Procedure: General Linear Model

UNISTAT statistical package extends Excel with General Linear Model support.

Sample output

Here we provide annotated example report output from the UNISTAT Excel add-in for data analysis.

General Linear Model

ANOVA

Dependent Variable: Score

Due To	Sum of Squares	DoF	Mean Square	F-Stat	Signif
Constant	105868.167	1	105868.167	23.848	0.0000
Subject	2959.278	5	591.856	4.800	0.0018
Dial	2370.333	2	1185.167	9.611	0.0005
Subject � Dial	155.889	10	15.589	0.126	0.9993
Explained	5485.500	17	322.676	2.617	0.0075
Error	4439.333	36	123.315
Total	9924.833	53	187.261

R-squared	0.5527
Adjusted R-squared	0.3415

Table of Least Squares Means (LSMeans)

	Least Squares Means	Standard Error	t-Statistic	Lower 95%	Upper 95%
Constant	44.2778	1.5112	29.3005	41.2130	47.3426
Subject = 1	46.4444	3.7016	12.5472	38.9373	53.9516
2	37.5556	3.7016	10.1458	30.0484	45.0627
3	57.6667	3.7016	15.5790	50.1595	65.1738
4	38.1111	3.7016	10.2959	30.6040	45.6182
5	37.5556	3.7016	10.1458	30.0484	45.0627
6	48.3333	3.7016	13.0575	40.8262	55.8405
Dial = 1	37.3889	2.6174	14.2847	32.0805	42.6972
2	42.2222	2.6174	16.1313	36.9139	47.5306
3	53.2222	2.6174	20.3339	47.9139	58.5306
Subject � Dial = 1 � 1	37.6667	6.4113	5.8750	24.6639	50.6694
1 � 2	47.3333	6.4113	7.3828	34.3306	60.3361
1 � 3	54.3333	6.4113	8.4746	41.3306	67.3361
2 � 1	30.0000	6.4113	4.6792	16.9973	43.0027
2 � 2	36.6667	6.4113	5.7191	23.6639	49.6694
2 � 3	46.0000	6.4113	7.1748	32.9973	59.0027
3 � 1	52.6667	6.4113	8.2146	39.6639	65.6694
3 � 2	55.3333	6.4113	8.6306	42.3306	68.3361
3 � 3	65.0000	6.4113	10.1383	51.9973	78.0027
4 � 1	30.3333	6.4113	4.7312	17.3306	43.3361
4 � 2	35.0000	6.4113	5.4591	21.9973	48.0027
4 � 3	49.0000	6.4113	7.6427	35.9973	62.0027
5 � 1	31.3333	6.4113	4.8872	18.3306	44.3361
5 � 2	36.3333	6.4113	5.6671	23.3306	49.3361
5 � 3	45.0000	6.4113	7.0188	31.9973	58.0027
6 � 1	42.3333	6.4113	6.6029	29.3306	55.3361
6 � 2	42.6667	6.4113	6.6549	29.6639	55.6694
6 � 3	60.0000	6.4113	9.3585	46.9973	73.0027

Coefficients

	Coefficient	Standard Error	t-Statistic	Significance	Lower 95%	Upper 95%
Constant	60.0000	6.4113	9.3585	0.0000	46.9973	73.0027
Subject = 1	-5.6667	9.0670	-0.6250	0.5359	-24.0553	12.7220
2	-14.0000	9.0670	-1.5441	0.1313	-32.3887	4.3887
3	5.0000	9.0670	0.5515	0.5847	-13.3887	23.3887
4	-11.0000	9.0670	-1.2132	0.2330	-29.3887	7.3887
5	-15.0000	9.0670	-1.6544	0.1067	-33.3887	3.3887
6	*
Dial = 1	-17.6667	9.0670	-1.9485	0.0592	-36.0553	0.7220
2	-17.3333	9.0670	-1.9117	0.0639	-35.7220	1.0553
3	*
Subject � Dial = 1 � 1	1.0000	12.8226	0.0780	0.9383	-25.0055	27.0055
1 � 2	10.3333	12.8226	0.8059	0.4256	-15.6722	36.3388
1 � 3	*
2 � 1	1.6667	12.8226	0.1300	0.8973	-24.3388	27.6722
2 � 2	8.0000	12.8226	0.6239	0.5366	-18.0055	34.0055
2 � 3	*
3 � 1	5.3333	12.8226	0.4159	0.6799	-20.6722	31.3388
3 � 2	7.6667	12.8226	0.5979	0.5536	-18.3388	33.6722
3 � 3	*
4 � 1	-1.0000	12.8226	-0.0780	0.9383	-27.0055	25.0055
4 � 2	3.3333	12.8226	0.2600	0.7964	-22.6722	29.3388
4 � 3	*
5 � 1	4.0000	12.8226	0.3119	0.7569	-22.0055	30.0055
5 � 2	8.6667	12.8226	0.6759	0.5034	-17.3388	34.6722
5 � 3	*
6 � 1	*
6 � 2	*
6 � 3	*

