To obtain this output:

1. File, Open, point to gss 93 subset.sav.
2. Statistics, General Linear Model GLM - Multivariate.
3. In the MANOVA dialog box, select blues, blugras, and jazz as the "dependents", and select agecat4 and race as the "factors."
4. Click on Options and check all the options, then Continue.
5. When the output comes up, go to the "Descriptives" table. Click on the table to select it. Right-click
6. Click on Plots and let agecat4 be the "Horizontal Axis", then click Add, Continue.

   Comments in blue are by the instructor and are not part of SPSS output.

   Notes

   Output Created		19 Mar 98 08:07:01
   Comments
   Input	Data	Y:\PC\spss95\GSS93 subset.sav
   	Filter	<none>
   	Weight	<none>
   	Split File	<none>
   	N of Rows in Working Data File	1500
   Missing Value Handling	Definition of Missing	User-defined missing values are treated as missing.
   	Cases Used	Statistics are based on all cases with valid data for all variables in the model.
   Syntax		GLM blues blugrass jazz BY agecat4 race /METHOD = SSTYPE(3) /INTERCEPT = INCLUDE /POSTHOC = agecat4 race ( TUKEY BONFERRONI ) /PLOT = PROFILE( agecat4 ) /PRINT = DESCRIPTIVE ETASQ PARAMETER HOMOGENEITY RSSCP TEST(SSCP) /PLOT = SPREADLEVEL RESIDUALS /CRITERIA = ALPHA(.05) /DESIGN .
   Resources	Elapsed Time	0:00:06.70

   
   

   
   
   
   

   Between-Subjects Factors

   		Value Label	N
   Age Categories	1.00	18-29	219
   	2.00	30-39	309
   	3.00	40-49	280
   	4.00	50+	483
   Racew of Respondent	1	white	1118
   	2	black	118
   	3	other	55

   
   

   Descriptive Statistics

   	Age Categories	Racew of Respondent	Mean	Std. Deviation	N
   Blues or R & B Music	18-29	white	2.56	1.12	181
   		black	1.71	.55	24
   		other	2.21	1.12	14
   		Total	2.45	1.10	219
   	30-39	white	2.38	.96	270
   		black	2.23	1.03	26
   		other	2.23	.73	13
   		Total	2.36	.96	309
   	40-49	white	2.46	.95	235
   		black	1.86	.99	29
   		other	2.56	1.09	16
   		Total	2.41	.98	280
   	50+	white	2.66	1.00	432
   		black	1.97	1.11	39
   		other	3.33	1.07	12
   		Total	2.63	1.03	483
   	Total	white	2.54	1.01	1118
   		black	1.95	.98	118
   		other	2.56	1.08	55
   		Total	2.48	1.02	1291
   Bluegrass Music	18-29	white	2.88	1.07	181
   		black	3.58	.97	24
   		other	3.36	1.08	14
   		Total	2.99	1.08	219
   	30-39	white	2.61	.88	270
   		black	3.38	1.10	26
   		other	3.54	1.05	13
   		Total	2.71	.95	309
   	40-49	white	2.54	1.00	235
   		black	3.17	.93	29
   		other	2.75	.77	16
   		Total	2.62	1.00	280
   	50+	white	2.44	1.00	432
   		black	3.08	.98	39
   		other	2.92	.79	12
   		Total	2.51	1.01	483
   	Total	white	2.57	1.00	1118
   		black	3.27	1.00	118
   		other	3.13	.96	55
   		Total	2.66	1.02	1291
   Jazz Music	18-29	white	2.57	1.14	181
   		black	2.04	1.08	24
   		other	2.64	1.15	14
   		Total	2.52	1.14	219
   	30-39	white	2.46	.97	270
   		black	2.00	1.17	26
   		other	2.08	.95	13
   		Total	2.40	1.00	309
   	40-49	white	2.60	1.02	235
   		black	1.76	.99	29
   		other	2.25	1.29	16
   		Total	2.49	1.06	280
   	50+	white	2.91	1.10	432
   		black	2.13	1.08	39
   		other	3.00	1.13	12
   		Total	2.84	1.12	483
   	Total	white	2.68	1.08	1118
   		black	1.99	1.07	118
   		other	2.47	1.17	55
   		Total	2.61	1.10	1291

   
   
   
   
   MANOVA and MANCOVA assume that for each group (each cell in the factor design matrix) the covariance matrix is similar. Box's M tests this assumption. We want M not to be significant in order to conclude there is insufficient evidence that the covariance matrices differ. Here M is significant, so we have violated an assumption. That is, the various music groups differ in their covariance matrices. Note, however, that the F test is quite robust even when there are departures from this assumption.

