Unistat Statistics Software | Four-Parameter Logistic Regression in Excel

Four-Parameter Logistic Model in Excel with UNISTAT

The UNISTAT statistics add-in extends Excel with Four-Parameter Logistic Model capabilities.

For further information visit UNISTAT User's Guide section 10.4. Four-Parameter Logistic Model.

Here we provide a sample output from the UNISTAT Excel statistics add-in for data analysis.

UNISTAT Bioassay Analysis	Version 10.11
User: unist	Role: Supervisor
Date: 07/06/2020 21:07:41	File: BioPharma9

Four-Parameter Logistic Model

Valid Number of Cases: 40, 4 Omitted
Model selected: EP

Regression Results

	Coefficient	Standard Error	t-Statistic	Lower 90%	Upper 90%
Upper asymptote	3.1960	0.0327	97.7429	3.1407	3.2512
Lower asymptote	0.1455	0.0143	10.2042	0.1214	0.1695
Hill slope	1.1244	0.0294	38.2340	1.0747	1.1741
Standard S ED50	0.1348	0.0037	36.4278	0.1285	0.1410
Preparation T ED50	0.0924	0.0026	35.7697	0.0880	0.0967

Total Residual Variance	0.0012
Degrees of Freedom	35

Case (Diagnostic) Statistics

	Response	Dose	Preparations	Estimated Response	95% lb Actual Y	95% lb Mean of Y	95% ub Mean of Y	95% ub Actual Y
1	2.912	1	Standard S	2.9061	2.8311	2.8787	2.9335	2.9811
2	2.579	0.5	Standard S	2.6277	2.5540	2.6041	2.6513	2.7014
3	2.13	0.25	Standard S	2.1803	2.1047	2.1513	2.2094	2.2559
4	1.651	0.125	Standard S	1.6063	1.5309	1.5778	1.6349	1.6817
5	1.073	0.0625	Standard S	1.0500	0.9752	1.0230	1.0771	1.1249
6	0.585	0.03125	Standard S	0.6397	0.5661	0.6163	0.6631	0.7133
** 7	0.463	0.015625	Standard S	0.3939	0.3219	0.3762	0.4117	0.4660
8	0.266	0.0078125	Standard S	0.2647	0.1928	0.2474	0.2820	0.3366
9	0.228	0.00390625	Standard S	0.2013	0.1285	0.1805	0.2222	0.2742
10	0.176	0.001953125	Standard S	0.1713	0.0975	0.1472	0.1955	0.2452
11	2.917	1	Standard S	2.9061	2.8311	2.8787	2.9335	2.9811
12	2.654	0.5	Standard S	2.6277	2.5540	2.6041	2.6513	2.7014
13	2.212	0.25	Standard S	2.1803	2.1047	2.1513	2.2094	2.2559
14	1.638	0.125	Standard S	1.6063	1.5309	1.5778	1.6349	1.6817
** 15	0.973	0.0625	Standard S	1.0500	0.9752	1.0230	1.0771	1.1249
16	0.666	0.03125	Standard S	0.6397	0.5661	0.6163	0.6631	0.7133
17	0.356	0.015625	Standard S	0.3939	0.3219	0.3762	0.4117	0.4660
18	0.234	0.0078125	Standard S	0.2647	0.1928	0.2474	0.2820	0.3366
19	0.197	0.00390625	Standard S	0.2013	0.1285	0.1805	0.2222	0.2742
20	0.215	0.001953125	Standard S	0.1713	0.0975	0.1472	0.1955	0.2452
21	3.017	1	Preparation T	3.0000	2.9223	2.9659	3.0340	3.0776
22	2.801	0.5	Preparation T	2.7987	2.7252	2.7755	2.8220	2.8723
23	2.401	0.25	Preparation T	2.4453	2.3707	2.4189	2.4716	2.5199
