|
A New View of Statistics | |
Important stats are colored, in bold, or [commented] on.
WITHOUT individual differences 1
21:30 Monday, June 1, 1998
The MIXED Procedure
Class Level Information
Class Levels Values
ATHLETE 24 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20 21 22 23
24
GRP 2 control exptal
TEST 3 1 2 3
Parameter Search
COVP1 COVP2 COVP3 COVP4 COVP5 COVP6 RLL
25.0000 1.0000 0.0000 25.0000 1.0000 0.0000 -148.138
Parameter Search
-2RLL Objective
296.2764 174.9765
WITHOUT individual differences 2
21:30 Monday, June 1, 1998
REML Estimation Iteration History
Iteration Evaluations Objective Criterion
1 3 173.77952015 0.00180714
2 1 173.60840164 0.00004607
3 1 173.60432225 0.00000005
4 1 173.60431808 0.00000000
Convergence criteria met.
Covariance Parameter Estimates (REML)
Cov Parm Subject Group Estimate Std Error Z
LIN(1) ATHLETE GRP control 28.37564414 12.24929742 2.32
LIN(2) ATHLETE GRP control 0.93713368 0.39057869 2.40
LIN(3) ATHLETE GRP control 0.32209133 0.92661491 0.35
LIN(1) ATHLETE GRP exptal 29.96635541 12.89193471 2.32
LIN(2) ATHLETE GRP exptal 0.71480766 0.29577343 2.42
LIN(3) ATHLETE GRP exptal 0.06505026 0.64523382 0.10
WITHOUT individual differences 3
21:30 Monday, June 1, 1998
Covariance Parameter Estimates (REML)
Pr > |Z| Alpha Lower Upper
0.0205 0.05 4.3675 52.3838 [between variance]
0.0164 0.05 0.1716 1.7027 [within variance]
0.7281 0.05 -1.4940 2.1382 [indiff variance]
0.0201 0.05 4.6986 55.2341
0.0157 0.05 0.1351 1.2945
0.9197 0.05 -1.1996 1.3297
[Take the square root of the above variances to get standard
deviations. If the variance is negative, make it positive, take
the square root, then make the resulting SD negative.
Note that to get the usual between-subject SD, you have to add the
between and within variances, then take the square root. You can't
combine the lower and upper limits like that, though.]
Model Fitting Information for DISTANCE
Description Value
Observations 72.0000
Res Log Likelihood -147.452
Akaike's Information Criterion -153.452
Schwarz's Bayesian Criterion -160.021
-2 Res Log Likelihood 294.9042
PARMS Model LRT Chi-Square 1.3722
PARMS Model LRT DF 5.0000
PARMS Model LRT P-Value 0.9273
WITHOUT individual differences 4
21:30 Monday, June 1, 1998
Tests of Fixed Effects
Source NDF DDF Type III F Pr > F
GRP 1 22 671.94 0.0001
TEST 2 44 23.39 0.0001
GRP*TEST 2 44 17.78 0.0001
[P value for the test of whether the pattern of change in the mean
distance differs between the two groups. The other two tests aren't
informative.]
ESTIMATE Statement Results
[These are the comparisons for the difference between specific tests
between groups.]
Parameter Estimate Std Error DF t
grp*test 2-1 0.33082497 0.52471283 44 0.63
grp*test 3-2 2.73163325 0.55460378 44 4.93
ESTIMATE Statement Results
Pr > |t| Alpha Lower Upper
0.5316 0.05 -0.7267 1.3883
0.0001 0.05 1.6139 3.8494
WITH individual differences 5
21:30 Monday, June 1, 1998
The MIXED Procedure
Class Level Information
Class Levels Values
ATHLETE 24 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20 21 22 23
24
GRP 2 control exptal
TEST 3 1 2 3
REML Estimation Iteration History
Iteration Evaluations Objective Criterion
0 1 311.73867656
1 3 193.00124620 1.20211524
2 2 191.15202472 0.00138111
3 2 191.05670678 0.00014911
4 1 191.04158591 0.00000149
5 1 191.04144279 0.00000000
Convergence criteria met.
WITH individual differences 6
21:30 Monday, June 1, 1998
Covariance Parameter Estimates (REML)
Cov Parm Subject Estimate Std Error Z Pr > |Z|
INTERCEPT ATHLETE 29.48549791 9.00663783 3.27 0.0011
V33 ATHLETE 3.87638105 2.25949020 1.72 0.0862
Residual 0.92523945 0.22427315 4.13 0.0001
Covariance Parameter Estimates (REML)
Alpha Lower Upper
0.05 17.5337 59.7021 [between variance]
0.05 1.5992 19.1956 [indiff variance]
0.05 0.6055 1.5877 [within variance]
Model Fitting Information for DISTANCE
Description Value
Observations 72.0000
Res Log Likelihood -156.171
Akaike's Information Criterion -159.171
Schwarz's Bayesian Criterion -162.455
-2 Res Log Likelihood 312.3413
WITH individual differences 7
21:30 Monday, June 1, 1998
Tests of Fixed Effects
Source NDF DDF Type III F Pr > F
GRP 1 33 661.84 0.0001
TEST 2 33 9.31 0.0006
GRP*TEST 2 33 6.43 0.0044 [See above.]
