Chapter 3b Example: Means by session for RT outcome



Summarize


Case Processing SummaryCase Processing Summary, table, 3 levels of column headers and 1 levels of row headers, table with 7 columns and 5 rows
  Cases
Included Excluded Total
N Percent N Percent N Percent
rt: Response Time in Milliseconds * session: Occasion (1-6) 606 100.0% 0 0.0% 606 100.0%
ReportReport, table, rt: Response Time in Milliseconds, 1 layers, 1 levels of column headers and 1 levels of row headers, table with 6 columns and 10 rows
rt: Response Time in Milliseconds
session: Occasion (1-6) N Mean Std. Error of Mean Minimum Maximum
1 101 1961.89 54.680 1055 4159
2 101 1815.17 50.654 991 3954
3 101 1750.03 48.068 993 4086
4 101 1717.80 46.410 930 3612
5 101 1707.18 45.825 983 3291
6 101 1672.14 44.134 918 3226
Total 606 1770.70 20.071 918 4159


Eq 3b.10: Between-Person Independent ANOVA



Mixed Model Analysis


Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 7 columns and 7 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables Number of Subjects
Fixed Effects Intercept 1   1    
session 6   5    
Repeated Effects session 6 Identity 1 PersonID 101
Total 13   7    
a. Dependent Variable: rt: Response Time in Milliseconds.
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Restricted Log Likelihood 9155.433
Akaike's Information Criterion (AIC) 9157.433
Hurvich and Tsai's Criterion (AICC) 9157.439
Bozdogan's Criterion (CAIC) 9162.829
Schwarz's Bayesian Criterion (BIC) 9161.829
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: rt: Response Time in Milliseconds.


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 5 rows
Source Numerator df Denominator df F Sig.
Intercept 1 600 8023.388 .000
session 5 600.000 4.735 .000
a. Dependent Variable: rt: Response Time in Milliseconds.
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 12 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1672.136012 48.421925 600 34.533 .000 1577.038953 1767.233072
[session=1] 289.757355 68.478944 600 4.231 .000 155.269803 424.244907
[session=2] 143.036372 68.478944 600 2.089 .037 8.548820 277.523924
[session=3] 77.898636 68.478944 600 1.138 .256 -56.588915 212.386188
[session=4] 45.660447 68.478944 600 .667 .505 -88.827104 180.147999
[session=5] 35.039719 68.478944 600 .512 .609 -99.447833 169.527271
[session=6] 0b 0 . . . . .
a. Dependent Variable: rt: Response Time in Milliseconds.
b. This parameter is set to zero because it is redundant.


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 5 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Repeated Measures Variance 236812.968016 13672.403083 17.321 .000 211476.121559 265185.409147
a. Dependent Variable: rt: Response Time in Milliseconds.
Residual Covariance (R) MatrixaResidual Covariance (R) Matrix, table, 1 levels of column headers and 1 levels of row headers, table with 7 columns and 10 rows
  [session = 1] [session = 2] [session = 3] [session = 4] [session = 5] [session = 6]
[session = 1] 236812.968016 0 0 0 0 0
[session = 2] 0 236812.968016 0 0 0 0
[session = 3] 0 0 236812.968016 0 0 0
[session = 4] 0 0 0 236812.968016 0 0
[session = 5] 0 0 0 0 236812.968016 0
[session = 6] 0 0 0 0 0 236812.968016
Identity
a. Dependent Variable: rt: Response Time in Milliseconds.


Estimated Marginal Means



session: Occasion (1-6)