   Box's Test of Equality of Covariance Matrices(a)

   Box's M	102.598
   F	1.478
   df1	66
   df2	27292
   Sig.	.007
   Tests the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups.
   a Design: Intercept+AGECAT4+RACE+AGECAT4 * RACE

   
   

   In the context of MANOVA without repeated measures, as here, a finding of significance means that the residual covariances among the multiple dependent variables include at least one significant non-zero correlation and hence the MANOVA model cannot be said to completely explain the dependent variables.

   
   

   Bartlett's Test of Sphericity(a)

   Likelihood Ratio	.000
   Approx. Chi-Square	526.137
   df	5
   Sig.	.000
   Tests the null hypothesis that the residual covariance matrix is proportional to an identity matrix.
   a Design: Intercept+AGECAT4+RACE+AGECAT4 * RACE

   
   

   
   The "multivariate tests" section simultaneously tests each factor effect on the dependent groups. This is the most important table in the SPSS output. Each factor (agecat4 and race in this example) and each covariate (in MANCOVA) has a main effect, as does the intercept. Interactions among the factors (here agecat4*race) are also assessed. SPSS offers four alternative multivariate significance tests. Hotelling's Trace is commonly used for two dependent groups, and Wilks' Lambda if there are more than two groups, as there are in this example. The significance of the F tests show if that effect is significant. Here all effects are significant except the interaction effect. Eta-squared is the proportion of the total variability in the dependent variable accounted for by the variation in the independent variable. Note that the covariate serves as a control. Thus, for the table below, race accounts for about 5% of the variability in the music variables. Significance, of course, is the chance of making a Type I error (thinking you have something when you don't), whereas power (the last column, below) is the chance of making a Type II error thinking you don't have something when you do). One wants the power level to be high (ex., above .90).

   
   

   Multivariate Tests(d)

   Effect		Value	F	Hypothesis df	Error df	Sig.	Eta Squared	Noncent. Parameter	Observed Power(a)
   Intercept	Pillai's Trace	.770	1426.005(b)	3.000	1277.000	.000	.770	4278.014	1.000
   	Wilks' Lambda	.230	1426.005(b)	3.000	1277.000	.000	.770	4278.014	1.000
   	Hotelling's Trace	3.350	1426.005(b)	3.000	1277.000	.000	.770	4278.014	1.000
   	Roy's Largest Root	3.350	1426.005(b)	3.000	1277.000	.000	.770	4278.014	1.000
   AGECAT4	Pillai's Trace	.031	4.417	9.000	3837.000	.000	.010	39.750	.999
   	Wilks' Lambda	.969	4.432	9.000	3108.033	.000	.010	32.321	.992
   	Hotelling's Trace	.031	4.439	9.000	3827.000	.000	.010	39.949	.999
   	Roy's Largest Root	.023	9.636(c)	3.000	1279.000	.000	.022	28.907	.998
   RACE	Pillai's Trace	.097	21.823	6.000	2556.000	.000	.049	130.939	1.000
   	Wilks' Lambda	.903	22.284(b)	6.000	2554.000	.000	.050	133.707	1.000
   	Hotelling's Trace	.107	22.745	6.000	2552.000	.000	.051	136.473	1.000
   	Roy's Largest Root	.102	43.515(c)	3.000	1278.000	.000	.093	130.544	1.000
   AGECAT4 * RACE	Pillai's Trace	.020	1.448	18.000	3837.000	.099	.007	26.064	.911
   	Wilks' Lambda	.980	1.449	18.000	3612.387	.099	.007	24.584	.890
   	Hotelling's Trace	.020	1.450	18.000	3827.000	.098	.007	26.093	.912
   	Roy's Largest Root	.014	2.974(c)	6.000	1279.000	.007	.014	17.845	.906
   a Computed using alpha = .05
   b Exact statistic
   c The statistic is an upper bound on F that yields a lower bound on the significance level.
   d Design: Intercept+AGECAT4+RACE+AGECAT4 * RACE

   
   

   
   MANOVA and MANCOVA assume that each dependent variable will have similar variances for all groups (all cells in the factor design matrix), Levene's test tests this assumption. If the Levene statistic is significant at the .05 level or better, the researcher rejects the null hypothesis that the groups have equal variances. The Levene test is robust in the face of departures from normality. Note, however, that failure to meet the assumption of homogeneity of variances is not fatal to ANOVA, which is relatively robust, particularly when groups are of equal sample size. For these data, the homogeneity of variances assumption is met for bluegrass and jazz but not for blues.

