28 SPSS UPDATE 7-9 Figure 1.27b a ama SE EEEEWWEMEEEEEEWEEEEEREEEEEEEREEEEEEH TESTS OF SIGNIFICANCE FOR RESP USING SEOUENTIAL SUMS OF SOVARES SOURCE OF VARIATION SUM OF SOUARES DF MEAN SOUARE F SIG. OF F RESIDUAL ; 13.40499 54 . 24824 CONSTANT 14697.66168 1 14697.66168 59207.32736 0.0 BLOCK 9.41435 3 3.13812 1264143 0.0 MIX 145.717B5 2 T2..85893 293.50127 0.0 LAB BY MIX . 33926 4 .0B482 34167 849 TEM BY MIX 43 ..6B696 4 10.92174 43.99659 0.0 LAB BY TEM BY MIX 1.07740 8 13467 .54252 -B19 ERROR 1 lb. IboH 6 %.6B49/ LAB 40 .66356 2 20.33178 7.5'T244 23 ERROR 2 9.88335 18 .54907 TEM 3119.50650 2 1559.75325 2840 .69330 0.0 LAB BY TEM 4 .93650 4 1.25412 2.24764 -104 a A NIN EEEWEERSEEEEIMEEEDEEWEEEEIENEEEE 1.28 Analysis of Carry-over Effects If different treatments are applied in seguence to the same unit, residual or carry-over effects may be present in the experiment. By including dunimy factors, MANOVA enables the user to perform an analysis of variance with residual effects, The following example is taken from Coehran and Cox (1957, p. 133). The experiment compares three feeding methods (A, B, and C) on the milk yield of dairy cows. The experiment consists of two 3 x 3 Latin sguares. The rows of the sguares represent the successive periods of application, while the columns represent the cows. The data are as follows: Sguare 1 Sguare 2 Cow 1 Cow 2 Cow 3 Cow 4 Cow 5 Cow 6 Period 1 A(38) B(109) C(124) A(86) B(75) C(101) Period 2 B(25) C(86) A(72) C(76) A(35) B(63) Period 3 C(15) A(39) B(27) B(46) C(34) A(1) In addition to the direct (treatment) effects 1,, 7, and 1,, the treatments also contain the residual effects r,, rs, and r, for the period immediately following the one in which they are applied. Thus for cow 2 in the third period, the expected total treatment effect is 1, tt r,, since A is applied in this period and C in the preceding period. Similarly, the expected total treatment effect is 1, r, for cow 2 in the second period. If we let CEFFECT be the (dummy) factor of residual effects and assign CEFFECT < 1 if no residual effects 2 if r, is the residual effect 3 if rs is the residual effect 4 if r. is the residual effect then the values of CEFFECT in this example would be Sguare 1 Sguare 2 Cow 1 Cow 2 Cow 3 Cow 4 Cow 5 Cow 6 Periodl 1 1 1 1 1 1 Period2 2 3 4 2 3 4 Period3 3 4 2 4 2 3 If the effects of CEFFECT are divided into groups using the following contrasts: (1 1 1 1) (3 -1 -1 -t) (0 2-1 -l) (0 0 1-1) and the pooled effect of second and third contrasts is CEFFECT(2), then CEFFECT(2) can be used to obtain a test ofr, — r; < 1.. Since the second contrast (0, 2, -1, -1) specifies a test on r, — ( r,)/2, and the third contrast (0,0, 1, -1) a test of ra