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Shachar Oz
Shachar Oz
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???? ????? " ?? ??? " ?????????? ????? : ??? ??? ???? : ????? ?? ? " ? ?????? ????? ??????? ???????? 6 ????? , 2007 ???? ????? ?? ?????? ?????? ??? ??? ????? ! ?? ??????? ??????? ?? ?????? ??????? . ???? ????? ????? ?????? ??? ????? ????????? ??????? ??????? ?????? ???????
??? ???? ??? / ??????? ????? ??? / ??? ?????? ???? ???? ????? ??? ?????? ??? ?????? ???? ??? ???? ?????? ?????? ??????? ???? ??? ???? ?????? ???? ?????? ??? , ???? , ??? - ?? ??? ', ??? ???? ????? ???? ??????? ??????? ????????? ???? ????? ????? ?????? ??? ?????
???? ??????? ??? ???? ????? ???? ?????? ??? ??? . ???? ??????? ???????? ????????? ??? ???? ????? ???? ?????? ???? . ???? ????? ?????? ?????? ??????? ??? ??? ???? ????? ?????? ?????? ??????? ?? ???????? ???? Mode ????? Median ????? Mean ???? ????? ????? . ??? Xi-Mean) = 0 Median = n / 2 ??? ????? ??????? ??????? ????????? ???? ????? ????? ??????
????? ???? ?????? ???? : ????? ???? ?????? ???? ????? ?? ?????? ???? ????? ??? , ???? ????? ????? ???? ????? ????? . ???? ?????? ????? ??? ??? ????? ?????? ??????? ???? ???? ???? ???? ? / ?? ?? ????? ???? ???? ( ??? 30). ??? ????? ??? ??? ???? ???? ????? ?????? ?????? ???? ???? ????? ???? ????? ????? ??? ????? ??????? ??????? ????????? ???? ????? ????? ??????
???? ????? ?? ??????? ???????? ????? ??????? ????????? ???? ??? ?? ????? . ???? ????? ????? ?? ?????? ???????? ??????? ?? ????? ??????? ?? abs(Xi-Mean)) /n Xmax ¨C X min ??? ????? ????? ????? ???? ?????? ?? ????? . ????? ?? ?????? ????????? ? ? ??? Xi ¨C Xm) ? ??? n-1) ??? ????? ????? ????? ???? ?????? ?? ????? . ????? ?? ?????? ????????? ???? Range ??? ???? ????? ?? ????? ??????? ????? ????? Mean spread ????? Variance ????? ??? Standard deviation ?? abs(Xi-Median)) /n Varp (RANGE) Stdevp (RANGE) ????? ?????? ??? ????? ??????? ??????? ????????? ???? ?????
????? ??????? ?????? ???? : ????? ???? ?????? ???? ????? ?? ???? ???????? . ???? ????? ! ???? ???? ????? ????? ?? ?? ?????? ?????? . ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
????? ????? ??? ????? ??? ??? ???? ???? ????? ?????? ?????? ???? ???? ????? ???? ????? ????? ??? ????? ???? ?????? ???????? ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
??? ???? ??????? ??? ???? ???????? ??? ???? ??? ??????? ????? ??????? ?????? ????? ?? ?????? ??????? ?? ?????? ?? ?????? ????? . ?? ???? ????? . ???? ?????? ??? ???? ??? ????? ??????? ??????? ??????? ?? ????? ??????? ?? ????? ??????? ????? ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
?????? : ??????? ??????? , ?? - ????? ?????? ????? . ????? ?????? ???? ??????? ??? ????? ?? ??? ???????? . ????? = ?????? = ?????? . ??????? ?? ??? ????? ?? ?????? ?????? ??????? ???????? : ??????? ??????? ????? ????? ???? ? = 3.14159 e= 2.71828 ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
68.3% ????? ????? ??? ??? 95.4% ????? ??? ????? ??? 99.7% ????? ??? ????? ??? 34.13% ????? ????? ???? ??????? 13.59% ????? ????? ???? ?????? 2.15% ????? ????? ???? ??????? 0.15% ????? ????? ???? ??????? ????? ????? ???? ???? ???? Z ??????? ??????? ?????? : ??????? ??????? , ?? - ????? ?????? ????? . ????? ?????? ???? ??????? ??? ????? ?? ??? ???????? . ????? = ?????? = ?????? . 34% 13.7% 2.15% 0.15% 3 2 1 0 - 3 - 2 - 1 Z ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
???? : Z > 0 ???? ??? ?????? Z < 0 ???? ???? ?????? Z = 0 ???? ????? ?? ?????? ???? ???? ???? ??? ???? ????? ???? ?? ????? ????? ????????? ???? ??? ????? ???? ?????? ??????? ???? . ???? ????? ???? ( ? ) ?? ??? ?????? ( x ) ??????? ( ? ) . ?????? ?? ???? ???? ??? 0; ?????? ???? ??? ??? 1 ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
??? ???? ???? ???? ???? ????? ????? ? 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
???? - ??????? ??? ????? ?? ????? ???? ???????? ??? ??? ?????? . ????? ??????? ???? ???? ????? . ???? ????? ?? Pearson Cov (X,Y ) ??? ?????? ??????? ?? ??? ??????? : ????? ?? ????? ?????? ????? ???? ?? ??? ??????? . r xy = Cov (X,Y ) / ? x ? y ????? ?????? ???? ???? ???? . ????? ?????? ???? ??? . ???? D ??? ????? ??? ?????? ?? ???? ??????? ??????? ?????? ??? . ???? ????? ?? Spearman ????????? Cov (X,Y) = r X,Y = ???? ????? ????? ?????? ??? ????? ??????? ???????
