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Games-Howell 사후분석 표작성 관련하여 문의 드립니다.

분류: QnA 자료실 글쓴이: StatEdu 날짜: 2025-05-12 11:31

교수님 안녕하세요,  좋은 정보를 올려주셔서 통계공부 할 때 늘 도움 받고 있습니다. 

집단별로 만족도에 차이가 있는지를 알아보기 위해, ANOVA를 실시하였습니다. 

레비니 검정에서 유의확률이 .05 미만으로 나와 사후검정에서 Games-Howell 을 실시하였습니다.  교수님께서 올려주신 유튜브 영상을 보며... 집단간 비교를 표에 어떻게 작성해야 할지 고민을 해보았는데, 집단이 너무 많다보니... 이렇게 하는 게 맞는 건지 고민이 되어 이렇게 글을 올립니다. 

특히, g와c는 동일한 만족도 점수를 나타냈습니다. 그런데, f와 n이 g와는 차이가 있는데, c와 차이가 없다고 나와 더욱 헷갈리는 것 같습니다. 

(1), (2) 중에 어떤 게 맞는 건지 설명을 부탁드리고 싶습니다. 

(1) e, p, b < g 

(2) e, f, p, b, n < g, c

기술통계
　 N 평균 표준편차 표준오차 평균의
95% 신뢰구간		 최소값 최대값
하한 상한
만족도 a 45 3.8667 0.69413 0.10347 3.6581 4.0752 3.00 5.00
b 280 3.7036 0.86426 0.05165 3.6019 3.8052 1.00 5.00
c 140 4.0714 0.75525 0.06383 3.9452 4.1976 1.00 5.00
d 44 3.9545 0.83400 0.12573 3.7010 4.2081 1.00 5.00
e 254 3.7402 0.76703 0.04813 3.6454 3.8349 2.00 5.00
f 151 3.7748 0.73187 0.05956 3.6572 3.8925 1.00 5.00
g 202 4.0693 0.78236 0.05505 3.9608 4.1779 2.00 5.00
h 145 3.9172 0.77731 0.06455 3.7896 4.0448 1.00 5.00
i 39 3.9487 0.72361 0.11587 3.7141 4.1833 3.00 5.00
j 39 4.1538 0.77929 0.12479 3.9012 4.4065 2.00 5.00
k 51 3.7843 0.80781 0.11312 3.5571 4.0115 1.00 5.00
l 10 3.5000 0.52705 0.16667 3.1230 3.8770 3.00 4.00
m 84 3.9881 0.68537 0.07478 3.8394 4.1368 2.00 5.00
n 98 3.7347 0.75370 0.07614 3.5836 3.8858 2.00 5.00
o 81 3.9630 0.67905 0.07545 3.8128 4.1131 3.00 5.00
p 266 3.7669 0.79988 0.04904 3.6704 3.8635 1.00 5.00
q 20 3.6000 0.88258 0.19735 3.1869 4.0131 1.00 5.00
r 25 3.6000 0.81650 0.16330 3.2630 3.9370 2.00 5.00
전체 1974 3.8475 0.78928 0.01776 3.8127 3.8824 1.00 5.00


