Psychology Statistics

Class A
Class B
i
grade
xbar
1
56 67.813
2
79 67.813
3
62 67.813
xxbar (x-xbar)²
-11.813 139.547
11.187 125.149
-5.813
grade
xbar
79 75.938
X; – xbar (x; -xbar)²
3.062
9.376
80 75.938
4.062
16.500
33.791
80 75.938
4.062
16.500
4
70 67.813
2.187
4.783
69 75.938
-6.938
48.136
5
880.0 72 67.813
4.187
17.531
73 75.938
-2.938
8.632
6
800 € 77 67.813
9.187
84.401
82 75.938
6.062
36.748
7
60061 67.813 -6.813
46.417
77 75.938
1.062
1.128
8
62 67.813
9
10
11
12
71 67.813
13
68 67.813
14
62 67.813
15
42 67.813
16
70 67.813
-5.813
74 67.813 6.187
79 67.813 11.187 125.149
80 67.813 12.187 148.523
3.187
0.187
-5.813
-25.813
2.187
33.791
81 75.938
5.062
25.624
38.279
74 75.938
-1.938
3.756
79 75.938
10.157
0.035
33.791
666.311
61 75.938
90 75.938
90 75.938
3.062
-14.938
57 75.938
73 75.938
9.376
223.144
14.062 197.740
14.062 197.740
-18.938 358.648
-2.938
4.783
70 75.938
-5.938
8.632
35.260
xbar =
67.813
n =
16.000
80 SS
SS =1512.438
df =
15.000
2
S
= 100.829
EC
S =
10.041
xbar =
75.938
n =
16.000
df
SS=1196.940
= 15.000
2
S
s’ =
S =
79.796
8.933
Ho:
HA:
Please list all the assumptions of the one-way ANOVA and the tests for each (matching them)
Ston vw 10 ydW
2MClass C
grade
xbar
X-xbar (x-xbar)
Class D
grade
xbar
71 74.125 -3.125
x – xbar (x; – xbar)²
9.766
68
78.750
-10.750
115.563
70 74.125 -4.125 17.016
78 74.125 3.875
74 74.125 -0.125
77 74.125 2.875
76 74.125 1.875
62 74.125 -12.125
78 74.125 3.875
66 74.125 -8.125
86 74.125 11.875 141.016
88 74.125 13.875 192.516
76 78.750
-2.750
7.563
15.016
86 78.750
7.250
52.563
0.016
72 78.750
-6.750
45.563
8.266
79 78.750
0.250
0.063
3.516
77 78.750
-1.750
3.063
147.016
69 78.750
-9.750
95.063
15.016
80 78.750
1.250
1.563
66.016
91 78.750
77 74.125
65 74.125
2.875
-9.125
71 74.125 -3.125
8.266
83.266
9.766
87 78.750
76 74.125
1.875
3.516
77 78.750
71 74.125
-3.125
9.766
71 78.750
12.250 150.063
12.250 150.063
91 78.750
27.563
84 78.750 5.250
-8.750
70 78.750
76.563
3.250 10.563
82 78.750
8.250 68.063
-1.750 3.063
-7.750 60.063
xbar =
74.125
n =
16.000
SS = 729.756
df =
15.000
S
2 = 48.650
S=
6.975
xbar =
78.750
n =
16.000
SS =
df =
867.008
15.000
S²
2
S =
= 57.801
7.603
Grand Mean =
74.156
Size of effect of IV on DV?
k =
SSM =
dfM =
MSM=
Reject Ho?
Why or why not?
SSR =
dfr =
MSR=
F exp
=
Fα =
R² =
r =F exploded
k
SSM = Σ n; (x ; — x G ) ²
j=1
SSM
୮
MSM
dfM
MSM
Fexp
=
MSR
1
L
SSR
MSR =
dfR
dfм = k 1
k
M²
SSR = s² (n-1)
Σs
j=1
dfR = N – kYou are a research psychologist working for a high school. The principal of your school is
a francophile who has learned of a new teaching technique using mimes. He is very
optimistic about all things French and all things new and would like to replace all of the
boring traditional teachers with new and exciting French mimes. Before replacing all of
the teachers, you encourage the prinicipal to conduct a study first with a sample of
students randomly assigned to each type of instructor just to be safe. Because mimes
come from France, you are uncertain whether the grades of students taught by mimes
will be any better or worse than those taught by traditional teachers. You are certain,
however, that even if there is no difference at all at the population level, you can always
expect some differences just from variability in sampling. You decide that you will only
reject the null hypothesis if you observe a difference larger what you would expect to
see up to 95% of the time just from sampling variability (if there are in fact no
differences at the population level). Classes A and B are both math classes. Classes C
and D are both English classes. Classes A and C were taught by traditional teachers.