???? - ??? ?????? - ???? ???? ??????? ??? ????? ?????? ?? ???? ????? ????? ? 1, ???? ???? ???????? ????? ???? . ??? ????? ????? r= 1+ r= 1- r = 0 ??? ????? ????? ??? ??? ??????? ??? ????? ??? ????? ??? ??? ??? ??? ????????? ???? ????? ????? ?????? ??? ????? ??????? ???????
?????? ???? Y=aX+b ?? : ???? ?????? ?????? ??? ???? ?????? ???? ?????? ???? ??????? . ???? ?????? ??? ??????? ???? ?????? ???? ??? . ???? - ??? ?????? - ?? ?????? ??? ???? ????? ?? ???????? ????? ????? ????? . ???? ??? ????? ?? ??????? ???????? : b = Cov(X,Y ) / ? x 2 a= ? y -b* ? x ????????? ???? ????? ????? ?????? ??? ????? ??????? ???????
?? t ???? ???? ?? ???? ????????? ???????? ????? ?????? , ??? ?? ???? ????? ??? ??? 100 ?????? . ???? t - ??????? ??? ?????? ?????? ??? ?????? ?? ?????? ????? . ???? ????? ???? 2 ?????? ????? ???? ????? . t ??? ??? ?????? ??? ( N ); ??? ?????? ??? ?????? ??????? ?????? ??? ???? ??????? ??????? ????? ????????? ??????? ???? ????? ? ?????? ? 2 . ????? ???? ????? N ????? ?? ?????? ??????? . ????????? ???? ????? ????? ?????? ??? ?????
???? t ??? ????? ???? df\p 0.40 40% 0.25 25% 0.10 10% 0.05 5% 0.025 2.5% 0.01 1% 0.005 0.5% 0.0005 0.05% 1 0.324920 1.000000 3.077684 6.313752 12.70620 31.82052 63.65674 636.6192 2 0.288675 0.816497 1.885618 2.919986 4.30265 6.96456 9.92484 31.5991 3 0.276671 0.764892 1.637744 2.353363 3.18245 4.54070 5.84091 12.9240 4 0.270722 0.740697 1.533206 2.131847 2.77645 3.74695 4.60409 8.6103 5 0.267181 0.726687 1.475884 2.015048 2.57058 3.36493 4.03214 6.8688 ? 6 0.264835 0.717558 1.439756 1.943180 2.44691 3.14267 3.70743 5.9588 7 0.263167 0.711142 1.414924 1.894579 2.36462 2.99795 3.49948 5.4079 8 0.261921 0.706387 1.396815 1.859548 2.30600 2.89646 3.35539 5.0413 9 0.260955 0.702722 1.383029 1.833113 2.26216 2.82144 3.24984 4.7809 10 0.260185 0.699812 1.372184 1.812461 2.22814 2.76377 3.16927 4.5869 ? 11 0.259556 0.697445 1.363430 1.795885 2.20099 2.71808 3.10581 4.4370 12 0.259033 0.695483 1.356217 1.782288 2.17881 2.68100 3.05454 4.3178 13 0.258591 0.693829 1.350171 1.770933 2.16037 2.65031 3.01228 4.2208 14 0.258213 0.692417 1.345030 1.761310 2.14479 2.62449 2.97684 4.1405 15 0.257885 0.691197 1.340606 1.753050 2.13145 2.60248 2.94671 4.0728 ? 16 0.257599 0.690132 1.336757 1.745884 2.11991 2.58349 2.92078 4.0150 17 0.257347 0.689195 1.333379 1.739607 2.10982 2.56693 2.89823 3.9651 18 0.257123 0.688364 1.330391 1.734064 2.10092 2.55238 2.87844 3.9216 19 0.256923 0.687621 1.327728 1.729133 2.09302 2.53948 2.86093 3.8834 20 0.256743 0.686954 1.325341 1.724718 2.08596 2.52798 2.84534 3.8495 ? 21 0.256580 0.686352 1.323188 1.720743 2.07961 2.51765 2.83136 3.8193 22 0.256432 0.685805 1.321237 1.717144 2.07387 2.50832 2.81876 3.7921 23 0.256297 0.685306 1.319460 1.713872 2.06866 2.49987 2.80734 3.7676 24 0.256173 0.684850 1.317836 1.710882 2.06390 2.49216 2.79694 3.7454 25 0.256060 0.684430 1.316345 1.708141 2.05954 2.48511 2.78744 3.7251 ? 26 0.255955 0.684043 1.314972 1.705618 2.05553 2.47863 2.77871 3.7066 27 0.255858 0.683685 1.313703 1.703288 2.05183 2.47266 2.77068 3.6896 28 0.255768 0.683353 1.312527 1.701131 2.04841 2.46714 2.76326 3.6739 29 0.255684 0.683044 1.311434 1.699127 2.04523 2.46202 2.75639 3.6594 30 0.255605 0.682756 1.310415 1.697261 2.04227 2.45726 2.75000 3.6460 ? inf 0.253347 0.674490 1.281552 1.644854 1.95996 2.32635 2.57583 3.2905 ??????? ??????? ????????? ???? ????? ????? ?????? ??? ?????