다중비교
Games-Howell
종속변수 평균차이(I-J) 표준오차 유의확률 95%
신뢰구간
하한 상한
만족도 a b 0.16310 0.11565 0.994 -0.2563 0.5825
c -0.20476 0.12158 0.964 -0.6431 0.2335
d -0.08788 0.16284 1.000 -0.6741 0.4984
e 0.12651 0.11412 1.000 -0.2881 0.5412
f 0.09183 0.11939 1.000 -0.3394 0.5231
g -0.20264 0.11721 0.954 -0.6269 0.2216
h -0.05057 0.12196 1.000 -0.4901 0.3889
i -0.08205 0.15535 1.000 -0.6423 0.4782
j -0.28718 0.16211 0.944 -0.8724 0.2981
k 0.08235 0.15330 1.000 -0.4677 0.6324
l 0.36667 0.19618 0.889 -0.4304 1.1637
m -0.12143 0.12767 1.000 -0.5802 0.3373
n 0.13197 0.12847 1.000 -0.3292 0.5931
o -0.09630 0.12806 1.000 -0.5564 0.3638
p 0.09975 0.11451 1.000 -0.3161 0.5156
q 0.26667 0.22283 0.998 -0.5812 1.1145
r 0.26667 0.19332 0.994 -0.4497 0.9830
b a -0.16310 0.11565 0.994 -0.5825 0.2563
c -.36786* 0.08211 0.001 -0.6567 -0.0790
d -0.25097 0.13593 0.919 -0.7469 0.2450
e -0.03659 0.07060 1.000 -0.2841 0.2109
f -0.07126 0.07883 1.000 -0.3484 0.2058
g
 -.36574* 0.07548 0.000 -0.6306 -0.1009
h -0.21367 0.08267 0.468 -0.5045 0.0771
i -0.24515 0.12686 0.886 -0.7096 0.2193
j -0.45027 0.13505 0.115 -0.9458 0.0452
k -0.08074 0.12435 1.000 -0.5306 0.3691
l 0.20357 0.17449 0.997 -0.5646 0.9717
m -0.28452 0.09088 0.156 -0.6066 0.0375
n -0.03112 0.09200 1.000 -0.3565 0.2943
o -0.25939 0.09144 0.301 -0.5836 0.0648
p -0.06335 0.07122 1.000 -0.3130 0.1863
q 0.10357 0.20400 1.000 -0.6978 0.9049
r 0.10357 0.17127 1.000 -0.5498 0.7569
c a 0.20476 0.12158 0.964 -0.2335 0.6431
b .36786* 0.08211 0.001 0.0790 0.6567
d 0.11688 0.14101 1.000 -0.3948 0.6286
e
 .33127* 0.07994 0.006 0.0498 0.6127
f 0.29659 0.08730 0.073 -0.0108 0.6040
g 0.00212 0.08429 1.000 -0.2945 0.2987
h 0.15419 0.09078 0.966 -0.1655 0.4739
i 0.12271 0.13229 1.000 -0.3584 0.6039
j -0.08242 0.14016 1.000 -0.5935 0.4287
k 0.28711 0.12988 0.741 -0.1805 0.7547
l 0.57143 0.17847 0.250 -0.1994 1.3422
m 0.08333 0.09832 1.000 -0.2645 0.4312
n 0.33673 0.09935 0.077 -0.0143 0.6878
o 0.10847 0.09883 1.000 -0.2414 0.4583
p
 .30451* 0.08050 0.021 0.0212 0.5878
q 0.47143 0.20742 0.693 -0.3374 1.2803
r 0.47143 0.17533 0.426 -0.1924 1.1352
d a 0.08788 0.16284 1.000 -0.4984 0.6741
b 0.25097 0.13593 0.919 -0.2450 0.7469
c -0.11688 0.14101 1.000 -0.6286 0.3948
e 0.21439 0.13463 0.977 -0.2777 0.7064
f 0.17971 0.13912 0.998 -0.3261 0.6855
g -0.11476 0.13725 1.000 -0.6148 0.3853
h 0.03730 0.14133 1.000 -0.4754 0.5500
i 0.00583 0.17098 1.000 -0.6104 0.6220
j -0.19930 0.17714 1.000 -0.8378 0.4392
k 0.17023 0.16913 1.000 -0.4373 0.7778
l 0.45455 0.20877 0.748 -0.3699 1.2789
m -0.03355 0.14629 1.000 -0.5624 0.4953
n 0.21985 0.14699 0.988 -0.3110 0.7507
o -0.00842 0.14663 1.000 -0.5384 0.5215
p 0.18763 0.13496 0.994 -0.3054 0.6807
q 0.35455 0.23400 0.983 -0.5248 1.2339
r 0.35455 0.20609 0.953 -0.4024 1.1115
e a -0.12651 0.11412 1.000 -0.5412 0.2881
b 0.03659 0.07060 1.000 -0.2109 0.2841
c
 -.33127* 0.07994 0.006 -0.6127 -0.0498
d -0.21439 0.13463 0.977 -0.7064 0.2777
f -0.03468 0.07657 1.000 -0.3040 0.2346
g
 -.32915* 0.07312 0.001 -0.5858 -0.0725
h -0.17708 0.08052 0.753 -0.4605 0.1063