* omitted due to multicollinearity

Actual and Fitted Values

Row	Actual *	Fitted +	16.0000 77.0000
1	45.0000	37.6667	+ *
2	53.0000	47.3333	+ *
3	60.0000	54.3333	+ *
4	40.0000	37.6667	+ *
5	52.0000	47.3333	+ *
6	57.0000	54.3333	+ *
7	28.0000	37.6667	* +
8	37.0000	47.3333	* +
9	46.0000	54.3333	* +
10	35.0000	30.0000	+ *
11	41.0000	36.6667	+ *
12	50.0000	46.0000	+ *
13	30.0000	30.0000	*
14	37.0000	36.6667	*
15	47.0000	46.0000	+*
16	25.0000	30.0000	* +
17	32.0000	36.6667	* +
18	41.0000	46.0000	* +
19	60.0000	52.6667	+ *
20	65.0000	55.3333	+ *
21	75.0000	65.0000	+ *
22	58.0000	52.6667	+ *
23	54.0000	55.3333	*+
24	70.0000	65.0000	+ *
25	40.0000	52.6667	* +
26	47.0000	55.3333	* +
27	50.0000	65.0000	* +
28	50.0000	30.3333	+ *
29	48.0000	35.0000	+ *
30	61.0000	49.0000	+ *
31	25.0000	30.3333	* +
32	34.0000	35.0000	*+
33	51.0000	49.0000	+ *
34	16.0000	30.3333	* +
35	23.0000	35.0000	* +
36	35.0000	49.0000	* +
37	42.0000	31.3333	+ *
38	45.0000	36.3333	+ *
39	55.0000	45.0000	+ *
40	30.0000	31.3333	*+
41	37.0000	36.3333	*
42	43.0000	45.0000	* +
43	22.0000	31.3333	* +
44	27.0000	36.3333	* +
45	37.0000	45.0000	* +
46	56.0000	42.3333	+ *
47	60.0000	42.6667	+ *
48	77.0000	60.0000	+ *
49	40.0000	42.3333	* +
50	39.0000	42.6667	* +
51	57.0000	60.0000	* +
52	31.0000	42.3333	* +
53	29.0000	42.6667	* +
54	46.0000	60.0000	* +

Residuals

Row	Residuals	-19.6667 19.6667
1	7.3333	*
2	5.6667	*
3	5.6667	*
4	2.3333	*
5	4.6667	*
6	2.6667	*
7	-9.6667	*
8	-10.3333	*
9	-8.3333	*
10	5.0000	*
11	4.3333	*
12	4.0000	*
13	0.0000	*
14	0.3333	*
15	1.0000	*
16	-5.0000	*
17	-4.6667	*
18	-5.0000	*
19	7.3333	*
20	9.6667	*
21	10.0000	*
22	5.3333	*
23	-1.3333	*
24	5.0000	*
25	-12.6667	*
26	-8.3333	*
27	-15.0000	*
28	19.6667	*
29	13.0000	*
30	12.0000	*
31	-5.3333	*
32	-1.0000	*
33	2.0000	*
34	-14.3333	*
35	-12.0000	*
36	-14.0000	*
37	10.6667	*
38	8.6667	*
39	10.0000	*
40	-1.3333	*
41	0.6667	*
42	-2.0000	*
43	-9.3333	*
44	-9.3333	*
45	-8.0000	*
46	13.6667	*
47	17.3333	*
48	17.0000	*
49	-2.3333	*
50	-3.6667	*
51	-3.0000	*
52	-11.3333	*
53	-13.6667	*
54	-14.0000	*

Student-Newman-Keuls

For Score, classified by Dial
Comparisons are between Least Squares Means.
Mean Square Error: 123.314814814815, Degrees of Freedom: 36
** denotes significantly different pairs. Vertical bars show homogeneous subsets.
A pairwise test result is significant if its q stat value is greater than the table q.