Classes B and D were taught by new and exciting French mimes.
Because you are concerned about a-inflation, and a Bonferroni adjustment would be too
costly in terms of statistical power (i.e., you don’t have the funds to recruit more
participants to raise your sample size), you decide to carry out an omnibus test of
difference among any of the means. Because the DV is continuous, the IV is categorical,
and you only measured the DV once for each participant, you choose a one-way ANOVA
to statistically test for differences among the means. Please report the values for each
step in the calculation and interpret your findings in the boxes in the lower half of the
assignment.
Site of effect
Reject Hert
α 1-sided
α 2-sided
0.10000
0.20000
df
0.05000 0.02500 0.01000 0.00500 0.00250 0.00100 0.00050 0.00025 0.00010 0.00005
0.10000 0.05000 0.02000 0.01000 0.00500 0.00200 0.00100 0.00050 0.00020 0.00010
8201 2
3
Tear 3
Fear 4
88 57 1.4759
BET 6 1.4398)
8881 7 1.4149
TEA 81.3968
1.8595
rear 9
1.3830)
1.8331
2.2622
2.8214 3.2498
10
1.3722
1.8125
2.2281
3.0777 6.3138 12.7062 31.8205 63.6567 127.3213 318.3088 636.6192 1273.2393 3183.0988 6366.1977
1.8856 2.9200 4.3027 6.9646 9.9248 14.0890 22.3271 31.5991 44.7046 70.7001 99.9925
1.6377 2.3534 3.1824 4.5407 5.8409 7.4533 10.2145 12.9240 16.3263 22.2037 28.0001
41.5332 2.1318 2.7764 3.7469 4.6041 5.5976 7.1732 8.6103 10.3063 13.0337 15.5441
2.0150 2.5706 3.3649 4.0321 4.7733 5.8934 6.8688 7.9757 9.6776
1.9432 2.4469 3.1427
3.7074 4.3168 5.2076 5.9588 6.7883 8.0248
1.8946
2.9980
2.3646
3.4995 4.0293 4.7853 5.4079 6.0818 7.0634 7.8846
3.3554
2.8965
3.8325
2.3060
3.6897
11.1777
9.0823
4.5008
5.0413
5.6174
6.4420
7.1200
4.2968
4.7809
5.2907
6.0101
6.5937
2.7638
3.1693 3.5814
4.1437
4.5869
5.0490
5.6938
20811
6.2111
11
1.3634
1.7959
2.2010
2.7181
3.1058
3.4966
4.0247
4.4370
4.8633
5.4528
0812 1.3562
5.9212
1.7823 2.1788 2.6810
13
@TE 14
14
1.3502
1.3450
TAE 15
15 1.3406
1.7709
1.7613
1.7531 2.1314 2.6025
3.0545
2.1604 2.6503 3.0123
2.1448 2.6245 2.9768
2.9467
3.4284
3.3725 3.8520
3.3257
3.9296 4.3178 4.7165
5.2633
5.6945
4.2208
4.5975
5.1106
5.5125
3.7874
4.1405
4.4992
4.9850
5.3634
3.2860
3.7328
4.0728 4.4166
4.8800
5.2391
ADE 16
1.3368
1.7459
2.1199 2.5835
2.9208 3.2520
3.6862
4.0150
4.3463} 4.7909
5.1339
Bas 17
1.3334
1.7396
2.1098
2.5669
2.8982
3.2224
3.6458
3.9651
4.2858 4.7144
5.0438
EES 18
1.3304
1.7341
2.1009
2.5524
2.8784
3.1966
3.6105
3.9216
4.2332
4.6480
4.9657
091 19
1.3277
1.7291
2.0930
2.5395
2.8609
3.1737
3.5794
3.8834
4.1869
4.5899
4.8975
281 20
1.3253 1.7247
2.0860 2.5280 2.8453
3.1534
3.5518
3.8495
4.1460
4.5385
4.8373
ACT 21
1.3232
EOT 22
1.3212