i -0.20856 0.12547 0.965 -0.6689 0.2518
j -0.41369 0.13375 0.198 -0.9054 0.0780
k -0.04416 0.12293 1.000 -0.4896 0.4013
l 0.24016 0.17348 0.985 -0.5275 1.0078
m -0.24794 0.08893 0.331 -0.5634 0.0676
n 0.00546 0.09007 1.000 -0.3134 0.3244
o -0.22281 0.08949 0.542 -0.5405 0.0949
p -0.02676 0.06871 1.000 -0.2677 0.2142
q 0.14016 0.20313 1.000 -0.6594 0.9397
r 0.14016 0.17024 1.000 -0.5107 0.7910
f a -0.09183 0.11939 1.000 -0.5231 0.3394
b 0.07126 0.07883 1.000 -0.2058 0.3484
c -0.29659 0.08730 0.073 -0.6040 0.0108
d -0.17971 0.13912 0.998 -0.6855 0.3261
e 0.03468 0.07657 1.000 -0.2346 0.3040
g
 -.29447* 0.08110 0.035 -0.5797 -0.0093
h -0.14241 0.08783 0.978 -0.4516 0.1668
i -0.17388 0.13028 0.996 -0.6488 0.3011
j -0.37901 0.13827 0.378 -0.8843 0.1263
k -0.00948 0.12784 1.000 -0.4705 0.4515
l 0.27483 0.17699 0.964 -0.4948 1.0445
m -0.21326 0.09560 0.730 -0.5517 0.1252
n 0.04014 0.09666 1.000 -0.3015 0.3818
o -0.18813 0.09612 0.885 -0.5286 0.1523
p 0.00792 0.07715 1.000 -0.2634 0.2792
q 0.17483 0.20614 1.000 -0.6312 0.9809
r 0.17483 0.17382 1.000 -0.4850 0.8347
g a 0.20264 0.11721 0.954 -0.2216 0.6269
b
 .36574* 0.07548 0.000 0.1009 0.6306
c -0.00212 0.08429 1.000 -0.2987 0.2945
d 0.11476 0.13725 1.000 -0.3853 0.6148
e
 .32915* 0.07312 0.001 0.0725 0.5858
f .29447* 0.08110 0.035 0.0093 0.5797
h 0.15207 0.08484 0.944 -0.1464 0.4506
i 0.12059 0.12828 1.000 -0.3482 0.5894
j -0.08454 0.13639 1.000 -0.5841 0.4150
k 0.28499 0.12580 0.704 -0.1694 0.7394
l 0.56931 0.17552 0.243 -0.1994 1.3380
m 0.08121 0.09286 1.000 -0.2476 0.4101
n .33461* 0.09395 0.046 0.0025 0.6668
o 0.10634 0.09340 1.000 -0.2246 0.4373
p .30239* 0.07373 0.006 0.0436 0.5612
q 0.46931 0.20488 0.682 -0.3340 1.2726
r 0.46931 0.17233 0.407 -0.1867 1.1253
h a 0.05057 0.12196 1.000 -0.3889 0.4901
b 0.21367 0.08267 0.468 -0.0771 0.5045
c -0.15419 0.09078 0.966 -0.4739 0.1655
d -0.03730 0.14133 1.000 -0.5500 0.4754
e 0.17708 0.08052 0.753 -0.1063 0.4605
f 0.14241 0.08783 0.978 -0.1668 0.4516
g -0.15207 0.08484 0.944 -0.4506 0.1464
i -0.03148 0.13264 1.000 -0.5137 0.4507
j -0.23660 0.14049 0.962 -0.7487 0.2755
k 0.13293 0.13024 1.000 -0.3358 0.6016
l 0.41724 0.17873 0.655 -0.3538 1.1882
m -0.07085 0.09879 1.000 -0.4203 0.2786
n 0.18255 0.09982 0.933 -0.1700 0.5351
o -0.04572 0.09930 1.000 -0.3971 0.3057
p 0.15032 0.08107 0.926 -0.1350 0.4356
q 0.31724 0.20764 0.979 -0.4921 1.1266
r 0.31724 0.17560 0.924 -0.3472 0.9817
i a 0.08205 0.15535 1.000 -0.4782 0.6423
b 0.24515 0.12686 0.886 -0.2193 0.7096
c -0.12271 0.13229 1.000 -0.6039 0.3584
d -0.00583 0.17098 1.000 -0.6220 0.6104
e 0.20856 0.12547 0.965 -0.2518 0.6689
f 0.17388 0.13028 0.996 -0.3011 0.6488
g -0.12059 0.12828 1.000 -0.5894 0.3482
h 0.03148 0.13264 1.000 -0.4507 0.5137
j -0.20513 0.17029 0.999 -0.8202 0.4100
k 0.16440 0.16193 1.000 -0.4181 0.7469
l 0.44872 0.20299 0.727 -0.3631 1.2605
m -0.03938 0.13791 1.000 -0.5387 0.4600
n 0.21402 0.13865 0.984 -0.2875 0.7156
o -0.01425 0.13827 1.000 -0.5148 0.4863
p 0.18180 0.12582 0.991 -0.2796 0.6432
q 0.34872 0.22885 0.982 -0.5163 1.2137
r 0.34872 0.20023 0.947 -0.3900 1.0874
