_\7RZ � � H0L JMQ�I�R_I!TDI�JMK b�^�QMJ�_^�J ��g�i�i�j � N�R_^!c&LOKM\ I)K�\�] I L��O\�KKM\_[7RZLON�]_LO^�JP^�� ]SQ�\fKML�Z[7RZ\7N�I�J�[7LO\:I�JMKPKML�Z[���Z ]SQM\U_L ]���I ]_LO^�JR�[ QM\�R_\f]_QM\�T d L"��Q ]�e=\fN�^*[ \�RZ�a���7�T RZLO\��KM\_[7RZLON�]_LO^�JR9^���]_QM\�d \7I�$�MRZ\� ��^��"�O^*[ �

    F���Y�\7RZ[7\�J"]SI���\0k [7^�R_R_\�[�] _[�^�R_\d��^�RE]SQM\5L ]S\7dd�j V QM\5N=\�R_[�\7J ] I���\)^W� \0�MI d L JM\7\$I�J�Z[�\7RZLOJ�� ]SQ�\L ]S\�d �[7^�RZR_\�[�]�� T�� V QML� L" I�J�I#]��MR_I��0K�L�_[�R_\�N�I�JM[@Tfd \6I�Z�MR_\ L J�]SQ�\ [7^�J ]_\��&]W^���I�J T IW$_\$Zd \�J"]��

    g�� �:eR_\7R c�\�K�_[�^�R_\$KML"Z]_R_LOeR��]SL ^�J��j V QM\$KML� ]SRZLOe���]_LO^�JP^���]_QM\$JV�Mdfe�\7R:^���\���I�d LOJM\�\�:^�e0] I�L JMLOJ��I ZN=\�[7L"�M[)R_II[ _[�^�R_\W� ^�JR_LOK�\7R I &4k L ]S\7d ]S\Z]d[ L ]SQ \7I�[ Q L ]S\7d)XWKMLO[ Q�^�]S^�d ^����X ��L c�\�J ]_^�?\0�MI d L JM\7\�� ��\7JM^ ]S\ ��� � ]S^ e�\P]_QM\DJV�Mdfe�\7R�^���\0�MI d L JM\7\���\�]Z]SL J��f\�+�/1'2B�XML�9K�\��JM\�K I�

    � @ � ��� ��!�� D 24!�� �

    � � �:F32 �: �[ QM\7RZ\�!�� D L"�]SQM\$I6c�\7RSIW��\$RSII[ Z[7^�RZ\!��^�R ]SQM\$\0�MI d L JM\7\�[ QM^PI J�Z[�\7R ]SQM\ L ]S\�d [7^�R_R_\�[�]$� T�X!��PL�:]SQM\ I6c�\�RSI���\ RSII[ Z[7^�RZ\ ^W�9I��"� ]SQM\ \���I�d LOJ�\7\��X � � L�:]SQM\dZ]SI�JMK�I R_K K�\�c&L I ]_LO^�J ^�� RSII[_[7^�R_\��^�� I���� \���I�d LOJM\�\�7X�I JMK �:PL" ]SQM\ ^�e�Z\7R c�\7KPNMR_^�N�^�R ]SLO^�J�k [�^�R_RZ\7[�] ��^�R ]SQM\ L ]S\7d �

    X $Z�Md LOJ���]_Q�I ] ]_QM\ � I#]S\7J ]�c�I R_L I e��O\ �MJMKM\�R$� T&L J���L ]_\7d N=\�RZ��^�RZd I JM[7\�L� JM^�R_d I���� T:KML� ]SRZLOe���]_\7K`XY�\6I R$_^�J �gFIH�i�H � KM\�R_L c�\�-I_��^�R_d&�R� I;��^�R ]_QM\ [7^�RZR_\��OI ]SL ^�J5e�\�]-[�\7\7J ]SQM\ � I ]_\7J ]9c I�R_LOI�e�� \:I�JMK I[7^�J ]SL JV�M^���Z� T KML� ]SRZLOe���]_\7K [7R_L ]S\�R_LO^�J Z�M[ Q5I� I�]S\Z] _[7^�R_\�� V Q�\ �V��I�J ]SL ] T�X0[6I��"�O\7K$]SQ�\ ��/�)*,�.0/�\�>

  • 6�'2.�.�,�>f\�+�/1'2B 6�'*,�� 6�/1,�B(+�X�L�9[7^�d N��0]S\7K I�j� � � � � @ � �������

    �: �gF32 �: �� ��� 5�6 � �: �Z� �[ QM\7RZ\�� 5�6 � �: � L� ]_QM\ �:Rk4]_Q �V��I J"]_L�� \:^���]_QM\ Z]SI�JMK�I�RZK J�^�R_d I��`KML"Z]_R_LOeR��]SL ^�Jl���]_QM\7R9]_Q�I�J ]SQM\ eML"_\7RZL I�� [7^�RZR_\��OI ]SL ^�J5[7^&\ � [�LO\7J ]$&��e=^�]_Q L JM[��"�MKML J��f]SQM\ L ]S\7d I�JMK)\��0[��"�MKML J��L ] � ]_QM\7dd_\� c�\�7X/]SQ�L� Z]$�MK�T I��"_^5\���I�d LOJ�\�:]SQM\�LOR:d \6I�J X/c I�RZL I�J�[7\�X/I JMK ]_QM\$d L JMLOd;�Md I JMKd I2�0L d&�Md eML"_\�R_L IW��[7^�RZR_\��OI ]SL ^�J I��K�L�_[�R_\�N�I�JM[@T d \6I�Z�MR_\ e�\7[7I���_\ \6I�[ Q�^W�`]SQM\_\ �=�MI�J ]SL ]_LO\NMR_^!c&LOKM\-^�JM\�k4J=��dfe=\�R $�Md d I�RZT ^�� IW��� ]_QM\ eML�Z\7R_LOI��`[�^�R_RZ\�� I#]SLO^�J�[7^&\ � [7L \7J ]��

    S��? J"]_\7R_I�[�]_LO^�J�O I�$Z^0[�L I ]_LO^�J I�d ^�J�� ]_QM\�L ]S\�d j V QM\7RZ\ I�RZ\EJM^ N�I�RSI d \@]S\7RZ L JPI�J T#_L d N�� \ �MJMLfkc�I R_L I#]S\��� V d ^&KM\���]_^ I�KMKMRZ\�Z QM^*[ L ]S\�d �^�R7X&R_\�ZN=^�J�_\ ]S^�]_QM\�L ]_\7dd � LOJ ]S\�RSI�[@] O�IW$_^&[7LOI ]S\[ L ]SQ \7I�[ Q ^�]SQ�\7R�� V QM\�R_\���^�R_\ X�I J"T KML�Z[7RZ\7N�I�J�[�T

  • V QML��N�I�N�\7R�LOJ c�\Z]_L�� I ]_\�/]SQM\ N�\7RZ��^�R_d I�JM[7\ ^��0]SQM\?SI�d N�� \ ^&KMK��RSI#]SLO^U��R_\��\�R_RZ\7KE]_^�I�/]SQ�\'�5L52) .Z\�+7/1' QM\7RZ\6IW� ]_\7R � IW-I KML"_[�R_\7NMI�JM[�T�d \7I�$�MRZ\E[ L ]SQ N�^�Z]_\7RZLO^�R N�R_\7K�LO[�]_L c�\�[ Q�\7[��"LOJ��R��/L"��\ ]_QM\9JV�Mdfe�\7R ^���\0�MI d L JM\7\Y��\�]Z]SLOJR�:N�I�LORZ ^���L ]S\7dd [�^�R_RZ\7[�]7X�]SQM\9^&KMK�BR_I ]SL ^�GZQM^���� Ke=\ _\�J�_L ]SL c�\:]S^ \��&]SR_I IW$_^&[7LOI ]SL ^�J I�d ^�J��f]_QM\ L ]S\�d �

    ��� �,�-� ��� 7 � �a&(� � ����������� � �^7�6 &���������� ��79$�����_�1��� ��� ��&�� & �S&(��$��T� � � �����

    X _\�R_LO\:^��?_L d&��� I#]SLO^�J�Z]$�MKML \�:LOJDH0LOJMQMI�RSI6TDI JMK b�^�QMJ�Z^�J � g�i�i�j � I�N�N�� T)]SQM\fY Y �

    d \�]SQ�^0K�]_^ I�$Z\�Z�]_QM\ �M]9^W��]_QM\_FkSX�g kSX�I�J�K j�Y � d ^0KM\�4[ Q�\7J ]SQM\ ]_R$�M\:KMI ] Ifd ^0K�\���d I6T e=\:^�J�\^��W]SQ�\$I�e=^!c�\f]SQMRZ\7\ ^�R I ]_\�Z]$�O\@]:d ^&KM\� X`I ]-[�^Wk4KMLOd \7J�ZLO^�JMI�� d ^0K�\�� X�^�R I#)-%(,�,$5=,$5�B],�)�)U:3 ) 14B C FF /

    6-F7F 3 ) /2/ )

  • ]SQ�\ ]SI�e�� \��V QM\ ] I�e�� \fLOJ�KMLO[7I ]S\ ]SQ�I#]:]SQM\ ^&KMK� RSI#]SLO^��I�RZ\fc�\7R T N=^*[�\7Rg�a���BLOJ I�Z_\$_L J��)KML"e=\7RZ\7J ]

    I�ZN=\�[�]�:^W�Bd L"Z�M] ^��B]SQ�\;�� V d ^0KM\���X=\_N�\7[7LOI���� T5]SQM^�_\fRZ\�� I#]S\7K ]S^��OI�[�� ^W�Y�MJML KMLOd \7J�ZLO^�JMI��OL ] T��V QM\E^�e�_\�RZc�\7K _[�^�R_\EKML� ]SR_L e���]_LO^�J I�JMK)]SQM\EeML�Z\7R_LOI��/[7^�RZR_\� I ]_LO^�J [7^&\ � [�LO\7J ]$:I�R_\ ��Z\�a����LOJ�Z^�d \_\@]_]_LOJ����

    �"� � ��� � ��� �$� � � � � ���"�� ������� ������ � � ����

    �/\@]���-[�^�J�ZLOKM\�R-I$N�I�R ]�^�� ]_QM\ ^�� ]S\�J�k I�JMI�� T �7\�K d Lf�0\�K)JV�Md�e=\�R-K�I#] I!_\�]O��RZ^�d V I ]�Z�M^��#I�gFIH�H�i � � V Q�\fK�I ]SI<_\@]�[7^�J�_L KM\7RZ\7KDQ�I�-R_\_N�^�J�_\:^��Wj g�h d L KMK�� \�k-Z[ QM^&^��NZ]$�MKM\7J ]$�]S^�F!h d L �0\7KJV�Mdfe�\7RO$��e�]SR_I�[�]_LO^�J)NMR_^�e��O\�d ��^�R [ Q�LO[ Q ]SQM\ ��RSI�[@]SL ^�J�9KM^ Q�I6c�\EI [7^�d d ^�J)K�\7JM^�d LOJMI ]S^�R� V QM\L ]_\7d [ R_L ]_\7RZ�K�\�_L"��JM\�K)]_QM\ L ]S\�d ]_^$KML I���JM^�_\E ]��MK�\7J ] d I� ]S\7R T5^�J5]SQ�\ ��c�\ $�"L��"�� ��L c�\7J e�\�� ^ [ j

    � H��"L����GF�jbT I�ZLO[���RSI [�]SL ^�Jh$�Me0]SRSI [�]SL ^�Jl�

    � H��"L����+g�j H0LOd N�� L"� T�O R_\�K��M[�\ ��RSI�[@]SL ^�J5^�R d L �0\7K5JV�Mdfe�\7R�

    � H��"L����`jRj H0\7NMI�RSI ]_\E[ QM^��O\:JV�Md�e=\�RO��RZ^�d ��R_I�[�]_LO^�Jl�

    � H��"L����]S�jbT ^�RZR_^*[ ^�J�\ ��RZ^�d ]_QM\E[ QM^�� \:J=��dfe=\�R LOJ)I_��L c�\7J)d L ��\�K J=��dfe=\�R��

    � H��"L����+h�j ^�J c�\�RZ] I![ QM^��O\:JV�Mdfe�\7R9]S^ I&��RSI [�]SL ^�Jl�

    V I�eR�O\$g

  • ������ � ���2�16�6�� ���7��1�/� �W�� ������(�_�������#� ����$��.7 �� ���� 7� ,���/&�������� ��� �! 6 � �^�

    N B )

  • I�JMK �R_LOJR�5I�� I�RZ��\7RO��J�IW� N�^�Z]_\7R_L ^�R _I�d N��O\U_L���\f[6IW��_\:Q�I�R_KR� TPI�J TP[ Q�I J���\�:L JP]SQ�\fR_\$��� ]��^��]SQ�\ N�^� ]S\7RZLO^�R:N�R_\7K�LO[�]_L c�\ [ Q�\7[��V�� � \ ]SQ�\7J $�Md d I R_L���\�]SQ�\ ^���]SN��0]E^W��]_QM\!_\7[�^�JMK3NMR_^���RSI�d��R_I�NMQML [6I��"� T5I JMKPJV�Md \7RZLO[6IW��� T�� T \�[6I���Z\�]SQ�\�K�I ]SI Z\�]�L"3Zd IW��� X0]SQM\ [ QM^��O\�NMRZ^0[�\�$�] I�� \�:I e=^��0]j�i d LOJV��]_\����^�R�]_QM\ j�Y�� d ^0KM\��^�JDI5H��MJ T � I�KM\ F!i�i�i![ ^�R$�VZ]SI ]SL ^�J \��V�ML NMN�\7Kc[ L ]_Q H h�i � � �

    Y�� I�JMK)Q�I��"� ��L"� I�e T"]S\:^��G��X � �

    � &(��

    �'� �2$��6

    LORZZ]6X(� \�]O���\���I�d LOJ�\ ]_QM\ N=\�RZ��^�RZd I JM[7\ ^���]SQM\U�-IW_[ QPd ^&KM\��]��^�R ]_QML� \0�MI d N�� \�� L����MR_\F!_QM^*[O�e=^I�0N�� ^�]� �a[ Q�L�$� \7RZE^�� ]SQ�\ e�^I�0\� \��&]S\�JMKML J��)]_^5]SQM\ h#]_Q I�J�K H�h#]SQ N�\7R_[�\7J ]SL"�O\ � ��^�R]SQ�\ K�L�Z]_R_L e���]SL ^�J ^�� ]SQM\ R_\�N��OL [6I ]_\7K JV�Mdfe�\7R ^�� \0��I�d L JM\7\ �^���]�^�� j g�h � I JMK3N�^�L J"]$E��^�R�]SQM\^�e�Z\7R c�\7K JV�Mdfe�\7RZ���^�R�\6I [ Q Z[7^�RZ\�� X _^��OLOK#�OL JM\ �Z^�L J� ]_QM\f^�e�Z\7R c�\7K _[�^�R_\�� V QM\ N��O^ ]�_Q�^ [O

    0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

    510

    1520

    2530

    35

    �?���I7��/� �7�� � ��� ���� � 7����� �#��� � ��� � � ����� �� �K���"���� �$�� � � � ��� " ��

    �$������ ��� "$� ����� � ����� � � ������"�� ������� �� �$� � ��

    ]SQMI ]9]SQM\�^�e�Z\7R c�\7K JV�Mdfe�\7R ^�� \0��I�d L JM\7\ ��^�R9\6I�[ Q)RSII[ _[7^�R_\ �(�M[�]$��I ]_\��[7^�J�ZLOKM\�RSI�eR� T�� (�MR ]SQM\�R7X]SQ�\&��I�_[ QDd ^0K�\���N=\�RZ��^�RZd �N=^&^�RZ� T LOJ)]SQML" ZL ]��MI ]SL ^�J F ]_QM\ ^�e�Z\7RZc�\7K JV�Mdfe�\7R�^W�B\���I�d LOJM\�\��L"^���]$_L KM\:]SQM\ H�i� [7RZ\7KML e��O\:L J"]_\7R c�IW�]��^�R _\@c�\�J ^���]SQM\!F*J N�^�$ZLOe�� \:RSII[ Z[7^�RZ\���

    L�����R_\�gd_Q�^ [O-]SQM\E^�e�_\�RZc�\7K I�JMK NMR_\�KMLO[@]S\7K I6c�\7RSIW��\fI�J�KcZ]SI�JMK�I�RZK KM\@c0LOI ]SL ^�J)^��B]SQM\eML"_\7RZL I�� [7^�RZR_\��OI ]SL ^�J [7^&\ � [7L \7J ]�� 4]-L� [�� \6I�R9]SQMI ] ]SQM\U�-IW_[ QPd ^&KM\��NZ\�c�\�R_\� T �MJMKM\�R_NMRZ\7KML [�]$-]SQ�\I6c�\�RSI���\EI�JMK5c I�RZL I ]_LO^�J�^W��]_QM\Ee�L�_\�R_LOI�� [�^�R_RZ\�� I#]SLO^�J5[7^&\ � [7L \7J ]�O��^�R ]SQ�L�9\���I�d N�� \��

    # J

  • 0.65 0.75 0.85

    050

    100

    150

    Mean of biserial correlations0.0 0.10 0.20

    050

    100

    150

    200

    SD of biserial correlations

    �?���I7��/� � #"$� 7����� � � � � � ��� ��� � � ������ � � ��� � � ��� � � � � � � "$��� ����� � ��� � � ��� ����� �������� � �� � ��� " ��

    ����� �� � � "$� ����� � � ��$� � � ���� ���� ���������� ��� �� �

    L�����R_\ j!_QM^*[O-]_QM\�N=^� ]S\�R_LO^�R9NMR_\�KMLO[@]SL c�\EN=k4c I�����\:[7^�RZR_\�ZN=^�JMKMLOJR� ]_^ ]_QM\E^&KMK��RSI#]SLO^&��^�R\6I [ Q L ]S\7d N�I�L R7X���ZLOJ�� I_ZT&dfe�^��/I� KM\_[�R_LOe�\7K)LOJ5]_QM\E�O\��\7JMK)^���]SQM\E�(���MR_\W�YX ]_R_LOI�J���� \�LOJMK�LO[6I#]S\�

    2 4 6 8 10 12 14

    24

    68

    10

    12

    14

    Item ID

    Ite

    m ID

    24

    68

    10

    12

    14

    P−value>0.95P−value

  • �MJMK�\7R_N�R_\7K�LO[�]_LO^�J]� �-^�R_L���^�J ] I��/I JMK c�\7RZ]_LO[7I��N��R_L K�k-� LOJM\ I ]�d&��� ]SLONR�O\� ^��Wh0X�c�\7RZ]_LO[7I���I2�0L�gk � I�e�\��" ^�J]SQ�\ERZL���Q ]O_L KM\ ^�� ]_QM\ �(���MRZ\�X�I�JMK I K�L I���^�J�I��l� LOJM\ I�RZ\:]SQM\�R_\ ��^�R [7^�J c�\�JMLO\�JM[7\W� V QM\EN��O^�] QMI�9]S^&^d I�J T5]SR_LOI�J���� \� I�J�KPLOJ c�\7RZ]_\7KP]_R_LOI�J���� \�7X�LOJMKML [6I ]_LOJ�� ]_Q�I ] ]SQM\U��I�_[ Q d ^&KM\��l�I�L"�� ]_^ NMRZ\7KML [�]�]SQM\I�Z_^&[7L I#]SLO^�J��I�d ^�J�� ]_QM\�L ]S\�d � ��c�\7R_I�����X�]_QM\U�-I�Z[ Q d ^0KM\��I�NMN�\6I�RZ-]S^ e=\�LOJMI�KM\��V��I#]S\U��^�R�]_QM\d Lf�0\7K JV�Mdfe�\7RO$��e�]SR_I�[�]_LO^�J K�I ]SI__\�]��

    ����� &���$�� ��� � �2$ �6 �

    T ^�]SQ ]SQM\$g Y � I�J�KDj�Y�� d ^&KM\��"-N�\7Rg��^�R_d ZLOd L�� I R$� T [ L ]_QPR_\_N�\7[@]:]S^ ]_QM\�KML"_[�R_\7NMI�JM[�Td \6I�Z�MR_\-\0�MI d L JM\7K`XM]_QM\�j�Y��

  • V QM\fN�� ^�]�O��^�R ]SQM\fe�L�_\�R_LOI��+[7^�RZR_\� I ]_LO^�J�;�J�^�]�ZQM^*[ JDQM\7RZ\ � ZQM^*[ ]SQ�I ]-]SQM\fg�Y�� d ^&KM\��I�JMK ]SQ�\Ej�Y � d ^&KM\�`NMR_\�KMLO[@] ]SQM\�d I�KM\��=�MI ]S\� T��

    L�����R_\ hd$�Md d I R_L���\��]SQM\fN�^� ]S\7RZLO^�R-NMR_\�KMLO[@]SL c�\fN�k c I����M\!��YWYWYGk4c I��"�M\� � ��^�R-]_QM\f^&KMK�RSI#]SLO^��N�R_\7K�LO[�]_\7K e"T I j�Y��0.95P−value

  • SI d \ I JMK I�JD\���I�d LOJ�\7\;[ L ]SQDJM^ �"JM^*[O�O\�K���\ ^�� d Lf�0\7KPJ=��dfe=\�RE$�Me0]SRSI [�]SL ^�JD[6I JD\6I�ZL�� T#_^�� c�\]SQMI ] L ]S\�d � � (�MRZ]_QM\7R�X�I2� ]S\7RbZ^�d \�NMRZ\��OL d L J�I�R Tf[ QM\�[��=�X(� ^���$Z^� \@]9I��7� ��g�i�i�j � I�RZ���M\ ]SQ�I#]�]_QM\7RZ\-L"\7J�^�����Q LOJ���^�R_d I ]SL ^�J ]_^_�M] ]SQ�\ �a�R_LO^�J5d ^&KM\��4[ L ]_Q ]_QMR_\�\ KML"e=\7RZ\7J ]O_\@]� ^���L ]_\7dd ^�J�� T�X�I�[�[7^�RZKMLOJR�]S^ ]SQM\�LOR�$�"L��"�/R_\��V�ML R_\�d \�J"]$�M`^�JM\�^�� ]SQM^�Z\;Z\�]� [7^�J�ZL� ]��^��P4]S\7dd�j0X F!i0X=I JMK FISd[ QML�� \�I�J�^�]SQM\�R[7^�J"]SI�LOJRE4]S\7ddEg0XNSMX Q�X H0X/I�JMK F�F�� V QML" I�_N�\7[@]�^���]_QM\7L R�N�I�N�\7R d I ]S[ Q�\��c�\�RZT [�O^�Z\�� T#[ L ]_Q^��MR3��JMKML J���:QM\�R_\��&T \7[7I���_\ ]_QM\ K�I ]SI�_\�] L" ]S^&^ _d I��"� X [ \ ]SR T KMLfe \�R_\�J"] N�R_LO^�R KML"Z]SRZLOe��0]SLO^�J�^�JP]_QM\fN�I RSI�d \�]_\7R$&�\W� ��� X`d ^�R_\�JM^�J�LOJR��^�RZd I#]SL c�\EN�R_LO^�R$�^�JP]SQ�\fL ]_\7d N�I�R_I�d \@]S\�R$-]_^�\�� LOd LOJ�I#]S\]SQ�\�N�^�Z_LOe�L��OL ] T ^W��]_QM\ NMR_L ^�R$ IWe=\7[@]SL J�� ]SQM\�YWYWYPk c I����M\ � F ]SQ�\�NMI ]_]_\7R_J)^�� I�$Z^0[�L I ]_LO^�JR c&LORZ]$��I��"� TR_\�d I LOJ�b�MJM[ QMI�J���\�K I�d ^�J��:]SQM\-N�I�LORZWKM\�Z[7R_L e=\�K5I�e�^!c�\_� ]SQM\-^�J�� T N�I�L Rb��^�R?[ QML [ Q ]_QM\�YWYWYGk4c I�����\_^�d \@]SLOd \�9e�\7[�^�d \�O�O\$ \��&]SRZ\7d \ L� ]SQ�\�NMI�LOR��VF6i �IFIS�� � �

    �-\7J�[7\�X�]SQM\EK�I ]SI _Q�^ [O3_^�d \; ]SRZ�M[�]$�MR_\�]SQ�I ]�]SQ�\;_L d NR�O\E�� V d ^0K�\��� [7I�JMJM^�]-\��0N��OI�LOJI�KM\��V��I ]S\� T�XWI�JMK QM\�JM[7\ ]_QM\7RZ\5L�ENMR_^�eMI�e�� T RZ^0^�d ��^�RU�M]Z]SLOJR�DIPd ^�R_\ [7^�d N��OL [6I ]_\7K3d ^&KM\��7�

    (�MRZ]_QM\7R�X�]_QM\U�I [�]�]SQ�I ]-]SQM\�YWY � *d \�]_QM^&K�7X4�"JM^*[ JP]S^�e�\�[7^�J�Z\7R c�I#]SL c�\�X=Q�I6c�\f\�JM^�����QPN=^*[�\7R]S^ Z������\Z] I�N�^�Z_LOeR�O\�d L�g�M]�\@c�\�J ��^�R3$�M[ Q I�Zd I��"�/K�I ] I�Z\�] �j g�h \0�MI d L JM\7\:I�JMK F�h L ]S\�d �_Q�^ [O ]SQMI ] ]SQM\ d \�]SQ�^0K Q�I�9N�R_^�d L�Z\��

    � � � ��� ��������������� ��� � ��� � � �����

    V QML� \0��I�d NR�O\�RZ\�� I#]S\��]S^f]SQ�\�R_\_N�^�J�_\ ^���IfRSI�JMK�^�d Z�Me�Z\�]�^��bF!i�X i�i�iE\���I�d LOJM\�\� ]S^_K�Qd&��� ]SL N��O\-[ QM^�LO[�\:L ]_\7dd ^���]SQM\:c�\�R_e�IW�+d \7I�$�MRZ\:^�� I_[ L KM\�� T���Z\7K I�KMd L�Z_LO^�J� ]S\Z]�� V Q�\�^�e �Z\7[@]SL c�\LOJ)]SQML"-\0��I�d NR�O\�L� ]S^�,�++^�R_L"��LOJ�IW��� T$d \6I J"]-I_��RZ^��MN)^�� L ]S\�d 9^�J)I$[7^�J ]_\7J ]�I R_\6If]_Q�I ]�L�9KM\@c�\�O^�N�\7KPI��I�MJML ]�I JMKDI �R�0\�K JV�Mdfe�\7R�^�� NMR_\�KM\�]_\7R_d LOJ�\7K N�I#]SQ��]SQ�I ]�I�J \0�MI d L JM\7\�d I6Th��^��"�O^*[ � �

  • d \6I�J I Z�Me�_\@]�^�� L ]_\7dd���\7JM\�RSI ]_\7K#��RZ^�d I!_LOJR���O\ Z]_LOd&�R�����X($�M[ QDIW I$R_\7I�KMLOJR� [�^�d N�R_\7Q�\7J�ZLO^�JN�I�ZSI���\�� V QML" N�I N=\�R [ L��"� �R_\�]_QM\;�OI ]_]_\7R K�\��JML ]SL ^�JPQM\�JM[7\���^�RZ]_Q I�JMK�[ L"��� ��Z\�]SQM\E]S\7RZd +-,�)�+�>�,�+/9+-,�: ����ZLOJ�� ]SQM\�KM\���JML ]_LO^�J)^�� +-,�)�+�>�,�+�L J�T R_I�K�� ^ [ \�] I��1� X F*H�H�H � ]_^ KM\_[7RZLOe�\�]_QM\;Z\7[�^�JMKP] T&N�\f^��L ]_\7dd��

    V QM\:\7L"��Q ] N�I�R ]�9L J ]SQM\-c�\7RZe�I��`d \6IW$�MRZ\�XML J ]SQM\ ^�R_KM\�R LOJ�[ Q�LO[ Q�]SQ�\�T5I NMN=\7I�R L J ]SQM\-]S\� ]e�^0^��V� \�] R_\�[7\�L c�\�K e T5]_QM\ $�Me�_I�d N��O\ ^���\���I�d LOJM\�\� [7^�J�_L KM\7RZ\7K`X�I�RZ\�I� ��^���� ^*[O�j

    F��?4]S\7ddYFk�F!iRjPF!i9KML"_[�R_\�]_\BL ]_\7dd`R_\��=��LOR_L J�� I�J \���I�d LOJ�\7\ ]S^9[�^�d N��O\@]S\BI _\�J ]S\7J�[7\ ���Z[�^�d NR�O\�]_LO^�JL ]S\�d ��$QM\7JM[�\��^�R ]SQ �

    g��?4]S\7ddhF�Fk g�jRjcF!j KML"_[7RZ\�]_\)L ]S\�d L J"c�^�� c&L J��c[ ^�R_K R_\��OI ]SL ^�J�ZQMLON� ��� � � L ]S\7dd��c��^�R!�a�0]��MRZ\R_\��\�R_\�JM[7\ �

    jR�?4]S\7dd-gWSWk j�JRj F!jf]_\�Z]$�O\@]-L ]S\�d eMI�_\�KP^�J)I!_Q�I�RZ\7K Z]_LOd&���"��9d I ]S\�R_L IW�

    S��?4]S\7dd�jLK k S"h�jYH KML"_[7RZ\�]_\E[�^�d NR�O\�]_LO^�J L ]S\�d

    h��?4]S\7ddOSLJ2k h�F�jYJ � � L ]_\7dd

    JR�?4]S\7dd-h�g k h�K�jYJf]S\Z]$�O\�]�L ]S\7dd9e�I�Z\7K)^�J I!ZQ�I�RZ\7K Z]SL d&���"��9d I#]S\7RZL I��

    K��?4]S\7dd-h�Q2k-J�JRjYHf]S\Z]$�O\�]�L ]S\7dd9e�I�Z\7K)^�J I!ZQ�I�RZ\7K Z]SL d&���"��9d I#]S\7RZL I��

    QR�?4]S\7dd�JLK k�K�QRj F�g�]_\�Z]$�O\@]-L ]S\�d eMI�_\�KP^�J)I!_Q�I�RZ\7K Z]_LOd&���"��9d I ]S\�R_L IW�

    V QM\_��RZZ]:]SQ�R_\7\$N�I RZ]����^�R_d ]_QM\&��RZZ] _\�N�I�RSI#]S\�� TLk4]SL d \�K _\�[�]SL ^�Jl��Y I�R ]� SWkgK ��^�R_d ]_QM\__\�[7^�J�K_\�[�]_LO^�J I�JMK

  • ^���]_N���] I�JMK� ]S^�RZ\� I ��J�I���N=^�Z]S\�R_L ^�R _I�d N��O\�^��NZL��7\UF�X i�i�i ��^�R I��"��]SQM\-d ^&KM\��"�� � \ ]_QM\7J [7^�d N���]_\]SQ�\�YWYWYGk4c I�����\�O��^�R9]SQM\�KML�Z[7RZ\7N�I�J�[7LO\�� V QM\�R_\$��� ]��^�� ]_QM\�N=^� ]S\�R_LO^�R�N�R_\7K�LO[�]_L c�\E[ QM\�[��V�Q�I�RZK�� T[ Q�I�JR��\�[ QM\7Jh[�\ c I�R T ]_QM\:JV�Mdfe�\7R9^���L ]_\7R_I ]SL ^�J� ^W��]_QM\ � � I�JMK5]SQ�\���J�I��`N�^� ]S\7RZLO^�R SI�d N��O\_L�7\W� U c�\7J ]SQ�^�����QD]SQ�\ K�I ] I Z\�]�L���OI�R$��\h�gF!i � i�i�i � K�Q�KMI ] I5N�^�LOJ ]� � X`]_QM\&[ QM^�� \ NMR_^&[7\$ ^��[7^�d N��0] I ]_LO^�JP]SI���\�I�e=^���]_F�g QM^��MR$E��^�R ]_QM\$j�Y��?d ^&KM\���^�J I)H��MJ T � I KM\�F!i�i�i

  • 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78

    050

    100

    150

    200

    250

    300

    �?���I7��/��� � � ��� �� � � 7����� � � � � ��� � � � ��� �� �_� �"���� �$� � ��� � ��� "��

    ����� �� � � "�� ����������

    ��� �$� � � � � ��� �� �

    0.50 0.52 0.54

    050

    100

    150

    200

    Average biserial correlation0.0 0.04 0.08

    050

    100

    150

    200

    250

    SD of biserial correlations

    �?���I7��/��� #"$� 7����� � � � � � ��� ��� � � ������ � � ��� � � ��� � � � � � � "$��� ����� � ��� � � ��� ����� �������� � �� � ��� " ��

    ����� �� � � "$� � ����������� �$� ���� � ��� ���

    'W]

  • 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78

    050

    100

    150

    200

    250

    300

    �?���I7��/��� � � ������ � � � �$��� �#��� � ��� � � � ��� �� �_� �"���� �$� � � ��� �

    ����� �� � � "�� � ����������� �$����� � ��� ���

    0.51 0.53 0.55

    050

    100

    150

    200

    Average biserial correlation0.100 0.115 0.130

    050

    100

    150

    SD of biserial correlations

    �?���I7��/��� #"$� 7����� � � � � � ��� ��� � � ������ � � ��� � � ��� � � � � � � "$��� ����� � ��� � � ��� ����� �������� � �

    � � ��

    �$��� �� �� � "$� � ����������� �$� ���� � ��� ���

    ' #

  • ^���]SQM\ eML"_\�R_L IW�`[7^�RZR_\� I ]_LO^�J�[�^0\C� [7LO\�J ]���

    L�����R_\EF!i $�Md d I�R_L�7\�B]_QM\ YWYWYGk4c I��"�M\�b��^�RB]SQM\ ^&KMK� RSI ]_LO^�WNMRZ\7KML [�]_\7K e T IEg�Y��Pd ^0KM\�1�

    V QM\:N�� ^�] ZQM^*[O9]SQ�I ] ]SQM\�R_\�\0��L"Z]$ I&_L���JML"��[7I�J ]9I�d ^��MJ ]9^W��I�$Z^0[�L I ]_LO^�J5I d ^�JR��]SQM\ L ]S\�d ]SQ�I#] I

    Item ID

    Ite

    m ID

    0 5 10 20 30 40 50 60 70 80

    01

    02

    03

    04

    05

    06

    07

    08

    0

    0 5 10 20 30 40 50 60 70 80

    01

    02

    03

    04

    05

    06

    07

    08

    0

    P−value>0.975P−value

  • 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78

    050

    100

    150

    200

    250

    �?���I7��/� � � � � ��� ���� � 7����� � � � � �� � � � �������K� � ��� ������ � � � � �

    ����� �� ��� "$� ����������

    ��� �$� � � � � ��� �� �

    NMRZ\7KML [�]S\�K J=��dfe=\�R$9]S^*[ I�R_KR ]_QM\E�O^*[ _[�^�R_\ R_I�J���\d�9[ QM\7RZ\ ]_QM\7RZ\ I�R_\:[�^�J�ZLOKM\�RSI�e�� T

  • 0.50 0.52 0.54

    050

    100

    150

    200

    Average biserial correlation0.090 0.100 0.110

    050

    100

    150

    200

    SD of biserial correlations

    �?���I7��/� ��� "$� 7����� � � � � � �"����� � ������� � � � � � � � �"����� � � � � "$��������� ����� � � ��� ����� ���� �$��� �� � � ��

    �$��� �� �� � "$� � ����������� �$� ���� � ��� ���e�\fI JV�Md�e=\�R ^��B[7I�_\ ��^�R�[ QMLO[ QP]_QM\�d ^&KM\��N[ L��"�N�MJMKM\�R_NMRZ\7KML [�]:^�R-^!c�\�R_NMRZ\7KML [�] �Z�RZ]�e T)[ Q�I�J�[7\\�c�\7J3L"�B]SQ�\ d ^&KM\���L��]SRZ�M\�M/QM^*[�\�c�\7R7X�]SQM\ N�\7RZ[7\�J"]SI���\$^���N�I�L R$ ��^�R3[ QMLO[ Q ]SQM\ ^�e�_\�RZc�\�K ^&KMK�RSI#]SLO^ KM^0\�JM^�] �I���� [ L ]_QMLOJDI H�h � N�R_\7K�LO[�]_LO^�JDL J ]S\7R c I�� ��LOd N��OL \7K)e"T ]SQM\ RZ\7N�� LO[7I ]S\�K�O NMRZ\7KML [�]S\�K^&KMK� RSI ]_LO^� � L�EF K=� h0XR$�Me� ] I�J ]_L I��"� T�d ^�RZ\�]SQ�I�J [ Q�I#]-[7I�J)e=\�I ]Z]SR_L e���]_\7K ]S^$[ Q�I�JM[�\�� H0^$]SQM\�j�Y��d ^0KM\�+I�NMN�\6I R$9]S^ e=\ L J�I�KM\��=�MI ]S\E��^�R ]_QM\ K�I ] I_Z\�]3_^!�I�R I� NMR_\�KMLO[@]SL J�� ]SQM\ ^&KMK� RSI ]_LO^� I d ^�JR�L ]_\7dd�I�R_\ [7^�JM[7\�R_JM\�Kl� �-^*[ \@c�\�R7X=]_QM\ _L ]$��I ]_LO^�J L� [�^�J�_L KM\7R_I�e�� T e=\@]_]S\�R�]_Q�I�J ]SQ�I#]3��^�R L"���MRZ\_F!i�L7� \W� X(��^�R ]SQ�\ g�Y�� d ^&KM\� � F \_N�\7[�L I��"� T�XM]_QM\�N�\7RZ[7\�J"]SI���\f^W�Y_L"��JML"�M[6I�J ]�^!c�\7RZNMR_\�KMLO[@]SL ^�J�!�I ] h ��O\@c�\� � RZ\7K��M[�\E��R_^�d gWSf]S^!QR� Q �a[ QML"�O\�]SQM\ JV�Mdfe�\7R9^�� ZL���JMLf��[6I J"] �MJMKM\�R_NMRZ\7KML [�]SL ^�J�9RZ\7d I�LOJ5I e=^��0]]SQ�\ _I�d \ � [ QM\�J#[�\U��^_��RZ^�d I g�Y�� d ^0K�\�� ]_^ j�Y �3d ^&KM\��7�

    ��RZ]SQ�\7R�[7I�R_\��a��� \���I�d LOJMI ]SL ^�JP^��W]_QM\ N��O^ ]�R_\@c�\7I����I�JV�Mdfe�\7R�^W��L J ]S\7RZ\� ]SLOJR�5N�I ]_]_\7RZJ�R_\� I�RZKMLOJ��)I�Z_^&[7LOI ]SL ^�J I�d ^�J��)]_QM\$L ]_\7dd�� V Q�\ N�� ^�] _QM^*[OU��R_^���N�E^W� L ]_\7dd�[ L ]_Q3L J"c�\7R ]S\7K]SRZL I�JR���O\d�a[ QML [ Q d \6I�J �MJMKM\�R_NMRZ\7KML [�]_LO^�J e T ]_QM\$d ^&KM\� � ��^�R d ^�Z]�^���]SQM\ N�I�L R$�[ L ]_QMLOJ ]SQ�\��RZ^��MN`XML JMKML [6I ]_LOJ��$I_�O\@c�\�+^�� IW$_^&[7LOI ]SL ^�J I�d ^�J�� ]SQ�\7d ]_Q�I ]9]SQ�\Ej�Y �3d ^&KM\�� �I�L��" ]S^$\��0N��OI�LOJ]�

    � ^�Z] c&L�ZLOe�� \5^���]SQ�\�_\ ��RZ^��MN� I�R_\ ]SQ�^�_\h[ L ]_Q 4]_\7dd�g�Q k j�J I�JMK 4]S\�d J g k-J�JR�

    J ]S\�R_\� ]SL J���� T�XWe=^�]_Q ]SQM\_\h��R_^��MN� [7^�J�_L"Z]$^���L ]_\7ddfe�I�Z\7K ^�J _QMI�R_\�K ]SLOd;�������d I ]_\7RZL I����]_\� ]��O\@]�L ]S\7dd � I�JMK I�NMN�\6I�R ]S^*[ I�R_K ]_QM\�\�JMKD^�� ]_QM\7L R-RZ\�_N�\7[@]SL c�\__\�[�]_LO^�J�� ��\7JM[�\�X`NMRZ^�e�I�eR� T)I[7^�dfeMLOJMI ]SL ^�J ^W� ]S\Z]�� \�] \e=\7[�]:I�JMK�ZN=\�\7KM\�KMJM\$ \e=\7[@]:[6I��R_\�]_QM\U�I�L"���MRZ\ ^��B]SQM\�j�Y�� d ^&KM\��+]_^\��0N��OI�LOJ5]_QM\�IW$_^&[7LOI ]SL ^�J�[ L ]_QMLOJ5]_QM\�Z\U��RZ^��MN�� ��JR��^�R ]��MJ�I#]S\�� T�XM]_\�Z]$�O\@]-L ]S\�d I�N�N=\7I�R�I ] ]SQM\ \7J�K^��WIW���+]SQM\E]SQMRZ\7\;Z\7[@]SLO^�J��LOJ)]SQM\�]S\Z] F _^�]_QM\7RZ\�L�-JM^

  • Item ID

    Ite

    m I

    D

    0 5 10 20 30 40 50 60 70 80

    01

    02

    03

    04

    05

    06

    07

    08

    00 5 10 20 30 40 50 60 70 80

    01

    02

    03

    04

    05

    06

    07

    08

    0

    P−value>0.975P−value

  • L ]_\7dd�� V QM\;��RZ^��MN��^���]S\� ]�� \�]-L ]S\�d ��^�R [ QML [ QP]SQ�\7R_\�L��Q�I�RZK�� T5I�J T ^�c�\7R_I���� �MJMK�\7R_N�R_\7K�LO[�]_LO^�J ^��^&KMK� RSI ]_LO^� I�R_\ 4]S\�d -gWS2k g�KfI�J�K h�g*k h�h0X&]SQM\E��RZZ]O��\[ L ]_\7dd9^���]_QM\ N�I�ZSI���\��

    ��]_QM\7R���RZ^��MN�O[ L ]_QPQML"��Q ^�R�d ^&KM\7R_I ]S\� T5QML"��Q)J=��dfe=\�R-^W�BLOJ c�\�RZ]_\7KP]_R_L I J����O\ I�R_\ ]SQ�^�_\[ L ]_Qc4]S\�d UF�Fk�FISMX=g�Fk g�jc��^�R7X�d ^�R_\ ��\7JM\�RSI��"� T�X F�F�k g�j � X�I�JMKcSLJ k h�i F I������ � L ]S\7dd�� V QM\&_I�d \NMQM\�JM^�d \7JM^�J ^&[7[���R$ ��^�R:L ]_\7d N�I LOR$�[ L ]SQ ^�JM\ L ]_\7d ��RZ^�d ]_QM\ Z\�] F�g k�F*Q I�JMK3I�JM^�]_QM\7RE��R_^�dSLJ2k SLHR�?T ^�]_QP^���]SQM\_\ _\@]� [�^�J�ZL�Z]�^�� � �*L ]S\�d M�]SQ�\7R_\���^�R_\ X Z�M[ Qc�MJ�KM\7RZNMR_\�KMLO[@]SLO^�J�7X�LOJ�KMLO[7I ]SL J��I�Z_^&[7L I#]SLO^�J5I�d ^�J��f]SQ�\:L ]S\�d �X�NMRZ^�e�I�eR� T N=^�L J ] ]S^ ]SQ�\�_\ L ]S\7dd K�\��JML J�� IfKMLOd \7JR_LO^�J�[ L ]SQ�LOJ�]SQ�\]S\Z]��

    �-JMKM\�R_NMRZ\7KML [�]_LO^�J)L��I��"_^$NMR_\@c I��O\�J"]O��^�R [�^�d NR�O\�]_LO^�J5L ]S\�d �X�I�� ]_QM^�����Q ]_^ I!�O\$Z\7R�\��&]S\�J"]��

    �^�R�\���I�d N��O\ X�]_QM\7RZ\ I�R_\ ��\[ LOJ c�\7RZ]_\7K ]_R_L I J����O\���^�R�]_QM\&_\@]:jLK*k-S"h I�JMK���^�R�]SQM\EN�I�L R$O[ L ]SQP^�JM\��R_^�d Fk�F!i$I�JMK I�JM^�]_QM\7R ��R_^�d jLK k S"h�� V Q�\7R_\EI�RZ\�d ^&KM\7R_I ]S\� T�Q�L���Q JV�Mdfe�\7R ^���LOJ c�\�RZ]_\7K ]_R_LOI�J���� \�[ L ]_QMLOJ 4]_\7dd Fk�HR�

    �/\@] ���\0�MI d L JM\�]SQ�\ [6I�Z\�E��^�R [ QML [ Q ]SQM\$j�Y � d ^&KM\��^!c�\�R_NMRZ\7KML [�]$ ]_QM\ ^&KMK�:RSI#]SLO^�����JM\$JM^�]_LO[7\7I�e�� \$I�_N�\7[@]�I d ^�JR��]SQM\$^!c�\�R_NMRZ\7KML [�]SL ^�J� L��]_Q�I ] ]SQ�\ j�Y � d ^&KM\�BI��Od ^� ] I��"[ I6T=^!c�\�R_NMRZ\7KML [�]�:]_QM\ I�Z_^&[7L I#]SLO^�J�3[ QM\�JM\�c�\7R�KM\6IW�OLOJR� [ L ]_Q c�\�RZTDKML)� [���� ]�L ]_\7dd�� V QML"�L�-]SR$��\;��^�R

    4]S\�d F!i�X0j g0XMj�h0XRS"h&X�I�J�K)h�F�X�[ Q�LO[ Q5Q�I6c�\�]_QM\�� \6I� ] N�\7R_[�\7J ] IW��\:[7^�RZR_\�[�] Z[7^�RZ\� �^���] ^��+]_QM\ ]_^�] I��K�Q$L ]_\7dd�L J5]SQM\ ]S\Z] � F F!j0X g=F�XNF�h0X H�X�I�J�K g�i$R_\_N�\7[@]SL c�\�� T�� T \�[6I��R_\E]_QM\�Z\�L ]S\7dd NMR_^!c&LOK�\ � L ]Z]��O\LOJ���^�R_d I ]SL ^�J5I�e�^���] ]_QM\E\0��I�d L JM\7\7X�]SQ�\7R_\�L�9c&LOR ]���IW��� T JM^ ^�e�Z\7RZc�\7K I�Z_^&[7LOI ]SL ^�J5^��BI J"T ^W� ]SQ�\�_\L ]_\7dd�[ L ]SQ)]SQM\E^�]SQM\�R L ]S\7dd�LOJ ]_QM\E]_\� ] [ QML"�O\EI�[7[�^�R_KML J�� ]_^ ]SQ�\fj�Y��

  • L�QO�I�RZ\ ]SRZ�M\��YX3 I�J ^���]S[�^�d \�XRZ^�d \:^��/]SQM\:\0�MI d L JM\7\ I ] ]SQ�\ESI�d \�d ^0KM\�fk4NMR_\�KMLO[@]S\7K NMR_^��M[7LO\�JM[�T�O\@c�\� ��\@]�KMLfe \�R_\�J"] _[�^�R_\�^�J ]_QM\E]-[�^5L ]_\7dd FG]SQM\ \7J�K�k RZ\�$�R� ]�L" I J ^�e�Z\7RZc�\7K ^&KMK� R_I ]SL ^ � ^*[ \�R]SQMI�J)]_QM\ NMR_\�KMLO[@]S\�K �I�JMK QM\7J�[7\EI QML"��Q5N�k c�IW���M\ � ��^�R ]SQ�I#] L ]S\�d N�I�L R��

    D L c�\7J ]SQ�I#]�]_QM\$]S\� ]�� \�]EL ]S\�d �I�N�N=\7I�R:]S^)[6I�N�]$�MR_\ I)K�L"e=\7R_\�J ]�KML d \�J�_L ^�J ��R_^�d ]_QM\KML"_[7RZ\�]_\�L ]_\7dd7X�]SQM\�I�e�^�c�\�NMQ�\7JM^�d \7J�^�JDL��[7^�JR_L� ]S\�J"]3[ L ]_Q ^�e�Z\7RZc I ]_LO^�JR7X4$�M[ Q I��� Q�I�J�� I�JMKH&]_^���]

  • Item ID

    Ite

    m I

    D

    0 5 10 20 30 40 50 60 70 80

    01

    02

    03

    04

    05

    06

    07

    08

    00 5 10 20 30 40 50 60 70 80

    01

    02

    03

    04

    05

    06

    07

    08

    0

    P−value>0.975P−value

  • X �"_^MX`Y YWYGk4c I��"�M\� I R_\__L"��JMLf��[6I�J ]$� T �O^*[�\7R���^�R�L ]S\�d N�I LOR$3[ L ]SQDe�^�]_Q�� � L ]_\7dd���L c�\7J ^�]_QM\7R�I�[@]S^�RZ��

    V QM\7RZ\��^�RZ\�X�I�J�I�� T�ZL� ^�� ]SQM\ NMRZ\7KML [�]S\�K3^&KMK� R_I ]SL ^�:NMR_^!c&LOK�\� Z] I#]SL� ]SL [6I�� \@c&LOKM\�JM[7\ ^��_L"��JMLf��[6I�J ]�I�$Z^0[�L I ]_LO^�J LOJP]_QM\ K�I ]SI�X L JMKMLO[7I ]SL J�� I�d&��� ]_LOKML d \�J�_L ^�J�I��Y�\6I [ Q ^W�B]SQM\�]_QMR_\�\ L ]_\7d] T&N=\Ed \6IW$�MRZLOJ��h$� L���Q ]$� T K�L"e=\7R_\�J ]UZ�"L����" � I�J�K ZN=\�\7KM\�K

  • � � � � � ���� �" � � �� � � � ��� � � ����V QML�:\0�MI d N�� \ R_\� I ]_\��]S^5]_QM\ R_\_N�^�J�_\E^W� Q�X J�Q�J�\0��I�d L JM\7\�]S^)I _\�N�I�RSI#]S\�� TP]_LOd \7K

    _\�[�]_LO^�J [ L ]_Q S"h d&�R� ]SL N��O\ [ QM^�LO[�\ L ]S\�d L J ]_QM\ [ R_L ]SLOJR� I�$Z\�$Zd \�J ]5N�I�R ]$^��:I R_\�[7\7J ]$� TI�KMd LOJ�L�Z]_\7RZ\7K$e�I�ZLO[�$�"L��"�� ]S\Z]�� V QM\3�MR$Z] g�h:L ]_\7ddWI�R_\�^��`^�JM\9] T0N�\_��^�J!��JMKML J��E\�R_RZ^�R$ � [ QML"�O\9]SQ�\� IWZ] g�i I R_\�^��WI�JM^ ]SQM\�R�] T&N�\ �^�JP[7^�R_R_\�[�]_LOJ�� \7R_RZ^�R$ � � V QM\E^�e �Z\�[�]SL c�\ELOJ ]SQML"-\0�MI d N�� \EL"9]S^ �MJMK^���] Lf�+]SQM\:]_\�Z] L" _N�\7\�KM\7K]� T ^�����Q ]S^�J X ��I R$�"LOJ`X�I�JMK���I�d I�d ^�]S^��LOJ5N�R_\�Z � ��JMK ]SQ�\:\��0L� ]S\7J�[7\ ^��$��e�Z]SI�J ]SL IW� ZN=\�\7KM\�KMJM\�Z LOJP]_QM\E]_\�Z]�I�JMK RZ\7[�^�d d \7J�K R_\�K��M[7L J�� ]_QM\;ZL��7\E^��B]SQ�\E]S\Z] e"T#_\@c�\�JL ]_\7dd FG]SQM\@T�KM^ JM^�]�N�\7RZ��^�R_d I�J T ] I ]_L� ]SLO[7I��lZL���JMLf��[6I JM[7\:]S\Z]7X�eR��]O��JMK ]SQM\ _N�\7\�KM\7K�JM\�Z�]S^$e=\^��WNMR_I�[�]_LO[7I�� ZL���J�L"��[7I�JM[7\U��^�R-]_QM\&� IWZ]�Z\�c�\7J L ]S\�d &��4]_\7dd:j�H2k S"h � �34]�[ L��"�/e=\f^W�WLOJ ]S\�R_\� ]:QM\�R_\]S^5\0��I�d L JM\fLf�B]SQM\fd ^&KM\�� �I�L��"-L J I

  • Item ID

    Ite

    m I

    D

    0 5 10 15 20 25 30 35 40 45

    05

    10

    15

    20

    25

    30

    35

    40

    45

    0 5 10 15 20 25 30 35 40 45

    05

    10

    15

    20

    25

    30

    35

    40

    45

    PPP−value > 0.975PPP−value < 0.025

    �?���I7��/� � � � � ��

    � � � ����� � �

    ����� � ������ � � � � ��� ��

    �$������ � � � "$� ��� ���� � " � ����� ���� �� � � � ����� �

    KM^�J�^�]�e�\�� ^�J�� ]_^5I ]S\Z]$�O\�] � I�J�K I<Z]$�MK�T ^��B]SQM\�LOR-[7^�J ]S\�J ]�:KM^&\��J�^�]�Z������\Z] I�J TPI�KMKML ]SL ^�J�I��[7^�JMJM\7[@]SL ^�J)I�d ^�J���]SQ�\7d �YX _L d L"� I�R N��O^ ] ��^�R ]_QM\ YWYWYPk c I����M\ ��^�R ]_QM\E� I� ]�g�ifL ]S\7dd ^W��]_QM\:K�I ]SI_\@]_��^�e�]SI�LOJM\�K)IW� ]S\�R9R$�MJMJ�LOJ��$]SQM\ � � ^�J R_\�ZN=^�J�_\-]S^$]SQ�^�_\ L ]_\7dd9^�J�� T � ZQM^*[O-]_Q�I ]�4]S\�d jLK k S"h&_\�\7d ]S^ [6I N�]��MRZ\�I$KMLfe \�R_\7J ]-KMLOd \7JR_LO^�Jh��RZ^�d 4]_\7dd gWJ2k j�J�M�]SQM\�d ^�Z]��OL"��\� T�\0�0N�� I�JMI ]SL ^�J`X��L c�\7J ]_Q�I ]�I����/]SQM\_\$I�RZ\fKML"_[7RZ\�]_\fL ]_\7dd ^�JD[�^�R_RZ\7[�]_LOJ�� \7R_RZ^�R$�X`L��]SQ�I#]�]SQM\;� I� ] ��\[ L ]S\7dd�I R_\_N�\7\�KM\7K X=I JMK Q�\7JM[�\�I�N�N=\7I�R9]S^$e=\ ^�J)I KMLfe \�R_\7J ]�KML d \�J�_L ^�J���R_^�d 4]S\7dd�g�J2k j�JR�

    J #

  • ��RZ]SQ�\7R7X�Id_L���JML"��[7I�J ]�J=��dfe=\�R-^W�P�MJMK�\7R_N�R_\7K�LO[�]_LO^�JR3��^�R L ]_\7dd [ L ]SQ�LOJ ]SQM\ ��R$ ] NMI�RZ]-^��]SQ�\$I�$Z\�$Zd \�J ]��a4]S\�d _Fk g�h � $������\�Z] ]_Q�I ]�]_QM\f]-[ ^ N�I RZ]�:L J ]SQM\f]_\� ] d \7I�$�MRZ\__L"��JML"�M[6I�J ]�� TKMLfe \�R_\7J ] $�"L"�����X`]SQ�I#] L�7X+]_QM\ ]S\� ]�L"�]-[ ^2k KML d \�J�_L ^�J�I��7� L����MR_\�F!h)I�N�N=\7I�R$:]S^ e�\!_LOd L��OI�R-]_^

    L"���MR_\!F*J0X [ Q�LO[ Q L"-I [7^�N T)^��WI N��O^ ]-L J H&LOJMQ�I RSI6T)I�JMK b�^�QMJ�_^�J � g i�i�j � ^�e�]SI�LOJ�\7K#��RZ^�d �M]Z]SLOJR�]SQ�\ j�Y�� d ^&KM\��+]_^�K�I ]SI

  • LOJ c�^�� c�\$]_QM\ [7^��"�O\�[�]SL ^�J ^��-I [ LOKM\�c I�RZLO\�] T ^��-\�c&LOKM\�JM[7\ I�e�^���]$d ^0K�\�� �M]7X�L JM[��"�MKML J��Z] I#]SL� ]SL [6I���]S\� ]��X�I�JMK ]_QM\7J d IW�&L J�� I�J L JR��^�RZd \�K �Z�MK���d \7J ] I�e�^���] d ^&KM\����M])I�JMK��_\��a���OJM\$�^��BI d ^0K�\��][ L ]SQ)I N�I�RZ]_LO[��� I�R _\�]�^���K�I ]SIR�

    V QM\9[7^�d d \7J ]BI�N�N��OL \� \��V��I���� TU[�\��"�0]_^�c0L RZ]$��I���� T \�c�\7RZTfd ^&KM\��&LOJfI�NMRSI�[@]SL [6I��0I�NMN�� LO[7I ]SL ^�J`Xd ^�R_\�]S^ d ^&KM\��"-L Jc�� V ��^�R�[ QMLO[ QDJM^ [ \���fk4\� ] I�e�� L�ZQM\7K#Z] I#]SL� ]SL [6I��+]S\Z]$:\��0L� ]I� V Q�\&��_\�R:^��WId ^0KM\� _QM^��R�OK IW�"[ I!T=-[ QM\7[��)]SQM\ �M] ^W� ]SQM\Ed ^&KM\�1� X3-]SQ�L��N�I�N�\7R ZQM^*[O7X=N=^� ]S\�R_LO^�R-NMRZ\7KML [�]_L c�\d ^0KM\�+[ QM\7[��"L J���NMRZ^�c&L KM\� Id ]SRSI L���Q ]$��^�RZ[ I�R_K [ I6T ]S^ N=\�RZ��^�RZd I [�^���� \7[@]SLO^�J)^W� [ QM\�[��=�X+I�L d \�KPI ]KMLfe \�R_\7J ]�I�ZN=\�[�]$E^�� ]SQ�\ d ^&KM\��7� ��JM[�\ I5d ^0K�\�� L"��M] ��ZLOJ��)I�J � � I�����^�R_L ]_QMd I�JMKD]SQ�\N�^�Z]_\7R_L ^�R�_I�d NR�O\& ]S^�RZ\7K`X+]SQ�\$Y Y � d \@]SQM^&KD[6I�J [ QM\�[�� c0L RZ]$��I���� T I�J T I�_N�\7[@] ^�� ]SQM\&�M] ^W�]SQ�\�d ^0KM\�N[ L ]SQPJM^�I�K�KML ]_LO^�J�IW�`]SQM\�^�R_\@]SLO[7I�� [ ^�RZ�)I�JMKDId�OL ]Z]�� \�\0�&]SRSI [7^�d N���]SI ]SL ^�J�I��+\�e ^�R ]I��X I�JPI�KMKM\�KDI ]_]_RSI�[@]SL ^�J`XM]SQ�\�YWY � d \@]SQM^&K)[6I�J NMR_^!c&LOKM\U��RSI NMQMLO[7I��+\�c&L KM\7JM[�\fI�e�^���]-\6I [ Q ^�� ]_QM\I�ZN=\�[�]��\���I�d LOJ�\7Kl�

    V QML� N�I�N�\7ROZQM^*[O-QM^*[ ]SQM\�YWY � d \�]SQ�^0K d I!T�e=\:QM\�ONR�a�R�+LOJ)I�$Z\�Z_LOJR� ]_QM\E�M]�^���]_QM\d ^0KM\��-LOJ �� V LOJDRZ\6I�� I�NMN�� LO[6I#]SLO^�J������JM\_Z]_R_^�JR� I�_N�\7[@]E^W� ]_QML� R_\7N�^�R ]:L� ]_QM\_��Z\ ^W��\7I�_L"� T[7^�d NMRZ\7QM\�J�_L e��O\�I�JMK)I ]_]_RSI�[@]SL c�\���R_I�NMQML [6I��=KML�ZN�� I6T= ]_^ KM\7d ^�J� ]SRSI#]S\�]SQ�\�Z]_R_\7JR��]SQ)^��/]SQM\�Y Y �

    d \�]SQ�^0Kl�G4]9L��[��O\7I�Rb��R_^�d ]SQML" N�I N=\�R�]SQMI ] ]_QM\:YWY � d \�]_QM^&K�[6I�J Z�M[7[�\�ZZ�a���"� T KM\�]_\7[�] K�L"e=\7R_\�J ]I�ZN=\�[�]�:^W�Bd L"Z�M] ^�� ]_QM\f[7^�d d ^�J��� V d ^&KM\��"�� V Q=�R7X`]SQ�L��R_\7N�^�R ]�NMRZ^�c�\�:]SQMI ] ]_QM\�N�^�Z]_\7RZLO^�RNMRZ\7KML [�]SL c�\ [ QM\�[��=-KM\�Z\7R c�\�d ^�RZ\ I ]_]_\7J ]SL ^�J ^���]_QM\ N�ZT&[ QM^�d \@]SR_L [7LOI�J���

    V QM\ [ QM^�LO[�\ ^���KML�Z[7R_\�N�I�JM[@T$d \7I�$��R_\�WL"BI:[7R$��[7L IW�ML�Z$�M\ LOJf]_QM\�I�NMN�� LO[7I ]SL ^�J�^���]SQ�\ Y Y �

    d \�]SQ�^0K��OX JV�Mdfe�\7R�^��BKML"_[�R_\7NMI�JM[�T d \6I�Z�MR_\�\���I�d LOJM\�KPL J)]_QML�-N�I�N�\7R-I�NMN�\6I�R�NMR_^�d L"_LOJR� L JI�Z_\�Z_L J��#�� V d ^0K�\�� ��]I� V Q�\ ^0KMKR:RSI ]_LO^MX`\0��I�d L JMLOJR� ]SQM\$IW$_^&[7LOI ]SL ^�J e�\�]-[�\7\�J L ]_\7d N�I�L R$7XNMRZ^�d L"_\ ]_^$e=\EI N�^*[ \�RZ�a���/KML"_[�R_\7NMI�JM[�T d \6IW$�MRZ\�� V Q�\E\0�MI d N�� \� QM\�R_\�X�]_^���\�]_QM\7RO[ L ]_Q ��JMKML J���LOJ H0LOJ�Q�I�RSI6TPI�JMK b�^�QMJ�_^�J � g�i�i�j � X�LOJMK�LO[6I#]S\ ]SQ�I ]-]SQM\E^0K�K��RSI#]SLO^ d I6T)e�\fI NMR_I�[�]_LO[7I���� T ��_\��a���d \6I�Z�MR_\ L J K�\�]S\�[�]_LOJ�� d&��� ]SL KMLOd \7J�ZLO^�JMI��OL ] T5I�JMK ZN=\�\7KM\�KMJM\�ZfLOJ ]_QM\$K�I ]SIR� V QM\$d \6I�Z�MR_\$L"[�� ^�_\� T5RZ\��OI ]S\�K)]_^ ]_QMR_\�\E\0��L"Z]_LOJ�� d \7I�$��R_\��^�� KM\�]_\7[�]_LOJ�� KML d \�J�_L ^�J�I�� L ] T����LOR$ ]-I�d ^�J�� ]SQM\�d L�� UBV U V � � QMI�J�� � H&]S^���]6XPFIH�H�H � X][ QMLO[ Q Z������\Z]$EI�KMI ] I2k4KMR_L c�\�JDLOJMKM\0� ^W��K�LOd \7J�ZLO^�J�IW�OL ] T�Xe���]EKM^&\��JM^�]�N�\7RZ��^�R_d I�J T _L"��JMLf��[6I�J�[7\$]S\� ]SL J���� V Q�\ Z\7[7^�JMK _L d L"� I�R \��0L� ]SLOJR� d \6I�Z�MR_\$L"�� � V U H V � H"]S^���]7X FIH�QLK � X=IdZ]SI ]SL"Z]SL [6I��`]_\� ]�e�I�Z\7K ^�J�$��d ^�� [7^�JMK�L ]SL ^�J�I�� [7^!c I�R_LOI�JM[7\3��^�R-I��"�N�^�$ZLOe�� \:L ]S\�d N�I LOR$ [ L ]SQML J I__N�\7[7Lf��\7K#$�Me0]S\� ]I� �-^�L�� ]SL J��c��g�i�iRF � N=\�RZ��^�RZd 9N�^� ]S\7RZLO^�R9N�R_\7K�LO[�]_L c�\

    J J

  • [ QM\�[��=-e�I�Z\7KP^�J I$KML"_[7RZ\7N�I JM[�T

    � � � ������ �

    5 ��� � � � ��� � � � � ��� � � �G���� � � �

    � � � �

    [ QM\�R_\�+��L� ]_QM\ _[7^�R_\�^��BI$N=\�R$Z^�J ^�J�4]S\�d �_X � � � � �� � b � L�9]_QM\ R_\� ]�Z[7^�RZ\�^���]SQM\ N�\7R$Z^�J`XI�JMK � � � � L" ]SQM\�JV�Mdfe�\7R ^�� N�\7RZ_^�JR-^�e0] I�L JMLOJ�� RZ\� ] Z[7^�RZ\�� � � � V QM\EI�K�c I�J ] I���\�^W� ]SQ�\EI NMNMR_^�I�[ Q$�R����\� ]S\�KDLOJ ]SQML" I�R ]SL [��O\:^!c�\7R-]_QM\�\0�0L�Z]_LOJ�� I�NMN�R_^ I�[ Q�\��L"�L ]����RSI NMQMLO[7I�� ��I6c�^�R7X4_LOd N�� LO[7L ] T5I�J�KLOJ ]$�ML ]_L c�\�I�NMN�\6I��7�

    V QM\7RZ\�I�RZ\�I JV�Mdfe�\7R ^�� �MJMRZ\�Z^�� c�\7K L"$$��\�9]SQ�I#]-RZ\��V�ML R_\�I ]_]_\7J ]SL ^�J)LOJ5]SQM\E�a��]$�MR_\W� H&^�d \^���]SQM\�d I�RZ\�j

    � U ��I�d LOJ�LOJ�� R_\6IW�OL���\7K KML�Z[7R_\�N�I�JM[�LO\_�1D:\�� d I JP\�]�I��1� X F*H�H�J � ]SQMI ]�I R_\U�a��JM[�]_LO^�J�-^��B]SQ�\�K�I ]SII�JMK ]SQM\ d ^0KM\�`N�I�R_I�d \�]S\�R$�

    � U �&]_\7JMKML J��$]SQM\E[�^�R$��]_^$]SI���\ L J"]_^ I�[7[�^��MJ ] N�^�� T&]_^�d ^��� L ]S\7dd��

    � ^�dfeML JMLOJ��EZ^�d \9^��=]_QM\ d \7I�$��R_\�B]_^�N�R_^!c&LOKM\�I:[7^�d N�^�_L ]S\ Z�Md d I�R Tf^���]SQM\ �M]W^W�`I:d ^0KM\�1�� \6I�Z�MR_\ [7^�J�ZLOKM\�R_\�K L JP]SQ�L� NMI�N=\�R�LOJ c�^�� c�\�]S^&^�d I�J T JV�Md�e=\�R$����^�R-\���I�d N��O\ X=]SQ�\ ^0KMKRRSI ]_LO^ d \6I�Z�MR_\-L J"c�^�� c�\ d I�J T J=��dfe=\�R$-I�JMK [7^�dfeMLOJ�LOJ��f]_QM\7d ]_^d��\�[ \�R [ L���� e=\E��Z\�a���7�

    J /

  • A &� &�� &���� 0�

    X ��R_\� ]SL�X(X;� � g i�i g � ���b\�+�,1C='2.0/16$\�> 5L\�+1\�\�B4\�> ^*)�/�)�E�a�\[ � ^�R$� j � L��O\@T��

    T L R_J"e�I��Md)X�XU� �gF*H�J�Q � �WH&^�d \E�OI ]S\�J ]�]_RSI�L ]9d ^0KM\��9I JMK)]_QM\7L R ��_\ L J)L JR��\7RZR_L J��$I�J)\���I�d LOJM\�\�� I�eML�� L ] T��P J � � � �+^�R_K � � � � ��a�^!c0L [�� � U K�� � X�� + \�+�/�)�+7/16$\�>N+9@(,�'2.0/1,�) (I'2. :]+�,�)�+)*6�'2.�,�)E�[ QMI�N�]S\�R$ F K k g�i � �P��\7I�KMLOJR�MX � XUj(X KMKML"_^�J=k �3\�$� \�T��

    T ^��R��Q ]S^�J`X i � X �/I�R$�"LOJ X i � X� ��I�d I d ^�]_^MX i � ��g�i�i�j � � � ^&KM\�OLOJR� KML"e=\7RZ\7J ]SLOI��l_N�\7\�KM\7K�JM\�Z��_L J�� I Q T&eMR_L K NRZT&[ QM^�d \�]_R_LO[�I�N�NMR_^ I [ Ql� � I�JV��_[�R_L N�]�LOJ NMR_\�N�I�R_I ]SL ^�Jl�

    T R_I�K��O^*[ X U � V � X �

  • �-^�L�� ]SL J���X �U�N� g�i�i�F � � ^�J�KML ]_LO^�J�IW� LOJ�KM\7N�\7JMK�\7JM[�\�I�J�K KMLfe \�R_\�J"]_L I�� L ]S\�d �a�MJ�[�]SL ^�JML J�� LOJ5]SQ�\]-[ ^Wk4N�I�R_I�d \@]S\�R�� ^���L"Z]SL [ d ^0K�\��1�G J#XU�(T ^&^�d Zd I0X � �(XU��bR�Mc�I J ����L��ZJ`X�� V �(X;� T �H0JML��ZK�\7R$U� U KR�� � X��b)�)�\�^ ) /9B /9+-,�: .�,�)-%('2BR)*,E+9@(,�'2.0^ E a�\[ � ^�R$� j�H0NMRZLOJ���\�Rgk �W\7R$�OI����

    �-^���� I JMK`XMY � � � �gF*H�H�i�I � � V QM\ ����]S[ Q)LOKM\�J ]SL ] T4jYX JM\�[ ]S^&^��]��^�R ]SQM\ Z]$�MK�T ^���L ]_\7d R_\�ZN=^�J�_\d ^&KM\��"����b)�^L6�@('2:� + \�+�/�)�+7/16�) � ���L�j � X�g�Q h k j�i�JR�

    �+^�R_K X � � � ��F*H�Q�i � ��� %L%4> /16$\�+�/1'2BR)&'�(E/9+-,�: .�,�)-%('2BR)*, +9@(,�'2.�^d+-'E%4.$\=6�+�/16$\�>l+-,�)�+7/9B=C %4.�' ��>�,�:;)�E�-L��"��ZK�I��O\ X�a bRj �/I*[ RZ\7JM[�\ U RZ�Oe�I���d X Z_^&[7L I#]S\��

    � I�RZL��X4D!� X� � I�R_L"7X U � ��g�i�i g � ��� .�,U\�+7+�/9+�`�5=,U/9+-,�:;) :�,!�%(,$\2AL,$5���� B \�B4\�> ^*)�/�)`V)�/9B=C *3\�^L,�)�/�\�Bc: ^ 5�/�\*C�B]'*)�+7/16 \2)�)*,�)�)�: ) (I'2.�)*'2:9> /fC=,�B]6�,U\�B45�\�+�+1\�/9B(:

  • � \7[��#I�_\ X � � �&� �gF*H�HLK � �GX � LOJM\7I�R � ^���L� ]SL [ d&��� ]SL KMLOd \7J�ZLO^�JMI���d ^&KM\�� ��^�R9KMLO[ Q�^�]S^�d ^���9L ]S\�dR_\�ZN=^�J�_\�K�I ]SIR�Y J � ��bR�Mc I�J KM\�R �/L JMKM\�J�� � � i � �-I�dfe�� \�]S^�J�� U K��� � X��E\�B45 ��'*'*A�'�(:9>5�/�\*C�B]'*)�/�)�)�^ )�+-,�: `L)�/9B=C 5L\�+ \h,��V\�: %4>�,�)�EWY I N=\�R�N�R_\�Z\7J ]S\�KDI ]9]_QM\�I�JMJV��I��+d \7\@]SLOJR� ^W�]SQM\�a I#]SLO^�J�I�� ^���JM[7L"�`^�J � \6I�Z�MR_\�d \�J ] L J U K���[6I ]_LO^�J`X QMLO[7I���^MX� �Y�

    �O�MeMLOJ X �&�(T � ��F*H�QRF � � U Z]SL d I#]SLO^�J�LOJ N�I�R_I���� \��=RSI�JMK�^�d L�7\�K)\0�0N=\�R_LOd \7J ]$�� �('2`�.0B4\�> '�(� 5�`(6$\�+�/1'2B4\�>�� + \�+�/�)�+7/16�) ��#X�jLK�K k S iRF��

    �O�MeMLOJ X �&�(T � ��F*H�Q�S � �bT I6T�\_L I J�� T��Z�RZ]SLf��I�e�� \:I�JMK)R_\�O\@c�I J"]O��RZ\��V�M\7J�[�T [6IW�O[��R� I ]_LO^�J� ��^�R ]SQM\I�NMN�� LO\7Kh ] I ]_L�Z]_LO[�L I�Jl� � B(B4\�> )&'�(�� +1\�+7/�)�+�/16�) ��� � XlF�F�h=Fk�F�F*K�g��

    �O�MeMLOJ X �&�(T � X� H&]_\7R_J X �U��H � ��F*H�H�S � � V \�Z]_LOJ�� LOJh�OI ]S\�J"] [� I�Z9d ^&KM\�� ��ZLOJ�� I N=^�Z]S\�R_L ^�RNMR_\�KMLO[@]SL c�\ [ QM\7[�� KML"Z]SRZLOe��0]SLO^�Jl�P JhX;�Mc�^�J U T�\ � � � � ^���� � U KR�� � X��l\�+�,�B(+?82\�.0/�\ ��>�,�)\�B4\�> ^ )�/�)�\�%L%4> /16$\�+�/1'2BR) (I'2. 5=,�8�,�>�'�%4:l.�,�)*,$\�.�6�@ ��NMNl�bS"g�i k-S j�Q � � V QM^���SI�J�K �:I��V7X XUjH�I���\�YY�Me�� LO[6I#]SLO^�J���

    H0[ QM\�LOJM\7X � � X ��^�L�� ]_LOJ���X � � X � T ^&^�d Zd I0XRX;� ��F*H�H�H � �YT I6T�\�_LOI�JP\Z]_LOd I ]SL ^�J5I�JMK ]S\Z]_LOJ��$^��Z]SRZ�M[�]$�MRSIW��\��V��I ]SL ^�J d ^&KM\���� �?)�^L6�@('2: ^2/9B=C %('*)�+�,�.0/1'2. %4.�,$5�/16�+�/98�,:�' \�> C='2.0/9+9@=:;)� .�,�8*/1,� � UBV H#��� k i�j2k iLK � � UBV H=X�YWRZLOJM[�\�]_^�J`X�a bR�

    J �

  • H&]_\7R_J X � � � g i�i�i � � ^�d d \7J ]$9^�J �ZYPk c I����M\ ��^�R9[7^�d N�^�_L ]S\:JV���"�`d ^&KM\���� � �('2`�.0B4\�>G'�(E+9@(,� : � )�)*'*6�/�\�+�/1'2B�������XlF�F�h�K k�F�FIJ�iR�

    H&]_^���]6X � � � �gF*H�QLK � �YX*J�^�JMN�I�R_I�d \�]SRZLO[ I�N�NMR_^ I [ Q ��^�R IW$_\$ZLOJ��d� I ]_\7J ]9]SR_I�L ] K�LOd \7J�ZLO^�J�IW�OL ] T���?)�^L6�@('2:9>N\�B45dA2B]' >�,$5*C=, \=6 X�`=/�)�/9+7/1'2B��NMN]�?S h�j2k-S�Q�Q � ��-L"����ZK�I�� \�X0a�bRjU RZ�Oe�IW�Md#�

    c I�J)KM\7J � ^����O\�J"e=\�R$�MX�XU� �Y� �gF*H�Q g � � V [ ^ JM\[ ]S\� ] ] I ]_L� ]SLO[ ��^�R ]SQ�\U��I�Z[ Q d ^0K�\��1��?)�^L6�@('2:


Recommended