???? X 2 ??? ????? ????? ???? ??????? ???????? ????? ????? ????? ?????? ????? ????? ????? ???? . ????? ?????? ??? ???? ??? ??? ??? ?????? ???? ??? ????? . ??????? ???????? ?? X 2 : ????? ?? ?????? ??????? . ???????? ? &quot; ? ????? ???? . ??????? ???????? ?????? , ?? ????? . ??? ?????? ????? ????? , ????? ??? ????? . ?? ???? ???? ???????? ???? ? -1. ???? ????? ??? ?? - ??? ????? ????? / ????? ??? ????? ?????? ?????? ???? . ??????? ??????? ????????? ???? ????? ????? ?????? ??? ????? X 2 ????? ????? ????? ????? ????? :
???? X 2 ??? ????? ???? df\area 0.995 99.5% 0.99 99% 0.975 97.5% 0.950 95% 0.90 90% 0.750 75% 0.50 50% 0.25 25% 0.1 10% 0.05 5% 0.025 2.5% 0.01 1% 0.005 0.5% 1 0.00004 0.00016 0.00098 0.00393 0.01579 0.10153 0.45494 1.32330 2.70554 3.84146 5.02389 6.63490 7.87944 2 0.01003 0.02010 0.05064 0.10259 0.21072 0.57536 1.38629 2.77259 4.60517 5.99146 7.37776 9.21034 10.59663 3 0.07172 0.11483 0.21580 0.35185 0.58437 1.21253 2.36597 4.10834 6.25139 7.81473 9.34840 11.34487 12.83816 4 0.20699 0.29711 0.48442 0.71072 1.06362 1.92256 3.35669 5.38527 7.77944 9.48773 11.14329 13.27670 14.86026 5 0.41174 0.55430 0.83121 1.14548 1.61031 2.67460 4.35146 6.62568 9.23636 11.07050 12.83250 15.08627 16.74960 ? 6 0.67573 0.87209 1.23734 1.63538 2.20413 3.45460 5.34812 7.84080 10.64464 12.59159 14.44938 16.81189 18.54758 7 0.98926 1.23904 1.68987 2.16735 2.83311 4.25485 6.34581 9.03715 12.01704 14.06714 16.01276 18.47531 20.27774 8 1.34441 1.64650 2.17973 2.73264 3.48954 5.07064 7.34412 10.21885 13.36157 15.50731 17.53455 20.09024 21.95495 9 1.73493 2.08790 2.70039 3.32511 4.16816 5.89883 8.34283 11.38875 14.68366 16.91898 19.02277 21.66599 23.58935 10 2.15586 2.55821 3.24697 3.94030 4.86518 6.73720 9.34182 12.54886 15.98718 18.30704 20.48318 23.20925 25.18818 ? 11 2.60322 3.05348 3.81575 4.57481 5.57778 7.58414 10.34100 13.70069 17.27501 19.67514 21.92005 24.72497 26.75685 12 3.07382 3.57057 4.40379 5.22603 6.30380 8.43842 11.34032 14.84540 18.54935 21.02607 23.33666 26.21697 28.29952 13 3.56503 4.10692 5.00875 5.89186 7.04150 9.29907 12.33976 15.98391 19.81193 22.36203 24.73560 27.68825 29.81947 14 4.07467 4.66043 5.62873 6.57063 7.78953 10.16531 13.33927 17.11693 21.06414 23.68479 26.11895 29.14124 31.31935 15 4.60092 5.22935 6.26214 7.26094 8.54676 11.03654 14.33886 18.24509 22.30713 24.99579 27.48839 30.57791 32.80132 ? 16 5.14221 5.81221 6.90766 7.96165 9.31224 11.91222 15.33850 19.36886 23.54183 26.29623 28.84535 31.99993 34.26719 17 5.69722 6.40776 7.56419 8.67176 10.08519 12.79193 16.33818 20.48868 24.76904 27.58711 30.19101 33.40866 35.71847 18 6.26480 7.01491 8.23075 9.39046 10.86494 13.67529 17.33790 21.60489 25.98942 28.86930 31.52638 34.80531 37.15645 19 6.84397 7.63273 8.90652 10.11701 11.65091 14.56200 18.33765 22.71781 27.20357 30.14353 32.85233 36.19087 38.58226 20 7.43384 8.26040 9.59078 10.85081 12.44261 15.45177 19.33743 23.82769 28.41198 31.41043 34.16961 37.56623 39.99685 ? 