j a 0.28718 0.16211 0.944 -0.2981 0.8724
b 0.45027 0.13505 0.115 -0.0452 0.9458
c 0.08242 0.14016 1.000 -0.4287 0.5935
d 0.19930 0.17714 1.000 -0.4392 0.8378
e 0.41369 0.13375 0.198 -0.0780 0.9054
f 0.37901 0.13827 0.378 -0.1263 0.8843
g 0.08454 0.13639 1.000 -0.4150 0.5841
h 0.23660 0.14049 0.962 -0.2755 0.7487
i 0.20513 0.17029 0.999 -0.4100 0.8202
k 0.36953 0.16842 0.752 -0.2369 0.9760
l 0.65385 0.20820 0.226 -0.1700 1.4777
m 0.16575 0.14548 0.999 -0.3623 0.6938
n 0.41915 0.14618 0.298 -0.1109 0.9492
o 0.19088 0.14582 0.997 -0.3383 0.7201
p 0.38693 0.13408 0.296 -0.1057 0.8796
q 0.55385 0.23349 0.631 -0.3246 1.4323
r 0.55385 0.20552 0.410 -0.2020 1.3097
k a -0.08235 0.15330 1.000 -0.6324 0.4677
b 0.08074 0.12435 1.000 -0.3691 0.5306
c -0.28711 0.12988 0.741 -0.7547 0.1805
d -0.17023 0.16913 1.000 -0.7778 0.4373
e 0.04416 0.12293 1.000 -0.4013 0.4896
f 0.00948 0.12784 1.000 -0.4515 0.4705
g -0.28499 0.12580 0.704 -0.7394 0.1694
h -0.13293 0.13024 1.000 -0.6016 0.3358
i -0.16440 0.16193 1.000 -0.7469 0.4181
j -0.36953 0.16842 0.752 -0.9760 0.2369
l 0.28431 0.20143 0.988 -0.5228 1.0914
m -0.20378 0.13560 0.988 -0.6905 0.2829
n 0.04962 0.13635 1.000 -0.4394 0.5386
o -0.17865 0.13597 0.997 -0.6666 0.3094
p 0.01740 0.12329 1.000 -0.4292 0.4639
q 0.18431 0.22747 1.000 -0.6759 1.0445
r 0.18431 0.19865 1.000 -0.5481 0.9167
l a -0.36667 0.19618 0.889 -1.1637 0.4304
b -0.20357 0.17449 0.997 -0.9717 0.5646
c -0.57143 0.17847 0.250 -1.3422 0.1994
d -0.45455 0.20877 0.748 -1.2789 0.3699
e -0.24016 0.17348 0.985 -1.0078 0.5275
f -0.27483 0.17699 0.964 -1.0445 0.4948
g -0.56931 0.17552 0.243 -1.3380 0.1994
h -0.41724 0.17873 0.655 -1.1882 0.3538
i -0.44872 0.20299 0.727 -1.2605 0.3631
j -0.65385 0.20820 0.226 -1.4777 0.1700
k -0.28431 0.20143 0.988 -1.0914 0.5228
m -0.48810 0.18267 0.470 -1.2632 0.2870
n -0.23469 0.18323 0.994 -1.0103 0.5409
o -0.46296 0.18295 0.546 -1.2384 0.3125
p -0.26692 0.17373 0.965 -1.0347 0.5009
q -0.10000 0.25831 1.000 -1.0922 0.8922
r -0.10000 0.23333 1.000 -1.0002 0.8002
m a 0.12143 0.12767 1.000 -0.3373 0.5802
b 0.28452 0.09088 0.156 -0.0375 0.6066
c -0.08333 0.09832 1.000 -0.4312 0.2645
d 0.03355 0.14629 1.000 -0.4953 0.5624
e 0.24794 0.08893 0.331 -0.0676 0.5634
f 0.21326 0.09560 0.730 -0.1252 0.5517
g -0.08121 0.09286 1.000 -0.4101 0.2476
h 0.07085 0.09879 1.000 -0.2786 0.4203
i 0.03938 0.13791 1.000 -0.4600 0.5387
j -0.16575 0.14548 0.999 -0.6938 0.3623
k 0.20378 0.13560 0.988 -0.2829 0.6905
l 0.48810 0.18267 0.470 -0.2870 1.2632
n 0.25340 0.10672 0.628 -0.1244 0.6312
o 0.02513 0.10623 1.000 -0.3515 0.4018
p 0.22118 0.08943 0.554 -0.0960 0.5383
q 0.38810 0.21104 0.909 -0.4292 1.2054
r 0.38810 0.17961 0.764 -0.2873 1.0635
n a -0.13197 0.12847 1.000 -0.5931 0.3292
b 0.03112 0.09200 1.000 -0.2943 0.3565
c -0.33673 0.09935 0.077 -0.6878 0.0143
d -0.21985 0.14699 0.988 -0.7507 0.3110
e -0.00546 0.09007 1.000 -0.3244 0.3134
f -0.04014 0.09666 1.000 -0.3818 0.3015
g
 -.33461* 0.09395 0.046 -0.6668 -0.0025
h -0.18255 0.09982 0.933 -0.5351 0.1700