24	1.918	0.125	Preparation T	1.9277	1.8517	1.8977	1.9576	2.0036
25	1.364	0.0625	Preparation T	1.3410	1.2659	1.3132	1.3689	1.4161
26	0.861	0.03125	Preparation T	0.8415	0.7671	0.8157	0.8673	0.9159
27	0.497	0.015625	Preparation T	0.5097	0.4370	0.4893	0.5302	0.5824
28	0.34	0.0078125	Preparation T	0.3241	0.2523	0.3074	0.3408	0.3958
29	0.242	0.00390625	Preparation T	0.2301	0.1578	0.2113	0.2489	0.3023
30	0.178	0.001953125	Preparation T	0.1849	0.1115	0.1623	0.2074	0.2582
31	2.987	1	Preparation T	3.0000	2.9223	2.9659	3.0340	3.0776
32	2.808	0.5	Preparation T	2.7987	2.7252	2.7755	2.8220	2.8723
33	2.45	0.25	Preparation T	2.4453	2.3707	2.4189	2.4716	2.5199
34	1.963	0.125	Preparation T	1.9277	1.8517	1.8977	1.9576	2.0036
35	1.299	0.0625	Preparation T	1.3410	1.2659	1.3132	1.3689	1.4161
36	0.854	0.03125	Preparation T	0.8415	0.7671	0.8157	0.8673	0.9159
37	0.496	0.015625	Preparation T	0.5097	0.4370	0.4893	0.5302	0.5824
38	0.344	0.0078125	Preparation T	0.3241	0.2523	0.3074	0.3408	0.3958
39	0.217	0.00390625	Preparation T	0.2301	0.1578	0.2113	0.2489	0.3023
40	0.125	0.001953125	Preparation T	0.1849	0.1115	0.1623	0.2074	0.2582
& 41	0.197	0.00363102569986	Standard S	*	*	*	*	*
* 42	*	0.001953125	Standard S	0.1713	0.0975	0.1472	0.1955	0.2452
* 43	*	1	Preparation T	3.0000	2.9223	2.9659	3.0340	3.0776
& 44	2.801	0.502943836867	Preparation T	*	*	*	*	*
	Residuals	Standardised Residuals	Studentised Residuals
1	0.0059	0.1718	0.0064
2	-0.0487	-1.4169	-0.0518
3	-0.0503	-1.4642	-0.0554
4	0.0447	1.3000	0.0490
5	0.0230	0.6688	0.0249
6	-0.0547	-1.5911	-0.0580
** 7	0.0691	2.0089	0.0714
8	0.0013	0.0380	0.0013
9	0.0267	0.7758	0.0279
10	0.0047	0.1355	0.0050
11	0.0109	0.3173	0.0119
12	0.0263	0.7650	0.0280
13	0.0317	0.9214	0.0348
14	0.0317	0.9218	0.0347
** 15	-0.0770	-2.2405	-0.0835
16	0.0263	0.7654	0.0279
17	-0.0379	-1.1040	-0.0392
18	-0.0307	-0.8930	-0.0317
19	-0.0043	-0.1260	-0.0045
20	0.0437	1.2701	0.0465
21	0.0170	0.4959	0.0195
22	0.0023	0.0662	0.0024
23	-0.0443	-1.2878	-0.0478
24	-0.0097	-0.2809	-0.0107
25	0.0230	0.6687	0.0251
26	0.0195	0.5671	0.0210
27	-0.0127	-0.3699	-0.0133
28	0.0159	0.4631	0.0164
29	0.0119	0.3470	0.0124
30	-0.0069	-0.1996	-0.0072
31	-0.0130	-0.3768	-0.0148
32	0.0093	0.2698	0.0098
33	0.0047	0.1377	0.0051
34	0.0353	1.0283	0.0391
35	-0.0420	-1.2223	-0.0458
36	0.0125	0.3635	0.0134
37	-0.0137	-0.3990	-0.0143
38	0.0199	0.5795	0.0205
39	-0.0131	-0.3803	-0.0136
40	-0.0599	-1.7415	-0.0632
& 41	*	*	*
* 42	*	*	*
* 43	*	*	*
& 44	*	*	*

Estimated responses marked by ‘*’ are predicted.
Doses marked by ‘&’ are predicted.
Responses marked by ‘**’ are outliers at 2 x Standard Deviation.