21 8.03365 8.89720 10.28290 11.59131 13.23960 16.34438 20.33723 24.93478 29.61509 32.67057 35.47888 38.93217 41.40106 22 8.64272 9.54249 10.98232 12.33801 14.04149 17.23962 21.33704 26.03927 30.81328 33.92444 36.78071 40.28936 42.79565 23 9.26042 10.19572 11.68855 13.09051 14.84796 18.13730 22.33688 27.14134 32.00690 35.17246 38.07563 41.63840 44.18128 24 9.88623 10.85636 12.40115 13.84843 15.65868 19.03725 23.33673 28.24115 33.19624 36.41503 39.36408 42.97982 45.55851 25 10.51965 11.52398 13.11972 14.61141 16.47341 19.93934 24.33659 29.33885 34.38159 37.65248 40.64647 44.31410 46.92789 ? 26 11.16024 12.19815 13.84390 15.37916 17.29188 20.84343 25.33646 30.43457 35.56317 38.88514 41.92317 45.64168 48.28988 27 11.80759 12.87850 14.57338 16.15140 18.11390 21.74940 26.33634 31.52841 36.74122 40.11327 43.19451 46.96294 49.64492 28 12.46134 13.56471 15.30786 16.92788 18.93924 22.65716 27.33623 32.62049 37.91592 41.33714 44.46079 48.27824 50.99338 29 13.12115 14.25645 16.04707 17.70837 19.76774 23.56659 28.33613 33.71091 39.08747 42.55697 45.72229 49.58788 52.33562 30 13.78672 14.95346 16.79077 18.49266 20.59923 24.47761 29.33603 34.79974 40.25602 43.77297 46.97924 50.89218 53.67196 ??????? ??????? ????????? ???? ????? ????? ?????? ??? ?????
????? ???? ????? ?????? ??? ?????? ??????? ?????? ?????? . ????? ???? ????? ?????? ?? ????? ?????? ??????? ?????? ?????? . ?????? ??????? Paired samples ?????? ?? ??????? Unpaired samples ???? ?????? ???? ?????? ( ?? ???? ???? 2 ?????? ). ?????? ????? ( ????? ????? ???? ) ???? ?????? ( ?? ???? ???? ???? ??? ). N-1 = df df= (N 1 -1)+(N 2 -1) ?????? ?? ?????? ?????? ?????? ???? ????? ????? : ???? ?????? ???? : ???? ?????? ?????? ????? df ?????? ??????? ????
???? ?????? ?????? ??? ???? : N¡Ü30 ???????? ?????????? ??? ???????? 30<N<100 ???????? ?????????? ???? ???????? N¡Ý100 ???? ?? ????????? . ??????? ???????? ??????? ?????? ???? ?????? ?????? ???? ????? ? &quot; ? ????? ????? ?????? ????? ??? ( N ), ???? ????? ?? ???????? ?????? ????? ??????? . ?????? ?? ?? ???????? ??? ? ????? ???? ??? ?????? N ???? ???? , ???? ???? ???? ???? . ?????? ??????? ????
??????? ??????? ?????? ???? ????? ??????? ???????? ???? : ?????? ??????? ???? X ??? ?????? : ????? ????????? ?? ?????? ????? ???? O ??? ?????? : ????? ????? ?? ?????? ????? R ????? ????? ?? ?????? ??? ??????? - - - - - ????? ?? ????? ?? ?????? ??? ??????? ???? ?????? ????? ???? ??? - ?????? ???? ???? - ??????
Pre-Post without Control ????? ???? Case Study Post with Control X O O1 X O2 X O1 - - - - O2 ?????? ??????? ???? ???? ?????? ????? ???? ??? - ?????? ???? ???? - ??????
????? ????? ?? ?????? ??????? ?????? ???????? ????? ?????? ????? ?????? ??????? , ?????? ???? ?????? ????? , ???? ?????? ??????? . R O1 X O2 R O3 O4 R O1 X O2 R O3 O4 R X O5 R O6 R X O1 R O2 Solomon 4 group design Post Only with Control Pre-Post with Control ????? ?? ??? ?????? ???? ??? : ????? ????? ?? ????? ( ???? ????? ?????? ). ????? ????? ???? ?????? ?????? ( ???? ????? ?????? ). ?????? ??????? ???? ???? ??? - ?????? ???? ???? - ?????? ???? ?????? ?????
Time Series Experiment Pre-Post with non equivalent Control O1 O2 O3 O4 X O5 O6 O7 O8 O1 X O2 - - - - - - - - O3 O4 ???? ????? ¨C ???? ??? ????? Evaluation Research ???? ??? - ?????? ?????? ??????? ???? ???? ?????? ????? ???? ???? - ??????
???? ?????? ?????
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???? ?????? ???? ?????????