i -0.21402 0.13865 0.984 -0.7156 0.2875
j -0.41915 0.14618 0.298 -0.9492 0.1109
k -0.04962 0.13635 1.000 -0.5386 0.4394
l 0.23469 0.18323 0.994 -0.5409 1.0103
m -0.25340 0.10672 0.628 -0.6312 0.1244
o -0.22827 0.10719 0.795 -0.6079 0.1513
p -0.03222 0.09056 1.000 -0.3528 0.2883
q 0.13469 0.21153 1.000 -0.6837 0.9531
r 0.13469 0.18018 1.000 -0.5422 0.8116
o a 0.09630 0.12806 1.000 -0.3638 0.5564
b 0.25939 0.09144 0.301 -0.0648 0.5836
c -0.10847 0.09883 1.000 -0.4583 0.2414
d 0.00842 0.14663 1.000 -0.5215 0.5384
e 0.22281 0.08949 0.542 -0.0949 0.5405
f 0.18813 0.09612 0.885 -0.1523 0.5286
g -0.10634 0.09340 1.000 -0.4373 0.2246
h 0.04572 0.09930 1.000 -0.3057 0.3971
i 0.01425 0.13827 1.000 -0.4863 0.5148
j -0.19088 0.14582 0.997 -0.7201 0.3383
k 0.17865 0.13597 0.997 -0.3094 0.6666
l 0.46296 0.18295 0.546 -0.3125 1.2384
m -0.02513 0.10623 1.000 -0.4018 0.3515
n 0.22827 0.10719 0.795 -0.1513 0.6079
p 0.19605 0.08999 0.764 -0.1233 0.5154
q 0.36296 0.21128 0.945 -0.4549 1.1809
r 0.36296 0.17989 0.841 -0.3132 1.0392
p a -0.09975 0.11451 1.000 -0.5156 0.3161
b 0.06335 0.07122 1.000 -0.1863 0.3130
c
 -.30451* 0.08050 0.021 -0.5878 -0.0212
d -0.18763 0.13496 0.994 -0.6807 0.3054
e 0.02676 0.06871 1.000 -0.2142 0.2677
f -0.00792 0.07715 1.000 -0.2792 0.2634
g
 -.30239* 0.07373 0.006 -0.5612 -0.0436
h -0.15032 0.08107 0.926 -0.4356 0.1350
i -0.18180 0.12582 0.991 -0.6432 0.2796
j -0.38693 0.13408 0.296 -0.8796 0.1057
k -0.01740 0.12329 1.000 -0.4639 0.4292
l 0.26692 0.17373 0.965 -0.5009 1.0347
m -0.22118 0.08943 0.554 -0.5383 0.0960
n 0.03222 0.09056 1.000 -0.2883 0.3528
o -0.19605 0.08999 0.764 -0.5154 0.1233
q 0.16692 0.20335 1.000 -0.6331 0.9669
r 0.16692 0.17051 1.000 -0.4845 0.8184
q a -0.26667 0.22283 0.998 -1.1145 0.5812
b -0.10357 0.20400 1.000 -0.9049 0.6978
c -0.47143 0.20742 0.693 -1.2803 0.3374
d -0.35455 0.23400 0.983 -1.2339 0.5248
e -0.14016 0.20313 1.000 -0.9397 0.6594
f -0.17483 0.20614 1.000 -0.9809 0.6312
g -0.46931 0.20488 0.682 -1.2726 0.3340
h -0.31724 0.20764 0.979 -1.1266 0.4921
i -0.34872 0.22885 0.982 -1.2137 0.5163
j -0.55385 0.23349 0.631 -1.4323 0.3246
k -0.18431 0.22747 1.000 -1.0445 0.6759
l 0.10000 0.25831 1.000 -0.8922 1.0922
m -0.38810 0.21104 0.909 -1.2054 0.4292
n -0.13469 0.21153 1.000 -0.9531 0.6837
o -0.36296 0.21128 0.945 -1.1809 0.4549
p -0.16692 0.20335 1.000 -0.9669 0.6331
r 0.00000 0.25615 1.000 -0.9549 0.9549
r a -0.26667 0.19332 0.994 -0.9830 0.4497
b -0.10357 0.17127 1.000 -0.7569 0.5498
c -0.47143 0.17533 0.426 -1.1352 0.1924
d -0.35455 0.20609 0.953 -1.1115 0.4024
e -0.14016 0.17024 1.000 -0.7910 0.5107
f -0.17483 0.17382 1.000 -0.8347 0.4850
g -0.46931 0.17233 0.407 -1.1253 0.1867
h -0.31724 0.17560 0.924 -0.9817 0.3472
i -0.34872 0.20023 0.947 -1.0874 0.3900
j -0.55385 0.20552 0.410 -1.3097 0.2020
k -0.18431 0.19865 1.000 -0.9167 0.5481
l 0.10000 0.23333 1.000 -0.8002 1.0002
m -0.38810 0.17961 0.764 -1.0635 0.2873
n -0.13469 0.18018 1.000 -0.8116 0.5422
o -0.36296 0.17989 0.841 -1.0392 0.3132
p -0.16692 0.17051 1.000 -0.8184 0.4845
q 0.00000 0.25615 1.000 -0.9549 0.9549