EstimatesaEstimates, table, 2 levels of column headers and 1 levels of row headers, table with 6 columns and 10 rows
session: Occasion (1-6) Mean Std. Error df 95% Confidence Interval
Lower Bound Upper Bound
1 1961.893 48.422 600 1866.796 2056.990
2 1815.172 48.422 600 1720.075 1910.269
3 1750.035 48.422 600 1654.938 1845.132
4 1717.796 48.422 600 1622.699 1812.894
5 1707.176 48.422 600 1612.079 1802.273
6 1672.136 48.422 600 1577.039 1767.233
a. Dependent Variable: rt: Response Time in Milliseconds.
Pairwise ComparisonsaPairwise Comparisons, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 37 rows
(I) session: Occasion (1-6) (J) session: Occasion (1-6) Mean Difference (I-J) Std. Error df Sig.c 95% Confidence Interval for Differencec
Lower Bound Upper Bound
1 2 146.721* 68.479 600 .033 12.233 281.209
3 211.859* 68.479 600 .002 77.371 346.346
4 244.097* 68.479 600 .000 109.609 378.584
5 254.718* 68.479 600 .000 120.230 389.205
6 289.757* 68.479 600 .000 155.270 424.245
2 1 -146.721* 68.479 600 .033 -281.209 -12.233
3 65.138 68.479 600 .342 -69.350 199.625
4 97.376 68.479 600 .156 -37.112 231.863
5 107.997 68.479 600 .115 -26.491 242.484
6 143.036* 68.479 600 .037 8.549 277.524
3 1 -211.859* 68.479 600 .002 -346.346 -77.371
2 -65.138 68.479 600 .342 -199.625 69.350
4 32.238 68.479 600 .638 -102.249 166.726
5 42.859 68.479 600 .532 -91.629 177.346
6 77.899 68.479 600 .256 -56.589 212.386
4 1 -244.097* 68.479 600 .000 -378.584 -109.609
2 -97.376 68.479 600 .156 -231.863 37.112
3 -32.238 68.479 600 .638 -166.726 102.249
5 10.621 68.479 600 .877 -123.867 145.108
6 45.660 68.479 600 .505 -88.827 180.148
5 1 -254.718* 68.479 600 .000 -389.205 -120.230
2 -107.997 68.479 600 .115 -242.484 26.491
3 -42.859 68.479 600 .532 -177.346 91.629
4 -10.621 68.479 600 .877 -145.108 123.867
6 35.040 68.479 600 .609 -99.448 169.527
6 1 -289.757* 68.479 600 .000 -424.245 -155.270
2 -143.036* 68.479 600 .037 -277.524 -8.549
3 -77.899 68.479 600 .256 -212.386 56.589
4 -45.660 68.479 600 .505 -180.148 88.827
5 -35.040 68.479 600 .609 -169.527 99.448
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
a. Dependent Variable: rt: Response Time in Milliseconds.
c. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).
Univariate TestsaUnivariate Tests, table, 1 levels of column headers and 0 levels of row headers, table with 4 columns and 5 rows
Numerator df Denominator df F Sig.
5 600.000 4.735 .000
The F tests the effect of session: Occasion (1-6). This test is based on the linearly independent pairwise comparisons among the estimated marginal means.
a. Dependent Variable: rt: Response Time in Milliseconds.


Eq 3b.10: Univariate Repeated Measures ANOVA



Mixed Model Analysis


Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 7 columns and 7 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables Number of Subjects
Fixed Effects Intercept 1   1    
session 6   5    
Repeated Effects session 6 Compound Symmetry 2 PersonID 101
Total 13   8    
a. Dependent Variable: rt: Response Time in Milliseconds.
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Restricted Log Likelihood 8353.355
Akaike's Information Criterion (AIC) 8357.355
Hurvich and Tsai's Criterion (AICC) 8357.375
Bozdogan's Criterion (CAIC) 8368.149
Schwarz's Bayesian Criterion (BIC) 8366.149
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: rt: Response Time in Milliseconds.


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 5 rows
Source Numerator df Denominator df F Sig.
Intercept 1 100.000 1519.795 .000
session 5 500.000 32.847 .000
a. Dependent Variable: rt: Response Time in Milliseconds.
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 12 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1672.136012 48.421925 128.689 34.533 .000 1576.329854 1767.942171
[session=1] 289.757355 25.999318 500.000 11.145 .000 238.675979 340.838731
[session=2] 143.036372 25.999318 500.000 5.502 .000 91.954996 194.117749
[session=3] 77.898636 25.999318 500.000 2.996 .003 26.817260 128.980013
[session=4] 45.660447 25.999318 500.000 1.756 .080 -5.420929 96.741824
[session=5] 35.039719 25.999318 500.000 1.348 .178 -16.041657 86.121095
[session=6] 0b 0 . . . . .
a. Dependent Variable: rt: Response Time in Milliseconds.
b. This parameter is set to zero because it is redundant.