  • 1. ???? ????? &quot; ?? ??? &quot; ?????????? ????? : ??? ??? ???? : ????? ?? ? &quot; ? ?????? ????? ??????? ???????? 6 ????? , 2007 ???? ????? ?? ?????? ?????? ??? ??? ????? ! ?? ??????? ??????? ?? ?????? ??????? . ???? ????? ????? ?????? ??? ????? ????????? ??????? ??????? ?????? ???????
  • 2. ??? ???? ??? / ??????? ????? ??? / ??? ?????? ???? ???? ????? ??? ?????? ??? ?????? ???? ??? ???? ?????? ?????? ??????? ???? ??? ???? ?????? ???? ?????? ??? , ???? , ??? - ?? ??? ', ??? ???? ????? ???? ??????? ??????? ????????? ???? ????? ????? ?????? ??? ?????
  • 3. ???? ??????? ??? ???? ????? ???? ?????? ??? ??? . ???? ??????? ???????? ????????? ??? ???? ????? ???? ?????? ???? . ???? ????? ?????? ?????? ??????? ??? ??? ???? ????? ?????? ?????? ??????? ?? ???????? ???? Mode ????? Median ????? Mean ???? ????? ????? . ??? Xi-Mean) = 0 Median = n / 2 ??? ????? ??????? ??????? ????????? ???? ????? ????? ??????
  • 4. ????? ???? ?????? ???? : ????? ???? ?????? ???? ????? ?? ?????? ???? ????? ??? , ???? ????? ????? ???? ????? ????? . ???? ?????? ????? ??? ??? ????? ?????? ??????? ???? ???? ???? ???? ? / ?? ?? ????? ???? ???? ( ??? 30). ??? ????? ??? ??? ???? ???? ????? ?????? ?????? ???? ???? ????? ???? ????? ????? ??? ????? ??????? ??????? ????????? ???? ????? ????? ??????
  • 5. ???? ????? ?? ??????? ???????? ????? ??????? ????????? ???? ??? ?? ????? . ???? ????? ????? ?? ?????? ???????? ??????? ?? ????? ??????? ?? abs(Xi-Mean)) /n Xmax ¨C X min ??? ????? ????? ????? ???? ?????? ?? ????? . ????? ?? ?????? ????????? ? ? ??? Xi ¨C Xm) ? ??? n-1) ??? ????? ????? ????? ???? ?????? ?? ????? . ????? ?? ?????? ????????? ???? Range ??? ???? ????? ?? ????? ??????? ????? ????? Mean spread ????? Variance ????? ??? Standard deviation ?? abs(Xi-Median)) /n Varp (RANGE) Stdevp (RANGE) ????? ?????? ??? ????? ??????? ??????? ????????? ???? ?????
  • 6. ????? ??????? ?????? ???? : ????? ???? ?????? ???? ????? ?? ???? ???????? . ???? ????? ! ???? ???? ????? ????? ?? ?? ?????? ?????? . ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
  • 7. ????? ????? ??? ????? ??? ??? ???? ???? ????? ?????? ?????? ???? ???? ????? ???? ????? ????? ??? ????? ???? ?????? ???????? ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
  • 8. ??? ???? ??????? ??? ???? ???????? ??? ???? ??? ??????? ????? ??????? ?????? ????? ?? ?????? ??????? ?? ?????? ?? ?????? ????? . ?? ???? ????? . ???? ?????? ??? ???? ??? ????? ??????? ??????? ??????? ?? ????? ??????? ?? ????? ??????? ????? ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
  • 9. ?????? : ??????? ??????? , ?? - ????? ?????? ????? . ????? ?????? ???? ??????? ??? ????? ?? ??? ???????? . ????? = ?????? = ?????? . ??????? ?? ??? ????? ?? ?????? ?????? ??????? ???????? : ??????? ??????? ????? ????? ???? ? = 3.14159 e= 2.71828 ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
  • 10. 68.3% ????? ????? ??? ??? 95.4% ????? ??? ????? ??? 99.7% ????? ??? ????? ??? 34.13% ????? ????? ???? ??????? 13.59% ????? ????? ???? ?????? 2.15% ????? ????? ???? ??????? 0.15% ????? ????? ???? ??????? ????? ????? ???? ???? ???? Z ??????? ??????? ?????? : ??????? ??????? , ?? - ????? ?????? ????? . ????? ?????? ???? ??????? ??? ????? ?? ??? ???????? . ????? = ?????? = ?????? . 34% 13.7% 2.15% 0.15% 3 2 1 0 - 3 - 2 - 1 Z ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
  • 11. ???? : Z > 0 ???? ??? ?????? Z < 0 ???? ???? ?????? Z = 0 ???? ????? ?? ?????? ???? ???? ???? ??? ???? ????? ???? ?? ????? ????? ????????? ???? ??? ????? ???? ?????? ??????? ???? . ???? ????? ???? ( ? ) ?? ??? ?????? ( x ) ??????? ( ? ) . ?????? ?? ???? ???? ??? 0; ?????? ???? ??? ??? 1 ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
  • 12. ??? ???? ???? ???? ???? ????? ????? ? 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015 1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177 1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545 1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857 2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890 2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964 2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 ???? ????? ????? ?????? ??? ????? ??????? ??????? ?????????