Existing replies

이일현 (2025-05-12 13:43:12)

c-b/c-e/c-p

g-b/g-e/g-f/g-n/g-p

에서 유의한 차이가 있으므로 정리하면

g>f,n,p,e,b

c>p,e,b

BigStep (2025-05-12 14:58:13)

교수님 답변 정말 감사드립니다 🙂 

교수님, 이에 더불어 수리적인 질문이 있습니다.

g와 c의 평균이 모두 4.07 입니다. 

그런데 g는 f, n, p, e, b보다 크고

c는 p,e,b 보다 크다 라고 결과가 나왔습니다.

f의 평균은 3.84, n의 평균은 3.24 인데, 

왜 g>f,n,p,e,b // c>p,e,b라는 결과가 나왔는지 이해가 잘 되지 않습니다. 

(직관적으로 생각해보면, 평균 크기에 따라서... e, f, p, b, n < g, c 라는 생각이 들거든요ㅜ)

평균이 같다 하더라도 어떤 요소(예를 들면 오차?) 에 따라서 차이가 날 거 같긴 한데.. 

정확히 어떤 수식으로 계산이 되는지 몰라 아마 제가 이해가 어려운 것 같습니다.

혹시 어떠한 요인들 때문에, 평균이 같다고 하더라도 이런 차이가 있을 수 있다 라는 설명을 부탁 드려도 될까요?

감사합니다.

이일현 (2025-05-12 16:45:25)

가장 영향을 받는 것은 표준편차입니다. 

평균값이 크더라도 표준편차가 크면 신뢰구간이 넓어지기 때문에 유의성이 떨어집니다. 

Legacy document_srl: 306799 / Legacy URL: http://www.statedu.com/QnA/306799

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