Weighted ANOVA

	Sum of Squares	Chi-Square	DoF	Probability	Pass/Fail
Preparations	0.001	0.530	1	0.4667	Pass
Regression	9.432	6600.317	1	0.0000
Non-parallelism	0.000	0.046	1	0.8306	Pass
Non-linearity	0.013	8.894	16	0.9177	Pass
Standard S Non-linearity	0.008	5.355	8	0.7191	Pass
Preparation T Non-linearity	0.005	3.539	8	0.8961	Pass
Treatments	9.445	6609.786	19	0.0000
Residual	0.029		20
Total	9.474		39
R-squared	0.996				Pass

ANOVA of Regression

Due To	Sum of Squares	DoF	Mean Square	F-Stat	Prob	Pass/Fail
Regression	42.193	4	10.548	8927.664	0.0000
Error	0.041	35	0.001
Total	42.235	39	1.083
R-squared	0.999					Pass

Potency

Assigned potency of Standard S: 0.4 IU/ml

	Estimated Potency	Lower 95%	Upper 95%
Preparation T	0.5835	0.5568	0.6116

	Relative Potency	Lower 95%	Upper 95%
Preparation T	145.89%	139.20%	152.90%

	Percent CI	Lower 95%	Upper 95%	Pass/Fail
Preparation T	100.00%	95.42%	104.81%	Pass

UNISTAT Bioassay Analysis	Version 10.11
User: unist	Role: Supervisor
Date: 07/06/2020 21:07:41	File: BioPharma9

Four-Parameter Logistic Model

Valid Number of Cases: 40, 0 Omitted
Model selected: Full Model USP

Regression Results

	Coefficient	Standard Error	t-Statistic	Lower 90%	Upper 90%
Standard S Upper asymptote	3.1675	0.0522	60.7274	3.0792	3.2559
Lower asymptote	0.1619	0.0190	8.5242	0.1298	0.1941
Hill slope	1.1580	0.0454	25.5298	1.0812	1.2349
ED50	0.1336	0.0053	25.3270	0.1247	0.1425
Preparation T Upper asymptote	3.2207	0.0446	72.2351	3.1451	3.2962
Lower asymptote	0.1243	0.0227	5.4649	0.0857	0.1628
Hill slope	1.0904	0.0410	26.6278	1.0211	1.1598
ED50	0.0926	0.0033	28.2874	0.0870	0.0981