   
   

   Levene's Test of Equality of Error Variances(a)

   	F	df1	df2	Sig.
   Blues or R & B Music	2.594	11	1279	.003
   Bluegrass Music	1.665	11	1279	.076
   Jazz Music	1.138	11	1279	.327
   Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
   a Design: Intercept+AGECAT4+RACE+AGECAT4 * RACE

   
   

   
   This section of output gives the univariate ANOVA effects for factor and interaction (and in MANCOVA each covariate). The significance of F and eta-squared have the same interpretation as in the multivariate analysis above. For instance, all univariate effects for race are significant, but for the agecat4 age categories factor, bluegrass is significant but not blues of jazz. The interaction of agecat4 and race is significant for blues. The "corrected model" effect reflects the variation in the dependent attributed to other effects (except the intercept) in the model, after corrected by the mean.

   
   

   Tests of Between-Subjects Effects

   Source	Dependent Variable	Type III Sum of Squares	df	Mean Square	F	Sig.	Eta Squared	Noncent. Parameter	Observed Power(a)
   Corrected Model	Blues or R & B Music	66.400(b)	11	6.036	6.050	.000	.049	66.554	1.000
   	Bluegrass Music	99.953(c)	11	9.087	9.364	.000	.075	103.003	1.000
   	Jazz Music	99.408(d)	11	9.037	7.958	.000	.064	87.535	1.000
   Intercept	Blues or R & B Music	1764.511	1	1764.511	1768.625	.000	.580	1768.625	1.000
   	Bluegrass Music	2919.174	1	2919.174	3008.259	.000	.702	3008.259	1.000
   	Jazz Music	1795.647	1	1795.647	1581.176	.000	.553	1581.176	1.000
   AGECAT4	Blues or R & B Music	10.949	3	3.650	3.658	.012	.009	10.975	.802
   	Bluegrass Music	13.775	3	4.592	4.732	.003	.011	14.195	.900
   	Jazz Music	13.130	3	4.377	3.854	.009	.009	11.561	.824
   RACE	Blues or R & B Music	34.544	2	17.272	17.312	.000	.026	34.625	1.000
   	Bluegrass Music	58.858	2	29.429	30.327	.000	.045	60.654	1.000
   	Jazz Music	43.839	2	21.920	19.301	.000	.029	38.603	1.000
   AGECAT4 * RACE	Blues or R & B Music	13.602	6	2.267	2.272	.035	.011	13.634	.798
   	Bluegrass Music	3.829	6	.638	.658	.684	.003	3.946	.265
   	Jazz Music	5.202	6	.867	.763	.599	.004	4.580	.307
   Error	Blues or R & B Music	1276.025	1279	.998
   	Bluegrass Music	1241.124	1279	.970
   	Jazz Music	1452.484	1279	1.136
   Total	Blues or R & B Music	9309.000	1291
   	Bluegrass Music	10486.000	1291
   	Jazz Music	10328.000	1291
   Corrected Total	Blues or R & B Music	1342.424	1290
   	Bluegrass Music	1341.077	1290
   	Jazz Music	1551.892	1290
   a Computed using alpha = .05
   b R Squared = .049 (Adjusted R Squared = .041)
   c R Squared = .075 (Adjusted R Squared = .067)
   d R Squared = .064 (Adjusted R Squared = .056)

   
   

   
   When MANOVA or MANCOVA are computed through the GLM (general linear model) module, coefficients are computed as part of GLM's full parameterization approach. This additional optional output allows the researcher to assess the significance of each parameter coefficient. For instance, for jazz music, the parameter associated with race=1 is not significant but it is significant for race=2 (there is no coefficient for race=3 as one category is left out as the reference category, similar to dummy variables).

   
   