Group	Cases	Mean	1	2	3
1	18	37.3889			**	\|
2	18	42.2222			**	\|
3	18	53.2222	**	**		\|

Comparison	Difference	Standard Error	q Stat	Table q	Significance	Lower 95%	Upper 95%	Result
3 - 1	15.8333	3.7016	6.0492	3.4568	0.0004	*	*	**
2 - 1	4.8333	3.7016	1.8466	2.8682	0.1999	*	*
3 - 2	11.0000	3.7016	4.2026	2.8682	0.0053	*	*	**

Homogeneous Subsets:
Group 1: 1 2
Pooled mean	39.8056
95% Confidence Interval	36.0520 <> 43.5591
Group 2: 3
Pooled mean	53.2222
95% Confidence Interval	47.9139 <> 58.5306

Between Homogeneous subsets:
Group 2 - Group 1
Difference	13.4167
95% Confidence Interval	5.5811 <> 21.2522

Tukey-HSD

Group	Cases	Mean	1	2	3
1	18	37.3889			**	\|
2	18	42.2222			**	\|
3	18	53.2222	**	**		\|

Comparison	Difference	Standard Error	q Stat	Table q	Significance	Lower 95%	Upper 95%	Result
3 - 1	15.8333	3.7016	6.0492	3.4568	0.0004	6.7856	24.8811	**
2 - 1	4.8333	3.7016	1.8466	3.4568	0.4013	-4.2144	13.8811
3 - 2	11.0000	3.7016	4.2026	3.4568	0.0142	1.9523	20.0477	**

Homogeneous Subsets:
Group 1: 1 2
Pooled mean	39.8056
95% Confidence Interval	36.0520 <> 43.5591
Group 2: 3
Pooled mean	53.2222
95% Confidence Interval	47.9139 <> 58.5306

Between Homogeneous subsets:
Group 2 - Group 1
Difference	13.4167
95% Confidence Interval	5.5811 <> 21.2522

Tukey-B

Group	Cases	Mean	1	2	3
1	18	37.3889			**	\|
2	18	42.2222			**	\|
3	18	53.2222	**	**		\|

Comparison	Difference	Standard Error	q Stat	Table q	Significance	Lower 95%	Upper 95%	Result
3 - 1	15.8333	3.7016	6.0492	3.4568	0.0004	6.7856	24.8811	**
2 - 1	4.8333	3.7016	1.8466	3.1625	0.1999	-4.2144	13.8811
3 - 2	11.0000	3.7016	4.2026	3.1625	0.0053	1.9523	20.0477	**

Homogeneous Subsets:
Group 1: 1 2
Pooled mean	39.8056
95% Confidence Interval	36.0520 <> 43.5591
Group 2: 3
Pooled mean	53.2222
95% Confidence Interval	47.9139 <> 58.5306

Between Homogeneous subsets:
Group 2 - Group 1
Difference	13.4167
95% Confidence Interval	5.5811 <> 21.2522

Duncan

Group	Cases	Mean	1	2	3
1	18	37.3889			**	\|
2	18	42.2222			**	\|
3	18	53.2222	**	**		\|

Comparison	Difference	Standard Error	q Stat	Table q	Significance	Lower 95%	Upper 95%	Result
3 - 1	15.8333	3.7016	6.0492	3.0144	*	*	*	**
2 - 1	4.8333	3.7016	1.8466	2.8674	*	*	*
3 - 2	11.0000	3.7016	4.2026	2.8674	*	*	*	**

Homogeneous Subsets:
Group 1: 1 2
Pooled mean	39.8056
95% Confidence Interval	36.0520 <> 43.5591
Group 2: 3
Pooled mean	53.2222
95% Confidence Interval	47.9139 <> 58.5306

Scheffe

Group	Cases	Mean	1	2	3
1	18	37.3889			**	\|
2	18	42.2222			**	\|
3	18	53.2222	**	**		\|

Comparison	Difference	Standard Error	q Stat	Table q	Significance	Lower 95%	Upper 95%	Result
3 - 1	15.8333	3.7016	4.2775	2.5532	0.0006	6.3824	25.2842	**
2 - 1	4.8333	3.7016	1.3058	2.5532	0.4348	-4.6176	14.2842
3 - 2	11.0000	3.7016	2.9717	2.5532	0.0193	1.5491	20.4509	**