  • 13. ???? - ??????? ??? ????? ?? ????? ???? ???????? ??? ??? ?????? . ????? ??????? ???? ???? ????? . ???? ????? ?? Pearson Cov (X,Y ) ??? ?????? ??????? ?? ??? ??????? : ????? ?? ????? ?????? ????? ???? ?? ??? ??????? . r xy = Cov (X,Y ) / ? x ? y ????? ?????? ???? ???? ???? . ????? ?????? ???? ??? . ???? D ??? ????? ??? ?????? ?? ???? ??????? ??????? ?????? ??? . ???? ????? ?? Spearman ????????? Cov (X,Y) = r X,Y = ???? ????? ????? ?????? ??? ????? ??????? ???????
  • 14. ???? - ??? ?????? - ???? ???? ??????? ??? ????? ?????? ?? ???? ????? ????? ? 1, ???? ???? ???????? ????? ???? . ??? ????? ????? r= 1+ r= 1- r = 0 ??? ????? ????? ??? ??? ??????? ??? ????? ??? ????? ??? ??? ??? ??? ????????? ???? ????? ????? ?????? ??? ????? ??????? ???????
  • 15. ?????? ???? Y=aX+b ?? : ???? ?????? ?????? ??? ???? ?????? ???? ?????? ???? ??????? . ???? ?????? ??? ??????? ???? ?????? ???? ??? . ???? - ??? ?????? - ?? ?????? ??? ???? ????? ?? ???????? ????? ????? ????? . ???? ??? ????? ?? ??????? ???????? : b = Cov(X,Y ) / ? x 2 a= ? y -b* ? x ????????? ???? ????? ????? ?????? ??? ????? ??????? ???????
  • 16. ?? t ???? ???? ?? ???? ????????? ???????? ????? ?????? , ??? ?? ???? ????? ??? ??? 100 ?????? . ???? t - ??????? ??? ?????? ?????? ??? ?????? ?? ?????? ????? . ???? ????? ???? 2 ?????? ????? ???? ????? . t ??? ??? ?????? ??? ( N ); ??? ?????? ??? ?????? ??????? ?????? ??? ???? ??????? ??????? ????? ????????? ??????? ???? ????? ? ?????? ? 2 . ????? ???? ????? N ????? ?? ?????? ??????? . ????????? ???? ????? ????? ?????? ??? ?????
  • 17. ???? t ??? ????? ???? df\p 0.40 40% 0.25 25% 0.10 10% 0.05 5% 0.025 2.5% 0.01 1% 0.005 0.5% 0.0005 0.05% 1 0.324920 1.000000 3.077684 6.313752 12.70620 31.82052 63.65674 636.6192 2 0.288675 0.816497 1.885618 2.919986 4.30265 6.96456 9.92484 31.5991 3 0.276671 0.764892 1.637744 2.353363 3.18245 4.54070 5.84091 12.9240 4 0.270722 0.740697 1.533206 2.131847 2.77645 3.74695 4.60409 8.6103 5 0.267181 0.726687 1.475884 2.015048 2.57058 3.36493 4.03214 6.8688 ? 6 0.264835 0.717558 1.439756 1.943180 2.44691 3.14267 3.70743 5.9588 7 0.263167 0.711142 1.414924 1.894579 2.36462 2.99795 3.49948 5.4079 8 0.261921 0.706387 1.396815 1.859548 2.30600 2.89646 3.35539 5.0413 9 0.260955 0.702722 1.383029 1.833113 2.26216 2.82144 3.24984 4.7809 10 0.260185 0.699812 1.372184 1.812461 2.22814 2.76377 3.16927 4.5869 ? 11 0.259556 0.697445 1.363430 1.795885 2.20099 2.71808 3.10581 4.4370 12 0.259033 0.695483 1.356217 1.782288 2.17881 2.68100 3.05454 4.3178 13 0.258591 0.693829 1.350171 1.770933 2.16037 2.65031 3.01228 4.2208 14 0.258213 0.692417 1.345030 1.761310 2.14479 2.62449 2.97684 4.1405 15 0.257885 0.691197 1.340606 1.753050 2.13145 2.60248 2.94671 4.0728 ? 16 0.257599 0.690132 1.336757 1.745884 2.11991 2.58349 2.92078 4.0150 17 0.257347 0.689195 1.333379 1.739607 2.10982 2.56693 2.89823 3.9651 18 0.257123 0.688364 1.330391 1.734064 2.10092 2.55238 2.87844 3.9216 19 0.256923 0.687621 1.327728 1.729133 2.09302 2.53948 2.86093 3.8834 20 0.256743 0.686954 1.325341 1.724718 2.08596 2.52798 2.84534 3.8495 ? 21 0.256580 0.686352 1.323188 1.720743 2.07961 2.51765 2.83136 3.8193 22 0.256432 0.685805 1.321237 1.717144 2.07387 2.50832 2.81876 3.7921 23 0.256297 0.685306 1.319460 1.713872 2.06866 2.49987 2.80734 3.7676 24 0.256173 0.684850 1.317836 1.710882 2.06390 2.49216 2.79694 3.7454 25 0.256060 0.684430 1.316345 1.708141 2.05954 2.48511 2.78744 3.7251 ? 26 0.255955 0.684043 1.314972 1.705618 2.05553 2.47863 2.77871 3.7066 27 0.255858 0.683685 1.313703 1.703288 2.05183 2.47266 2.77068 3.6896 28 0.255768 0.683353 1.312527 1.701131 2.04841 2.46714 2.76326 3.6739 29 0.255684 0.683044 1.311434 1.699127 2.04523 2.46202 2.75639 3.6594 30 0.255605 0.682756 1.310415 1.697261 2.04227 2.45726 2.75000 3.6460 ? inf 0.253347 0.674490 1.281552 1.644854 1.95996 2.32635 2.57583 3.2905 ??????? ??????? ????????? ???? ????? ????? ?????? ??? ?????