   Parameter Estimates

   		B	Std. Error	t	Sig.	95% Confidence Interval		Eta Squared	Noncent. Parameter	Observed Power(a)
   Dependent Variable	Parameter					Lower Bound	Upper Bound
   Blues or R & B Music	Intercept	3.333	.288	11.560	.000	2.768	3.899	.095	11.560	1.000
   	[AGECAT4=1.00]	-1.119	.393	-2.848	.004	-1.890	-.348	.006	2.848	.812
   	[AGECAT4=2.00]	-1.103	.400	-2.757	.006	-1.887	-.318	.006	2.757	.787
   	[AGECAT4=3.00]	-.771	.381	-2.021	.044	-1.519	-2.252E-02	.003	2.021	.524
   	[AGECAT4=4.00]	0(b)	.	.	.	.	.	.	.	.
   	[RACE=1]	-.669	.292	-2.289	.022	-1.242	-9.551E-02	.004	2.289	.628
   	[RACE=2]	-1.359	.330	-4.121	.000	-2.006	-.712	.013	4.121	.985
   	[RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=1.00] * [RACE=1]	1.018	.403	2.528	.012	.228	1.808	.005	2.528	.714
   	[AGECAT4=1.00] * [RACE=2]	.853	.471	1.812	.070	-7.040E-02	1.776	.003	1.812	.441
   	[AGECAT4=1.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=2.00] * [RACE=1]	.816	.407	2.003	.045	1.695E-02	1.615	.003	2.003	.517
   	[AGECAT4=2.00] * [RACE=2]	1.359	.473	2.872	.004	.431	2.287	.006	2.872	.819
   	[AGECAT4=2.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=3.00] * [RACE=1]	.570	.390	1.463	.144	-.195	1.335	.002	1.463	.309
   	[AGECAT4=3.00] * [RACE=2]	.659	.453	1.453	.147	-.231	1.548	.002	1.453	.306
   	[AGECAT4=3.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=4.00] * [RACE=1]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=4.00] * [RACE=2]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=4.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   Bluegrass Music	Intercept	2.917	.284	10.257	.000	2.359	3.475	.076	10.257	1.000
   	[AGECAT4=1.00]	.440	.388	1.137	.256	-.320	1.201	.001	1.137	.206
   	[AGECAT4=2.00]	.622	.394	1.577	.115	-.152	1.395	.002	1.577	.351
   	[AGECAT4=3.00]	-.167	.376	-.443	.658	-.905	.571	.000	.443	.073
   	[AGECAT4=4.00]	0(b)	.	.	.	.	.	.	.	.
   	[RACE=1]	-.475	.288	-1.646	.100	-1.040	9.104E-02	.002	1.646	.376
   	[RACE=2]	.160	.325	.493	.622	-.478	.798	.000	.493	.078
   	[RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=1.00] * [RACE=1]	1.372E-03	.397	.003	.997	-.778	.781	.000	.003	.050
   	[AGECAT4=1.00] * [RACE=2]	6.593E-02	.464	.142	.887	-.845	.977	.000	.142	.052
   	[AGECAT4=1.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=2.00] * [RACE=1]	-.457	.402	-1.137	.256	-1.245	.332	.001	1.137	.206
   	[AGECAT4=2.00] * [RACE=2]	-.314	.467	-.673	.501	-1.229	.601	.000	.673	.103
   	[AGECAT4=2.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=3.00] * [RACE=1]	.265	.385	.689	.491	-.489	1.019	.000	.689	.106
   	[AGECAT4=3.00] * [RACE=2]	.262	.447	.586	.558	-.615	1.139	.000	.586	.090
   	[AGECAT4=3.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=4.00] * [RACE=1]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=4.00] * [RACE=2]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=4.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   Jazz Music	Intercept	3.000	.308	9.752	.000	2.396	3.604	.069	9.752	1.000
   	[AGECAT4=1.00]	-.357	.419	-.852	.394	-1.180	.465	.001	.852	.136
   	[AGECAT4=2.00]	-.923	.427	-2.164	.031	-1.760	-8.615E-02	.004	2.164	.580
   	[AGECAT4=3.00]	-.750	.407	-1.843	.066	-1.548	4.838E-02	.003	1.843	.453
   	[AGECAT4=4.00]	0(b)	.	.	.	.	.	.	.	.
   	[RACE=1]	-9.491E-02	.312	-.304	.761	-.707	.517	.000	.304	.061
   	[RACE=2]	-.872	.352	-2.478	.013	-1.562	-.182	.005	2.478	.697
   	[RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=1.00] * [RACE=1]	2.664E-02	.430	.062	.951	-.816	.870	.000	.062	.050
   	[AGECAT4=1.00] * [RACE=2]	.271	.502	.539	.590	-.715	1.256	.000	.539	.084
   	[AGECAT4=1.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=2.00] * [RACE=1]	.474	.435	1.090	.276	-.379	1.326	.001	1.090	.193
   	[AGECAT4=2.00] * [RACE=2]	.795	.505	1.575	.116	-.195	1.785	.002	1.575	.350
   	[AGECAT4=2.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=3.00] * [RACE=1]	.445	.416	1.069	.285	-.371	1.261	.001	1.069	.188
   	[AGECAT4=3.00] * [RACE=2]	.380	.484	.787	.432	-.568	1.329	.000	.787	.123
   	[AGECAT4=3.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=4.00] * [RACE=1]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=4.00] * [RACE=2]	0(b)	.	.	.	.	.	.	.	.
   	[AGECAT4=4.00] * [RACE=3]	0(b)	.	.	.	.	.	.	.	.
   a Computed using alpha = .05
   b This parameter is set to zero because it is redundant.