ESTIMATE Statement Results [See above.]
Parameter Estimate Std Error DF t
grp*test 2-1 0.33082497 0.55534958 33 0.60
grp*test 3-2 2.46693105 0.79463508 33 3.10
ESTIMATE Statement Results
Pr > |t| Alpha Lower Upper
0.5554 0.05 -0.7990 1.4607
0.0039 0.05 0.8502 4.0836
Including a covariate 8
21:30 Monday, June 1, 1998
The MIXED Procedure
Class Level Information
Class Levels Values
ATHLETE 24 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 17 18 19 20 21 22 23
24
GRP 2 control exptal
TEST 3 1 2 3
Parameter Search
COVP1 COVP2 COVP3 COVP4 COVP5 COVP6 RLL
25.0000 1.0000 0.0000 25.0000 1.0000 0.0000 -140.648
Parameter Search
-2RLL Objective
281.2969 171.0243
Including a covariate 9
21:30 Monday, June 1, 1998
REML Estimation Iteration History
Iteration Evaluations Objective Criterion
1 2 170.74186801 0.00516738
2 1 170.22319240 0.00065213
3 1 170.16213382 0.00001957
4 1 170.16043232 0.00000002
5 1 170.16043046 0.00000000
Convergence criteria met.
Covariance Parameter Estimates (REML) [See above.]
Cov Parm Subject Group Estimate Std Error Z
LIN(1) ATHLETE GRP control 25.02509370 11.35855124 2.20
LIN(2) ATHLETE GRP control 0.92168749 0.39720935 2.32
LIN(3) ATHLETE GRP control 0.46476550 0.99650477 0.47
LIN(1) ATHLETE GRP exptal 21.11681713 9.58293562 2.20
LIN(2) ATHLETE GRP exptal 0.76907737 0.32799116 2.34
LIN(3) ATHLETE GRP exptal 0.11905897 0.73138682 0.16
Including a covariate 10
21:30 Monday, June 1, 1998
Covariance Parameter Estimates (REML)
Pr > |Z| Alpha Lower Upper
0.0276 0.05 2.7627 47.2874 [between]
0.0203 0.05 0.1432 1.7002 [within]
0.6409 0.05 -1.4883 2.4179 [indiff]
0.0276 0.05 2.3346 39.8990
0.0190 0.05 0.1262 1.4119
0.8707 0.05 -1.3144 1.5526
Model Fitting Information for DISTANCE
Description Value
Observations 72.0000
Res Log Likelihood -140.217
Akaike's Information Criterion -146.217
Schwarz's Bayesian Criterion -152.500
-2 Res Log Likelihood 280.4331
PARMS Model LRT Chi-Square 0.8638
PARMS Model LRT DF 5.0000
PARMS Model LRT P-Value 0.9728
Including a covariate 11
21:30 Monday, June 1, 1998
Tests of Fixed Effects
Source NDF DDF Type III F Pr > F
INDIFF 1 20 0.21 0.6529
GRP 1 20 759.27 0.0001
INDIFF*GRP 1 20 8.60 0.0082
TEST 2 40 21.51 0.0001
INDIFF*TEST 2 40 7.67 0.0015
GRP*TEST 2 40 14.13 0.0001
INDIFF*GRP*TEST 2 40 3.89 0.0287
[Only the bottom two tests are interesting.]
ESTIMATE Statement Results
Parameter Estimate Std Error DF t
grp*test 2-1 0.20591257 0.54910601 40 0.37
grp*test 3-2 2.69952322 0.59558936 40 4.53
indiff*grp*test 2-1 -0.43357590 0.61830657 40 -0.70
indiff*grp*test 3-2 1.83445952 0.67451441 40 2.72
[In blue are the shifts in the mean between tests, for experimental group
relative to control group.]
[Interpretation for red: subjects who differ by one standard deviation
of the covariate differ by 1.8 units (95%CI: 0.5 to 3.2) in throwing
distance between tests 2 and 3 (i.e. after the experimental treatment),
relative to the control group. Green is the difference between tests
1 and 2, which is due to noise, rather than to a real covariance.]
ESTIMATE Statement Results
Pr > |t| Alpha Lower Upper
0.7096 0.05 -0.9039 1.3157
Including a covariate 12
21:30 Monday, June 1, 1998
ESTIMATE Statement Results
Pr > |t| Alpha Lower Upper
0.0001 0.05 1.4958 3.9033
0.4872 0.05 -1.6832 0.8161
0.0096 0.05 0.4712 3.1977
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