Total Residual Variance	0.0012
Degrees of Freedom	32

Case (Diagnostic) Statistics

	Response	Dose	Preparations	Estimated Response	95% lb Actual Y	95% lb Mean of Y	95% ub Mean of Y	95% ub Actual Y
1	2.912	1	Standard S	2.9013	2.8170	2.8564	2.9462	2.9856
2	2.579	0.5	Standard S	2.6319	2.5544	2.6016	2.6622	2.7094
3	2.13	0.25	Standard S	2.1873	2.1078	2.1522	2.2225	2.2669
4	1.651	0.125	Standard S	1.6069	1.5287	1.5748	1.6391	1.6852
5	1.073	0.0625	Standard S	1.0433	0.9652	1.0115	1.0751	1.1215
6	0.585	0.03125	Standard S	0.6332	0.5555	0.6025	0.6638	0.7108
7	0.463	0.015625	Standard S	0.3931	0.3178	0.3689	0.4174	0.4685
8	0.266	0.0078125	Standard S	0.2701	0.1949	0.2464	0.2938	0.3453
9	0.228	0.00390625	Standard S	0.2114	0.1346	0.1830	0.2398	0.2882
10	0.176	0.001953125	Standard S	0.1843	0.1058	0.1516	0.2170	0.2628
11	2.917	1	Standard S	2.9013	2.8170	2.8564	2.9462	2.9856
12	2.654	0.5	Standard S	2.6319	2.5544	2.6016	2.6622	2.7094
13	2.212	0.25	Standard S	2.1873	2.1078	2.1522	2.2225	2.2669
14	1.638	0.125	Standard S	1.6069	1.5287	1.5748	1.6391	1.6852
** 15	0.973	0.0625	Standard S	1.0433	0.9652	1.0115	1.0751	1.1215
16	0.666	0.03125	Standard S	0.6332	0.5555	0.6025	0.6638	0.7108
17	0.356	0.015625	Standard S	0.3931	0.3178	0.3689	0.4174	0.4685
18	0.234	0.0078125	Standard S	0.2701	0.1949	0.2464	0.2938	0.3453
19	0.197	0.00390625	Standard S	0.2114	0.1346	0.1830	0.2398	0.2882
20	0.215	0.001953125	Standard S	0.1843	0.1058	0.1516	0.2170	0.2628
21	3.017	1	Preparation T	3.0056	2.9222	2.9624	3.0488	3.0890
22	2.801	0.5	Preparation T	2.7960	2.7189	2.7668	2.8253	2.8732
23	2.401	0.25	Preparation T	2.4377	2.3594	2.4054	2.4700	2.5160
24	1.918	0.125	Preparation T	1.9238	1.8452	1.8909	1.9568	2.0024
25	1.364	0.0625	Preparation T	1.3459	1.2684	1.3157	1.3762	1.4234
26	0.861	0.03125	Preparation T	0.8498	0.7716	0.8179	0.8818	0.9280
27	0.497	0.015625	Preparation T	0.5134	0.4370	0.4861	0.5406	0.5897
28	0.34	0.0078125	Preparation T	0.3200	0.2447	0.2960	0.3441	0.3953
29	0.242	0.00390625	Preparation T	0.2194	0.1425	0.1906	0.2482	0.2963
30	0.178	0.001953125	Preparation T	0.1697	0.0901	0.1344	0.2049	0.2492
31	2.987	1	Preparation T	3.0056	2.9222	2.9624	3.0488	3.0890
32	2.808	0.5	Preparation T	2.7960	2.7189	2.7668	2.8253	2.8732
33	2.45	0.25	Preparation T	2.4377	2.3594	2.4054	2.4700	2.5160
34	1.963	0.125	Preparation T	1.9238	1.8452	1.8909	1.9568	2.0024
35	1.299	0.0625	Preparation T	1.3459	1.2684	1.3157	1.3762	1.4234
36	0.854	0.03125	Preparation T	0.8498	0.7716	0.8179	0.8818	0.9280
37	0.496	0.015625	Preparation T	0.5134	0.4370	0.4861	0.5406	0.5897
38	0.344	0.0078125	Preparation T	0.3200	0.2447	0.2960	0.3441	0.3953
39	0.217	0.00390625	Preparation T	0.2194	0.1425	0.1906	0.2482	0.2963
40	0.125	0.001953125	Preparation T	0.1697	0.0901	0.1344	0.2049	0.2492
	Residuals	Standardised Residuals	Studentised Residuals
1	0.0107	0.3053	0.0138
2	-0.0529	-1.5095	-0.0584
3	-0.0573	-1.6366	-0.0659
4	0.0441	1.2578	0.0493
5	0.0297	0.8470	0.0331
6	-0.0482	-1.3754	-0.0533
7	0.0699	1.9954	0.0743
8	-0.0041	-0.1177	-0.0044
9	0.0166	0.4739	0.0181
10	-0.0083	-0.2371	-0.0093
11	0.0157	0.4481	0.0202
12	0.0221	0.6318	0.0244
13	0.0247	0.7046	0.0284
14	0.0311	0.8866	0.0348
** 15	-0.0703	-2.0081	-0.0786
16	0.0328	0.9372	0.0363
17	-0.0371	-1.0596	-0.0395
18	-0.0361	-1.0314	-0.0383
19	-0.0144	-0.4111	-0.0157
20	0.0307	0.8763	0.0345
21	0.0114	0.3252	0.0143
22	0.0050	0.1417	0.0054
23	-0.0367	-1.0485	-0.0412
24	-0.0058	-0.1662	-0.0066
25	0.0181	0.5155	0.0199
26	0.0112	0.3193	0.0125
27	-0.0164	-0.4668	-0.0177
28	0.0200	0.5701	0.0212
29	0.0226	0.6456	0.0247
30	0.0083	0.2377	0.0096
31	-0.0186	-0.5314	-0.0234
32	0.0120	0.3416	0.0131
33	0.0123	0.3505	0.0138
34	0.0392	1.1186	0.0442
35	-0.0469	-1.3403	-0.0518
36	0.0042	0.1194	0.0047
37	-0.0174	-0.4954	-0.0188
38	0.0240	0.6843	0.0255
39	-0.0024	-0.0682	-0.0026
40	-0.0447	-1.2754	-0.0514