  • 18. ???? X 2 ??? ????? ????? ???? ??????? ???????? ????? ????? ????? ?????? ????? ????? ????? ???? . ????? ?????? ??? ???? ??? ??? ??? ?????? ???? ??? ????? . ??????? ???????? ?? X 2 : ????? ?? ?????? ??????? . ???????? ? &quot; ? ????? ???? . ??????? ???????? ?????? , ?? ????? . ??? ?????? ????? ????? , ????? ??? ????? . ?? ???? ???? ???????? ???? ? -1. ???? ????? ??? ?? - ??? ????? ????? / ????? ??? ????? ?????? ?????? ???? . ??????? ??????? ????????? ???? ????? ????? ?????? ??? ????? X 2 ????? ????? ????? ????? ????? :
  • 19. ???? X 2 ??? ????? ???? df\area 0.995 99.5% 0.99 99% 0.975 97.5% 0.950 95% 0.90 90% 0.750 75% 0.50 50% 0.25 25% 0.1 10% 0.05 5% 0.025 2.5% 0.01 1% 0.005 0.5% 1 0.00004 0.00016 0.00098 0.00393 0.01579 0.10153 0.45494 1.32330 2.70554 3.84146 5.02389 6.63490 7.87944 2 0.01003 0.02010 0.05064 0.10259 0.21072 0.57536 1.38629 2.77259 4.60517 5.99146 7.37776 9.21034 10.59663 3 0.07172 0.11483 0.21580 0.35185 0.58437 1.21253 2.36597 4.10834 6.25139 7.81473 9.34840 11.34487 12.83816 4 0.20699 0.29711 0.48442 0.71072 1.06362 1.92256 3.35669 5.38527 7.77944 9.48773 11.14329 13.27670 14.86026 5 0.41174 0.55430 0.83121 1.14548 1.61031 2.67460 4.35146 6.62568 9.23636 11.07050 12.83250 15.08627 16.74960 ? 6 0.67573 0.87209 1.23734 1.63538 2.20413 3.45460 5.34812 7.84080 10.64464 12.59159 14.44938 16.81189 18.54758 7 0.98926 1.23904 1.68987 2.16735 2.83311 4.25485 6.34581 9.03715 12.01704 14.06714 16.01276 18.47531 20.27774 8 1.34441 1.64650 2.17973 2.73264 3.48954 5.07064 7.34412 10.21885 13.36157 15.50731 17.53455 20.09024 21.95495 9 1.73493 2.08790 2.70039 3.32511 4.16816 5.89883 8.34283 11.38875 14.68366 16.91898 19.02277 21.66599 23.58935 10 2.15586 2.55821 3.24697 3.94030 4.86518 6.73720 9.34182 12.54886 15.98718 18.30704 20.48318 23.20925 25.18818 ? 11 2.60322 3.05348 3.81575 4.57481 5.57778 7.58414 10.34100 13.70069 17.27501 19.67514 21.92005 24.72497 26.75685 12 3.07382 3.57057 4.40379 5.22603 6.30380 8.43842 11.34032 14.84540 18.54935 21.02607 23.33666 26.21697 28.29952 13 3.56503 4.10692 5.00875 5.89186 7.04150 9.29907 12.33976 15.98391 19.81193 22.36203 24.73560 27.68825 29.81947 14 4.07467 4.66043 5.62873 6.57063 7.78953 10.16531 13.33927 17.11693 21.06414 23.68479 26.11895 29.14124 31.31935 15 4.60092 5.22935 6.26214 7.26094 8.54676 11.03654 14.33886 18.24509 22.30713 24.99579 27.48839 30.57791 32.80132 ? 16 5.14221 5.81221 6.90766 7.96165 9.31224 11.91222 15.33850 19.36886 23.54183 26.29623 28.84535 31.99993 34.26719 17 5.69722 6.40776 7.56419 8.67176 10.08519 12.79193 16.33818 20.48868 24.76904 27.58711 30.19101 33.40866 35.71847 18 6.26480 7.01491 8.23075 9.39046 10.86494 13.67529 17.33790 21.60489 25.98942 28.86930 31.52638 34.80531 37.15645 19 6.84397 7.63273 8.90652 10.11701 11.65091 14.56200 18.33765 22.71781 27.20357 30.14353 32.85233 36.19087 38.58226 20 7.43384 8.26040 9.59078 10.85081 12.44261 15.45177 19.33743 23.82769 28.41198 31.41043 34.16961 37.56623 39.99685 ? 