UNISTAT - the ultimate Excel statistics add-in

General Linear Model in Excel with Unistat

The Unistat statistics add-in extends Excel with General Linear Model capabilities.

Further documentation is available at section 7.3.2 of the manual, General Linear Model.

Sample output

Here we provide annotated example report output from the Unistat Excel statistics 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

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