Homogeneous Subsets:
Group 1: 1 2
Pooled mean	39.8056
95% Confidence Interval	36.0520 <> 43.5591
Group 2: 3
Pooled mean	53.2222
95% Confidence Interval	47.9139 <> 58.5306

Between Homogeneous subsets:
Group 2 - Group 1
Difference	13.4167
95% Confidence Interval	2.3355 <> 24.4978

Least Significant Difference (LSD)

Group	Cases	Mean	1	2	3
1	18	37.3889			**	\|
2	18	42.2222			**	\|
3	18	53.2222	**	**		\|

Comparison	Difference	Standard Error	q Stat	Table q	Significance	Lower 95%	Upper 95%	Result
3 - 1	15.8333	3.7016	4.2775	2.0281	0.0001	8.3262	23.3405	**
2 - 1	4.8333	3.7016	1.3058	2.0281	0.1975	-2.6738	12.3405
3 - 2	11.0000	3.7016	2.9717	2.0281	0.0045	3.4929	18.5071	**

Homogeneous Subsets:
Group 1: 1 2
Pooled mean	39.8056
95% Confidence Interval	36.0520 <> 43.5591
Group 2: 3
Pooled mean	53.2222
95% Confidence Interval	47.9139 <> 58.5306

Bonferroni (Modified LSD)

Group	Cases	Mean	1	2	3
1	18	37.3889			**	\|
2	18	42.2222			**	\|
3	18	53.2222	**	**		\|

Comparison	Difference	Standard Error	q Stat	Table q	Significance	Lower 95%	Upper 95%	Result
3 - 1	15.8333	3.7016	4.2775	2.5110	0.0002	6.5385	25.1281	**
2 - 1	4.8333	3.7016	1.3058	2.5110	0.5925	-4.4615	14.1281
3 - 2	11.0000	3.7016	2.9717	2.5110	0.0135	1.7052	20.2948	**

Homogeneous Subsets:
Group 1: 1 2
Pooled mean	39.8056
95% Confidence Interval	36.0520 <> 43.5591
Group 2: 3
Pooled mean	53.2222
95% Confidence Interval	47.9139 <> 58.5306

Dunnett

For Score, classified by Dial
Comparisons are between Least Squares Means.
Control Group: 1, Two-Tailed Test
Mean Square Error: 123.314814814815, Degrees of Freedom: 36
** denotes significantly different pairs. Vertical bars show homogeneous subsets.
A pairwise test result is significant if its q stat value is greater than the table q.

Group	Cases	Mean	1
1	18	37.3889		\|
2	18	42.2222		\|
3	18	53.2222	**	\|

Comparison	Difference	Standard Error	q Stat	Table q	Significance	Lower 95%	Upper 95%	Result
3 - 1	15.8333	3.7016	4.2775	2.3020	0.0003	7.3123	24.3543	**
2 - 1	4.8333	3.7016	1.3058	2.3020	0.3317	-3.6877	13.3543

Homogeneous Subsets:
Group 1: 1 2
Pooled mean	39.8056
95% Confidence Interval	36.0520 <> 43.5591
Group 2: 3
Pooled mean	53.2222
95% Confidence Interval	47.9139 <> 58.5306

Between Homogeneous subsets:
Group 2 - Group 1
Difference	13.4167
95% Confidence Interval	2.3355 <> 24.4978

General Linear Model

ANOVA

Dependent Variable: Score

Due To	Sum of Squares	DoF	Mean Square	F-Stat		Signif
Constant	105868.167	1	105868.167	35.782		0.0000
Between Subjects	2959.278	5	591.856
Noise	468.167	1	468.167	0.752	a	0.4348
Error Between	2491.111	4	622.778
Within Subjects	6965.556	48	145.116
Period	3722.333	2	1861.167	63.389	b	0.0000
Period � Noise	333.000	2	166.500	5.671	b	0.0293
Dial	2370.333	2	1185.167	89.823	c	0.0000
Dial � Noise	50.333	2	25.167	1.907	c	0.2102
Dial � Period	10.667	4	2.667	0.336	d	0.8499
Dial � Period � Noise	11.333	4	2.833	0.357	d	0.8357
Error Within	467.556	32	14.611
Period � SubjWGrps	234.889	8	29.361
Dial � SubjWGrps	105.556	8	13.194
Dial � Period � SubjWGrps	127.111	16	7.944
Explained	6966.167	17	409.775	4.986		0.0000
Error	2958.667	36	82.185
Total	9924.833	53	187.261

a F-Statistic: Error Between
b F-Statistic: Period � SubjWGrps
c F-Statistic: Dial � SubjWGrps
d F-Statistic: Dial � Period � SubjWGrps