Responses marked by ‘**’ are outliers at 2 x Standard Deviation.

Effective Dose

	Dose	Standard Error	Lower 90%	Upper 90%
Standard S ED10	0.0200	0.0021	0.0165	0.0235
ED20	0.0404	0.0031	0.0351	0.0456
ED50	0.1336	0.0053	0.1247	0.1425
ED80	0.4422	0.0174	0.4128	0.4717
ED90	0.8908	0.0533	0.8006	0.9810
Preparation T ED10	0.0123	0.0012	0.0103	0.0144
ED20	0.0260	0.0018	0.0228	0.0291
ED50	0.0926	0.0033	0.0870	0.0981
ED80	0.3300	0.0147	0.3051	0.3550
ED90	0.6943	0.0468	0.6151	0.7735

ANOVA of Regression

Due To	Sum of Squares	DoF	Mean Square	F-Stat	Prob
Standard S Regression	19.911	3	6.637	3693.866	0.0000
Error	0.029	16	0.002
Total	19.940	19	1.049
R-squared	0.999
Preparation T Regression	22.054	3	7.351	11193.015	0.0000
Error	0.011	16	0.001
Total	22.064	19	1.161
R-squared	1.000

Measures of Variability

	Standard Deviation	Upper 95% Standard Deviation	Upper 95% GSD	Upper 95% %GCV	Upper 95% %CV
Total	0.0350	0.0442	1.0452	4.5217	4.4246

Mean Difference from Standard

	Mean Difference	Lower 90%	Upper 90%
Upper asymptote Preparation T	0.0531	-0.0140	0.1202
Lower asymptote Preparation T	-0.0377	-0.1234	0.0480
Hill slope Preparation T	0.0676	-0.0359	0.1711

Four-Parameter Logistic Model

Valid Number of Cases: 40, 0 Omitted
Model selected: Reduced Model USP

Regression Results

	Coefficient	Standard Error	t-Statistic	Lower 90%	Upper 90%
Upper asymptote	3.1960	0.0327	97.7429	3.1407	3.2512
Lower asymptote	0.1455	0.0143	10.2042	0.1214	0.1695
Hill slope	1.1244	0.0294	38.2340	1.0747	1.1741
Standard S ED50	0.1348	0.0037	36.4278	0.1285	0.1410
Preparation T ED50	0.0924	0.0026	35.7697	0.0880	0.0967