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 6 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Repeated Measures CS diagonal offset 34136.209933 2158.963482 15.811 .000 30156.475894 38641.147350
CS covariance 202676.758083 29469.617037 6.877 .000 144917.370052 260436.146113
a. Dependent Variable: rt: Response Time in Milliseconds.
Residual Covariance (R) MatrixaResidual Covariance (R) Matrix, table, 1 levels of column headers and 1 levels of row headers, table with 7 columns and 10 rows
  [session = 1] [session = 2] [session = 3] [session = 4] [session = 5] [session = 6]
[session = 1] 236812.968016 202676.758083 202676.758083 202676.758083 202676.758083 202676.758083
[session = 2] 202676.758083 236812.968016 202676.758083 202676.758083 202676.758083 202676.758083
[session = 3] 202676.758083 202676.758083 236812.968016 202676.758083 202676.758083 202676.758083
[session = 4] 202676.758083 202676.758083 202676.758083 236812.968016 202676.758083 202676.758083
[session = 5] 202676.758083 202676.758083 202676.758083 202676.758083 236812.968016 202676.758083
[session = 6] 202676.758083 202676.758083 202676.758083 202676.758083 202676.758083 236812.968016
Compound Symmetry
a. Dependent Variable: rt: Response Time in Milliseconds.


Estimated Marginal Means



session: Occasion (1-6)


EstimatesaEstimates, table, 2 levels of column headers and 1 levels of row headers, table with 6 columns and 10 rows
session: Occasion (1-6) Mean Std. Error df 95% Confidence Interval
Lower Bound Upper Bound
1 1961.893 48.422 128.689 1866.087 2057.700
2 1815.172 48.422 128.689 1719.366 1910.979
3 1750.035 48.422 128.689 1654.228 1845.841
4 1717.796 48.422 128.689 1621.990 1813.603
5 1707.176 48.422 128.689 1611.370 1802.982
6 1672.136 48.422 128.689 1576.330 1767.942
a. Dependent Variable: rt: Response Time in Milliseconds.
Pairwise ComparisonsaPairwise Comparisons, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 37 rows
(I) session: Occasion (1-6) (J) session: Occasion (1-6) Mean Difference (I-J) Std. Error df Sig.c 95% Confidence Interval for Differencec
Lower Bound Upper Bound
1 2 146.721* 25.999 500.000 .000 95.640 197.802
3 211.859* 25.999 500.000 .000 160.777 262.940
4 244.097* 25.999 500.000 .000 193.016 295.178
5 254.718* 25.999 500.000 .000 203.636 305.799
6 289.757* 25.999 500.000 .000 238.676 340.839
2 1 -146.721* 25.999 500.000 .000 -197.802 -95.640
3 65.138* 25.999 500.000 .013 14.056 116.219
4 97.376* 25.999 500.000 .000 46.295 148.457
5 107.997* 25.999 500.000 .000 56.915 159.078
6 143.036* 25.999 500.000 .000 91.955 194.118
3 1 -211.859* 25.999 500.000 .000 -262.940 -160.777
2 -65.138* 25.999 500.000 .013 -116.219 -14.056
4 32.238 25.999 500.000 .216 -18.843 83.320
5 42.859 25.999 500.000 .100 -8.222 93.940
6 77.899* 25.999 500.000 .003 26.817 128.980
4 1 -244.097* 25.999 500.000 .000 -295.178 -193.016
2 -97.376* 25.999 500.000 .000 -148.457 -46.295
3 -32.238 25.999 500.000 .216 -83.320 18.843
5 10.621 25.999 500.000 .683 -40.461 61.702
6 45.660 25.999 500.000 .080 -5.421 96.742
5 1 -254.718* 25.999 500.000 .000 -305.799 -203.636
2 -107.997* 25.999 500.000 .000 -159.078 -56.915
3 -42.859 25.999 500.000 .100 -93.940 8.222
4 -10.621 25.999 500.000 .683 -61.702 40.461
6 35.040 25.999 500.000 .178 -16.042 86.121
6 1 -289.757* 25.999 500.000 .000 -340.839 -238.676
2 -143.036* 25.999 500.000 .000 -194.118 -91.955
3 -77.899* 25.999 500.000 .003 -128.980 -26.817
4 -45.660 25.999 500.000 .080 -96.742 5.421
5 -35.040 25.999 500.000 .178 -86.121 16.042
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
a. Dependent Variable: rt: Response Time in Milliseconds.
c. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).
Univariate TestsaUnivariate Tests, table, 1 levels of column headers and 0 levels of row headers, table with 4 columns and 5 rows
Numerator df Denominator df F Sig.
5 500.000 32.847 .000
The F tests the effect of session: Occasion (1-6). This test is based on the linearly independent pairwise comparisons among the estimated marginal means.
a. Dependent Variable: rt: Response Time in Milliseconds.