21 8.03365 8.89720 10.28290 11.59131 13.23960 16.34438 20.33723 24.93478 29.61509 32.67057 35.47888 38.93217 41.40106 22 8.64272 9.54249 10.98232 12.33801 14.04149 17.23962 21.33704 26.03927 30.81328 33.92444 36.78071 40.28936 42.79565 23 9.26042 10.19572 11.68855 13.09051 14.84796 18.13730 22.33688 27.14134 32.00690 35.17246 38.07563 41.63840 44.18128 24 9.88623 10.85636 12.40115 13.84843 15.65868 19.03725 23.33673 28.24115 33.19624 36.41503 39.36408 42.97982 45.55851 25 10.51965 11.52398 13.11972 14.61141 16.47341 19.93934 24.33659 29.33885 34.38159 37.65248 40.64647 44.31410 46.92789 ? 26 11.16024 12.19815 13.84390 15.37916 17.29188 20.84343 25.33646 30.43457 35.56317 38.88514 41.92317 45.64168 48.28988 27 11.80759 12.87850 14.57338 16.15140 18.11390 21.74940 26.33634 31.52841 36.74122 40.11327 43.19451 46.96294 49.64492 28 12.46134 13.56471 15.30786 16.92788 18.93924 22.65716 27.33623 32.62049 37.91592 41.33714 44.46079 48.27824 50.99338 29 13.12115 14.25645 16.04707 17.70837 19.76774 23.56659 28.33613 33.71091 39.08747 42.55697 45.72229 49.58788 52.33562 30 13.78672 14.95346 16.79077 18.49266 20.59923 24.47761 29.33603 34.79974 40.25602 43.77297 46.97924 50.89218 53.67196 ??????? ??????? ????????? ???? ????? ????? ?????? ??? ?????
  • 20. ????? ???? ????? ?????? ??? ?????? ??????? ?????? ?????? . ????? ???? ????? ?????? ?? ????? ?????? ??????? ?????? ?????? . ?????? ??????? Paired samples ?????? ?? ??????? Unpaired samples ???? ?????? ???? ?????? ( ?? ???? ???? 2 ?????? ). ?????? ????? ( ????? ????? ???? ) ???? ?????? ( ?? ???? ???? ???? ??? ). N-1 = df df= (N 1 -1)+(N 2 -1) ?????? ?? ?????? ?????? ?????? ???? ????? ????? : ???? ?????? ???? : ???? ?????? ?????? ????? df ?????? ??????? ????
  • 21. ???? ?????? ?????? ??? ???? : N¡Ü30 ???????? ?????????? ??? ???????? 30<N<100 ???????? ?????????? ???? ???????? N¡Ý100 ???? ?? ????????? . ??????? ???????? ??????? ?????? ???? ?????? ?????? ???? ????? ? &quot; ? ????? ????? ?????? ????? ??? ( N ), ???? ????? ?? ???????? ?????? ????? ??????? . ?????? ?? ?? ???????? ??? ? ????? ???? ??? ?????? N ???? ???? , ???? ???? ???? ???? . ?????? ??????? ????
  • 22. ??????? ??????? ?????? ???? ????? ??????? ???????? ???? : ?????? ??????? ???? X ??? ?????? : ????? ????????? ?? ?????? ????? ???? O ??? ?????? : ????? ????? ?? ?????? ????? R ????? ????? ?? ?????? ??? ??????? - - - - - ????? ?? ????? ?? ?????? ??? ??????? ???? ?????? ????? ???? ??? - ?????? ???? ???? - ??????
  • 23. Pre-Post without Control ????? ???? Case Study Post with Control X O O1 X O2 X O1 - - - - O2 ?????? ??????? ???? ???? ?????? ????? ???? ??? - ?????? ???? ???? - ??????
  • 24. ????? ????? ?? ?????? ??????? ?????? ???????? ????? ?????? ????? ?????? ??????? , ?????? ???? ?????? ????? , ???? ?????? ??????? . R O1 X O2 R O3 O4 R O1 X O2 R O3 O4 R X O5 R O6 R X O1 R O2 Solomon 4 group design Post Only with Control Pre-Post with Control ????? ?? ??? ?????? ???? ??? : ????? ????? ?? ????? ( ???? ????? ?????? ). ????? ????? ???? ?????? ?????? ( ???? ????? ?????? ). ?????? ??????? ???? ???? ??? - ?????? ???? ???? - ?????? ???? ?????? ?????
  • 25. Time Series Experiment Pre-Post with non equivalent Control O1 O2 O3 O4 X O5 O6 O7 O8 O1 X O2 - - - - - - - - O3 O4 ???? ????? ¨C ???? ??? ????? Evaluation Research ???? ??? - ?????? ?????? ??????? ???? ???? ?????? ????? ???? ???? - ??????
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