1.7207 2.0796
1.7171 2.0739
2.5176
2.8314
3.1352
3.5272
3.8193 4.1096 4.4929 4.7839
2.5083
2.8188
23
1.3195 1.7139 2.0687
2.4999
2.8073
24
1.3178
1.7109
2.0639
2.4922
2.7969
25
1.3163
1.7081
2.0595
2.4851
2.7874
08026
1.3150 1.7056 2.0555
2.4786
2.7787
Bag 27
1.3137
1.7033 2.0518
2.4727
5028
1.3125
1.7011
2.0484 2.4671
FOC 29
1.3114
1.69913
2.0452
2.4620
MBB 30
1.3104
1.6973
2.0423
2.4573
1.6955
31 1.3095
2.0395
2.4528
2.7440
32
1.3086
1.6939
2.0369
2.4487
2.7385
33
1.3077
1.6924
2.0345
2.4448
2.7333
TOY 34
1.3070
1.6909
2.0322
2.4411
2.7284 3.0020
35
1.3062
1.6896
2.0301
2.4377
36
1.3055
1.6883
2.0281
2.4345
37
1.3049 1.6871
2.0262
Fox 38
1.3042 1.6860
2.0244
39
1.3036
1.6849
2.0227
2.4258
40
1.3031
1.6839 2.0211
41
1.3025
42
1.3020
43
1.3016
44
1.3011
45
46
1.3002
1.6787
2.0129
47
1.2998
1.6779
2.0117
2.4083
4.7361
4.4520
4.0474 4.4152 4.6932
4.0207
3.7454
4.3819
3.7251 3.9964 4.3517
3.4502
3.9742 4.3240
3.7066
3.4350
3.0669
3.9538
3.6896
3.4210
3.0565
2.7707
3.6739 3.9351
3.4082
2.7633 3.0469
3.6594
3.0380
3.9177
3.3962
2.7564
3.3852 3.6460 3.9016
2.7500 3.0298
4.2155
3.6335 3.8867
3.3749
3.8728
3.3653 3.6218
4.1983
3.3563 3.6109 3.8598 4.1822
3.8476
3.6007
3.3479
4.1672 4.4051
3.8362
4.3888
3.5911
3.3400
4.1531
2.7238 2.9960
3.8255
3.5821
4.1399 4.3735
3.3326
2.9905
2.7195
3.5737
3.3256
3.8154 4.1275
4.3591
2.9852
2.7154
2.4314
3.8059
3.5657
3.3190
2.9803
2.7116
2.4286
3.5581 3.7969
3.3128
2.9756
2.7079
4.0942
3.7884
3.3069 3.5510
2.7045 2.9712
2.4233
3.3013 3.5442
2.9670
2.7012
2.4208
2.0195
1.6829
3.5377
3.2960
2.9630
2.4185 2.6981
2.0181
1.6820
3.7654 4.0659
3.5316
3.2909
2.9592
2.6951
2.4163
1.6811 2.0167
3.7585
3.5258
3.2861
2.9555
2.6923
2.4141
2.0154
1.6802
3.7519
3.5203
3.2815
2.6896 2.9521
2.4121
2.0141
1.6794
1.3006
3.7456
3.5150
2.9488 3.2771
2.6870
2.4102
3.5099
2.9456
2.6846
3.1188
3.5050
3.7921
4.0769
3.1040)
3.4850
3.7676
3.0905
3.4668
4.6544
3.0782
4.6191
4.5870
4.2987
4.5575
4.2754
4.5305
4.2539
4.5055
4.2340 4.4824
3.0221
4.4610
3.0149
3.0082
4.4411
4.4225
4.1158
4.3456
4.1047
4.3328
4.3207
4.0843
3.7803
4.3093
3.7727 4.0749
4.2984
4.2881
4.0574
4.0493 4.2690
4.0416 4.2601
4.2783
3.2729
4.0343
3.7396
4.2516
48
1.2994
1.6772
2.0106
2.4066
2.6822
2.9426
3.2689
3.5051
4.0272
3.7339
4.2435
49
1.2991
1.6766
2.0096
2.4049
2.6800
2.9397
3.2651
3.5004
4.0205
3.7284
4.2357
50
1.2987
1.6759
2.4033
2.6778
2.0086
2.9370
3.2614
3.4960
51
1.2984
1.6753
2.4017
2.0076
52
1.2980
1.6747
2.4002
2.0066
53
1.2977
1.6741
2.3988
2.0057
2.9343
2.6757
2.9318
2.6737
2.9293
2.6718
3.4918
3.2579
3.2545 3.4877
3.7086
3.4838
3.2513
3.7231 4.0140
3.7181
4.2283
4.0079
4.2212
4.0020
3.7133
4.2144
3.9963
4.2079
☑
V V