Eq 3b.10: Multivariate Repeated Measures ANOVA



Mixed Model Analysis


Model DimensionaModel Dimension, table, 1 levels of column headers and 2 levels of row headers, table with 7 columns and 7 rows
  Number of Levels Covariance Structure Number of Parameters Subject Variables Number of Subjects
Fixed Effects Intercept 1   1    
session 6   5    
Repeated Effects session 6 Unstructured 21 PersonID 101
Total 13   27    
a. Dependent Variable: rt: Response Time in Milliseconds.
Information CriteriaaInformation Criteria, table, 0 levels of column headers and 1 levels of row headers, table with 2 columns and 8 rows
-2 Restricted Log Likelihood 8229.788
Akaike's Information Criterion (AIC) 8271.788
Hurvich and Tsai's Criterion (AICC) 8273.387
Bozdogan's Criterion (CAIC) 8385.124
Schwarz's Bayesian Criterion (BIC) 8364.124
The information criteria are displayed in smaller-is-better form.
a. Dependent Variable: rt: Response Time in Milliseconds.


Fixed Effects


Type III Tests of Fixed EffectsaType III Tests of Fixed Effects, table, 1 levels of column headers and 1 levels of row headers, table with 5 columns and 5 rows
Source Numerator df Denominator df F Sig.
Intercept 1 100.000 1519.795 .000
session 5 100.000 16.720 .000
a. Dependent Variable: rt: Response Time in Milliseconds.
Estimates of Fixed EffectsaEstimates of Fixed Effects, table, 2 levels of column headers and 1 levels of row headers, table with 8 columns and 12 rows
Parameter Estimate Std. Error df t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Intercept 1672.136012 44.134490 100.000 37.887 .000 1584.574442 1759.697583
[session=1] 289.757355 32.699996 100.000 8.861 .000 224.881495 354.633215
[session=2] 143.036372 26.203076 100.000 5.459 .000 91.050215 195.022529
[session=3] 77.898636 22.884193 100.000 3.404 .001 32.497050 123.300223
[session=4] 45.660447 20.785316 100.000 2.197 .030 4.422972 86.897923
[session=5] 35.039719 18.116801 100.000 1.934 .056 -.903498 70.982936
[session=6] 0b 0 . . . . .
a. Dependent Variable: rt: Response Time in Milliseconds.
b. This parameter is set to zero because it is redundant.


Covariance Parameters


Estimates of Covariance ParametersaEstimates of Covariance Parameters, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 25 rows
Parameter Estimate Std. Error Wald Z Sig. 95% Confidence Interval
Lower Bound Upper Bound
Repeated Measures UN (1,1) 301985.340995 42707.176487 7.071 .000 228879.968605 398440.923998
UN (2,1) 235658.842109 36577.945652 6.443 .000 163967.386003 307350.298214
UN (2,2) 259150.065653 36649.353754 7.071 .000 196414.364669 341923.853896
UN (3,1) 217994.111267 34350.421952 6.346 .000 150668.521387 285319.701146
UN (3,2) 230216.774233 33686.361737 6.834 .000 164192.718457 296240.830008
UN (3,3) 233368.004051 33003.219635 7.071 .000 176873.689513 307906.876736
UN (4,1) 202606.869554 32671.782393 6.201 .000 138571.352752 266642.386355
UN (4,2) 213231.676046 31913.037848 6.682 .000 150683.271226 275780.080865
UN (4,3) 205208.972033 30475.965818 6.733 .000 145477.176635 264940.767431
UN (4,4) 217543.648538 30765.317817 7.071 .000 164880.133862 287028.145299
UN (5,1) 192153.799582 31776.318520 6.047 .000 129873.359721 254434.239443
UN (5,2) 202091.999879 30952.589144 6.529 .000 141426.039928 262757.959830
UN (5,3) 196918.658683 29710.898067 6.628 .000 138686.368524 255150.948842
UN (5,4) 193675.585675 28922.433037 6.696 .000 136988.658577 250362.512772
UN (5,5) 212097.577205 29995.127023 7.071 .000 160752.461202 279842.572361
UN (6,1) 195360.125463 31237.175376 6.254 .000 134136.386748 256583.864179
UN (6,2) 193268.257923 29721.378479 6.503 .000 135015.426533 251521.089313
UN (6,3) 188604.430763 28545.202557 6.607 .000 132656.861820 244551.999707
UN (6,4) 185320.926712 27774.430296 6.672 .000 130884.043640 239757.809783
UN (6,5) 187840.341320 27750.787897 6.769 .000 133449.796499 242230.886141
UN (6,6) 196733.171652 27822.271952 7.071 .000 149107.509666 259570.701134
a. Dependent Variable: rt: Response Time in Milliseconds.
Residual Covariance (R) MatrixaResidual Covariance (R) Matrix, table, 1 levels of column headers and 1 levels of row headers, table with 7 columns and 10 rows
  [session = 1] [session = 2] [session = 3] [session = 4] [session = 5] [session = 6]
[session = 1] 301985.340995 235658.842109 217994.111267 202606.869554 192153.799582 195360.125463
[session = 2] 235658.842109 259150.065653 230216.774233 213231.676046 202091.999879 193268.257923
[session = 3] 217994.111267 230216.774233 233368.004051 205208.972033 196918.658683 188604.430763
[session = 4] 202606.869554 213231.676046 205208.972033 217543.648538 193675.585675 185320.926712
[session = 5] 192153.799582 202091.999879 196918.658683 193675.585675 212097.577205 187840.341320
[session = 6] 195360.125463 193268.257923 188604.430763 185320.926712 187840.341320 196733.171652
Unstructured
a. Dependent Variable: rt: Response Time in Milliseconds.