   
   

   
   Below is the error sums-of-squares and crossproducts (SSCP) matrix for the effects noted in earlier tables. The ratio of effect sums of squares and error sums of squares is what was used in testing the significance of each effect. Thus this optional table shows the researcher more about the data on the basis of which significance was computed.

   
   

   Between-Subjects SSCP Matrix

   			Blues or R & B Music	Bluegrass Music	Jazz Music
   Hypothesis	Intercept	Blues or R & B Music	1764.511	2269.562	1780.011
   		Bluegrass Music	2269.562	2919.174	2289.499
   		Jazz Music	1780.011	2289.499	1795.647
   	AGECAT4	Blues or R & B Music	10.949	-8.680	8.764
   		Bluegrass Music	-8.680	13.775	-3.550
   		Jazz Music	8.764	-3.550	13.130
   	RACE	Blues or R & B Music	34.544	-37.371	37.827
   		Bluegrass Music	-37.371	58.858	-47.597
   		Jazz Music	37.827	-47.597	43.839
   	AGECAT4 * RACE	Blues or R & B Music	13.602	-.388	3.398
   		Bluegrass Music	-.388	3.829	.273
   		Jazz Music	3.398	.273	5.202
   Error		Blues or R & B Music	1276.025	322.520	727.809
   		Bluegrass Music	322.520	1241.124	172.769
   		Jazz Music	727.809	172.769	1452.484
   Based on Type III Sum of Squares

   
   

   Residual SSCP Matrix

   		Blues or R & B Music	Bluegrass Music	Jazz Music
   Sum-of-Squares and Cross-Products	Blues or R & B Music	1276.025	322.520	727.809
   	Bluegrass Music	322.520	1241.124	172.769
   	Jazz Music	727.809	172.769	1452.484
   Covariance	Blues or R & B Music	.998	.252	.569
   	Bluegrass Music	.252	.970	.135
   	Jazz Music	.569	.135	1.136
   Correlation	Blues or R & B Music	1.000	.256	.535
   	Bluegrass Music	.256	1.000	.129
   	Jazz Music	.535	.129	1.000
   Based on Type III Sum of Squares

   
   

   Post Hoc Tests

   Age Categories

   
   If the F test establishes that there is an effect on the dependent variable, the researcher then proceeds to determine just which group means differ significantly from others. This helps specify the exact nature of the overall effect determined by the F test. Pairwise multiple comparison tests test each pair of groups to identify similarities and differences.

   Bonferroni test: If the Bonferroni test is requested, SPSS will print out a table of "Multiple Comparisons" giving the mean difference in the dependent variable between any two groups (ex., differences in test scores for any two educational groups). The significance of this difference is also printed, and an asterisk is printed next to differences significant at the .05 level or better. The Bonferroni method is preferred when the number of groups is small.

   Tukey test: If the Tukey test is requested, SPSS will produce a similar table which is interpreted in the same way. The Tukey method is preferred when the number of groups is large.

   Methods when the assumption of homogeneity of variances is not met: SPSS provides these alternate methods not shown here: Games-Howell, Tamhane's T2, Dunnett's T3, and Dunnett's C.

   
   

   Multiple Comparisons

   				Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
   Dependent Variable		(I) Age Categories	(J) Age Categories				Lower Bound	Upper Bound
   Blues or R & B Music	Tukey HSD	18-29	30-39	8.83E-02	.088	.749	-.14	.31
   			40-49	4.03E-02	.090	.970	-.19	.27
   			50+	-.18	.081	.127	-.39	3.13E-02
   		30-39	18-29	-8.83E-02	.088	.749	-.31	.14
   			40-49	-4.79E-02	.082	.938	-.26	.16
   			50+	-.27(*)	.073	.001	-.45	-7.91E-02
   		40-49	18-29	-4.03E-02	.090	.970	-.27	.19
   			30-39	4.79E-02	.082	.938	-.16	.26
   			50+	-.22(*)	.075	.019	-.41	-2.54E-02
   		50+	18-29	.18	.081	.127	-3.13E-02	.39
   			30-39	.27(*)	.073	.001	7.91E-02	.45
   			40-49	.22(*)	.075	.019	2.54E-02	.41
   	Bonferroni	18-29	30-39	8.83E-02	.088	1.000	-.14	.32
   			40-49	4.03E-02	.090	1.000	-.20	.28
   			50+	-.18	.081	.175	-.39	3.72E-02
   		30-39	18-29	-8.83E-02	.088	1.000	-.32	.14
   			40-49