Table of Means

	Cases	Mean	Standard Deviation	Standard Error	Lower 95%	Upper 95%
whole sample	54	44.2778	13.6843	1.8622	40.5427	48.0129
Noise = High	27	47.2222	12.7108	2.4462	42.1940	52.2504
Low	27	41.3333	14.2181	2.7363	35.7088	46.9578
Period = 1	18	54.3333	11.2616	2.6544	48.7331	59.9336
2	18	44.5000	11.9718	2.8218	38.5466	50.4534
3	18	34.0000	9.7317	2.2938	29.1605	38.8395
Period � Noise = 1 � High	9	53.7778	12.5576	4.1859	44.1251	63.4304
1 � Low	9	54.8889	10.5409	3.5136	46.7864	62.9914
2 � High	9	49.4444	12.2893	4.0964	39.9980	58.8909
2 � Low	9	39.5556	9.9261	3.3087	31.9257	47.1854
3 � High	9	38.4444	8.7050	2.9017	31.7532	45.1357
3 � Low	9	29.5556	9.0015	3.0005	22.6364	36.4748
Dial = 1	18	37.3889	12.8023	3.0175	31.0225	43.7553
2	18	42.2222	11.6091	2.7363	36.4492	47.9953
3	18	53.2222	12.0711	2.8452	47.2194	59.2251
Dial � Noise = 1 � High	3	47.3333	6.8069	3.9299	30.4242	64.2425
1 � Low	3	64.3333	11.1505	6.4377	36.6340	92.0327
2 � High	6	43.1667	12.2868	5.0161	30.2724	56.0609
2 � Low	3	38.0000	8.5440	4.9329	16.7755	59.2245
3 � High	3	60.6667	8.3267	4.8074	39.9821	81.3512
3 � Low	3	36.6667	6.5064	3.7565	20.5039	52.8295
Dial � Period = 1 � 1	3	45.3333	10.1160	5.8405	20.2038	70.4629
1 � 2	6	30.8333	10.7223	4.3773	19.5810	42.0856
1 � 3	3	32.6667	8.0208	4.6308	12.7419	52.5915
2 � 1	3	45.6667	5.1316	2.9627	32.9191	58.4143
2 � 2	3	28.6667	7.6376	4.4096	9.6938	47.6396
2 � 3	3	35.3333	9.2916	5.3645	12.2518	58.4149
3 � 1	18	37.3889	12.8023	3.0175	31.0225	43.7553
3 � 2	18	42.2222	11.6091	2.7363	36.4492	47.9953
3 � 3	18	53.2222	12.0711	2.8452	47.2194	59.2251
Dial � Period � Noise = 1 � 1 � High	9	40.1111	12.4644	4.1548	30.5301	49.6921
1 � 1 � Low	9	34.6667	13.2759	4.4253	24.4619	44.8714
1 � 2 � High	9	46.4444	10.5607	3.5202	38.3268	54.5621
1 � 2 � Low	9	38.0000	11.6082	3.8694	29.0772	46.9228
1 � 3 � High	9	55.1111	11.4285	3.8095	46.3264	63.8959
1 � 3 � Low	9	51.3333	13.0767	4.3589	41.2817	61.3850
2 � 1 � High	6	34.0000	13.0690	5.3354	20.2849	47.7151
2 � 1 � Low	3	30.0000	5.0000	2.8868	17.5793	42.4207
2 � 2 � High	3	52.6667	11.0151	6.3596	25.3035	80.0298
2 � 2 � Low	3	31.3333	10.0664	5.8119	6.3269	56.3398
2 � 3 � High	3	42.3333	12.6623	7.3106	10.8785	73.7882
2 � 3 � Low	6	41.1667	11.8561	4.8402	28.7245	53.6089
3 � 1 � High	3	36.6667	4.5092	2.6034	25.4651	47.8683
3 � 1 � Low	3	55.3333	9.0738	5.2387	32.7928	77.8738
3 � 2 � High	3	36.3333	9.0185	5.2068	13.9301	58.7365
3 � 2 � Low	3	42.6667	15.8219	9.1348	3.3628	81.9705
3 � 3 � High	6	51.6667	9.9532	4.0634	41.2214	62.1119
3 � 3 � Low	3	46.0000	4.5826	2.6458	34.6163	57.3837