Estimated Marginal Means



session: Occasion (1-6)


EstimatesaEstimates, table, 2 levels of column headers and 1 levels of row headers, table with 6 columns and 10 rows
session: Occasion (1-6) Mean Std. Error df 95% Confidence Interval
Lower Bound Upper Bound
1 1961.893 54.680 100.000 1853.409 2070.378
2 1815.172 50.654 100.000 1714.676 1915.669
3 1750.035 48.068 100.000 1654.668 1845.401
4 1717.796 46.410 100.000 1625.720 1809.873
5 1707.176 45.825 100.000 1616.259 1798.092
6 1672.136 44.134 100.000 1584.574 1759.698
a. Dependent Variable: rt: Response Time in Milliseconds.
Pairwise ComparisonsaPairwise Comparisons, table, 2 levels of column headers and 2 levels of row headers, table with 8 columns and 37 rows
(I) session: Occasion (1-6) (J) session: Occasion (1-6) Mean Difference (I-J) Std. Error df Sig.c 95% Confidence Interval for Differencec
Lower Bound Upper Bound
1 2 146.721* 29.821 100.000 .000 87.557 205.885
3 211.859* 31.366 100.000 .000 149.630 274.088
4 244.097* 33.643 100.000 .000 177.351 310.843
5 254.718* 35.846 100.000 .000 183.601 325.834
6 289.757* 32.700 100.000 .000 224.881 354.633
2 1 -146.721* 29.821 100.000 .000 -205.885 -87.557
3 65.138* 17.823 100.000 .000 29.777 100.499
4 97.376* 22.301 100.000 .000 53.132 141.620
5 107.997* 25.768 100.000 .000 56.873 159.120
6 143.036* 26.203 100.000 .000 91.050 195.023
3 1 -211.859* 31.366 100.000 .000 -274.088 -149.630
2 -65.138* 17.823 100.000 .000 -100.499 -29.777
4 32.238 20.023 100.000 .111 -7.487 71.964
5 42.859 22.609 100.000 .061 -1.997 87.715
6 77.899* 22.884 100.000 .001 32.497 123.300
4 1 -244.097* 33.643 100.000 .000 -310.843 -177.351
2 -97.376* 22.301 100.000 .000 -141.620 -53.132
3 -32.238 20.023 100.000 .111 -71.964 7.487
5 10.621 20.462 100.000 .605 -29.976 51.218
6 45.660* 20.785 100.000 .030 4.423 86.898
5 1 -254.718* 35.846 100.000 .000 -325.834 -183.601
2 -107.997* 25.768 100.000 .000 -159.120 -56.873
3 -42.859 22.609 100.000 .061 -87.715 1.997
4 -10.621 20.462 100.000 .605 -51.218 29.976
6 35.040 18.117 100.000 .056 -.903 70.983
6 1 -289.757* 32.700 100.000 .000 -354.633 -224.881
2 -143.036* 26.203 100.000 .000 -195.023 -91.050
3 -77.899* 22.884 100.000 .001 -123.300 -32.497
4 -45.660* 20.785 100.000 .030 -86.898 -4.423
5 -35.040 18.117 100.000 .056 -70.983 .903
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
a. Dependent Variable: rt: Response Time in Milliseconds.
c. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).
Univariate TestsaUnivariate Tests, table, 1 levels of column headers and 0 levels of row headers, table with 4 columns and 5 rows
Numerator df Denominator df F Sig.
5 100.000 16.720 .000
The F tests the effect of session: Occasion (1-6). This test is based on the linearly independent pairwise comparisons among the estimated marginal means.
a. Dependent Variable: rt: Response Time in Milliseconds.