Total Residual Variance	0.0012
Degrees of Freedom	35

Case (Diagnostic) Statistics

	Response	Dose	Preparations	Estimated Response	95% lb Actual Y	95% lb Mean of Y	95% ub Mean of Y	95% ub Actual Y
1	2.912	1	Standard S	2.9061	2.8311	2.8787	2.9335	2.9811
2	2.579	0.5	Standard S	2.6277	2.5540	2.6041	2.6513	2.7014
3	2.13	0.25	Standard S	2.1803	2.1047	2.1513	2.2094	2.2559
4	1.651	0.125	Standard S	1.6063	1.5309	1.5778	1.6349	1.6817
5	1.073	0.0625	Standard S	1.0500	0.9752	1.0230	1.0771	1.1249
6	0.585	0.03125	Standard S	0.6397	0.5661	0.6163	0.6631	0.7133
** 7	0.463	0.015625	Standard S	0.3939	0.3219	0.3762	0.4117	0.4660
8	0.266	0.0078125	Standard S	0.2647	0.1928	0.2474	0.2820	0.3366
9	0.228	0.00390625	Standard S	0.2013	0.1285	0.1805	0.2222	0.2742
10	0.176	0.001953125	Standard S	0.1713	0.0975	0.1472	0.1955	0.2452
11	2.917	1	Standard S	2.9061	2.8311	2.8787	2.9335	2.9811
12	2.654	0.5	Standard S	2.6277	2.5540	2.6041	2.6513	2.7014
13	2.212	0.25	Standard S	2.1803	2.1047	2.1513	2.2094	2.2559
14	1.638	0.125	Standard S	1.6063	1.5309	1.5778	1.6349	1.6817
** 15	0.973	0.0625	Standard S	1.0500	0.9752	1.0230	1.0771	1.1249
16	0.666	0.03125	Standard S	0.6397	0.5661	0.6163	0.6631	0.7133
17	0.356	0.015625	Standard S	0.3939	0.3219	0.3762	0.4117	0.4660
18	0.234	0.0078125	Standard S	0.2647	0.1928	0.2474	0.2820	0.3366
19	0.197	0.00390625	Standard S	0.2013	0.1285	0.1805	0.2222	0.2742
20	0.215	0.001953125	Standard S	0.1713	0.0975	0.1472	0.1955	0.2452
21	3.017	1	Preparation T	3.0000	2.9223	2.9659	3.0340	3.0776
22	2.801	0.5	Preparation T	2.7987	2.7252	2.7755	2.8220	2.8723
23	2.401	0.25	Preparation T	2.4453	2.3707	2.4189	2.4716	2.5199
24	1.918	0.125	Preparation T	1.9277	1.8517	1.8977	1.9576	2.0036
25	1.364	0.0625	Preparation T	1.3410	1.2659	1.3132	1.3689	1.4161
26	0.861	0.03125	Preparation T	0.8415	0.7671	0.8157	0.8673	0.9159
27	0.497	0.015625	Preparation T	0.5097	0.4370	0.4893	0.5302	0.5824
28	0.34	0.0078125	Preparation T	0.3241	0.2523	0.3074	0.3408	0.3958
29	0.242	0.00390625	Preparation T	0.2301	0.1578	0.2113	0.2489	0.3023
30	0.178	0.001953125	Preparation T	0.1849	0.1115	0.1623	0.2074	0.2582
31	2.987	1	Preparation T	3.0000	2.9223	2.9659	3.0340	3.0776
32	2.808	0.5	Preparation T	2.7987	2.7252	2.7755	2.8220	2.8723
33	2.45	0.25	Preparation T	2.4453	2.3707	2.4189	2.4716	2.5199
34	1.963	0.125	Preparation T	1.9277	1.8517	1.8977	1.9576	2.0036
35	1.299	0.0625	Preparation T	1.3410	1.2659	1.3132	1.3689	1.4161
36	0.854	0.03125	Preparation T	0.8415	0.7671	0.8157	0.8673	0.9159
37	0.496	0.015625	Preparation T	0.5097	0.4370	0.4893	0.5302	0.5824
38	0.344	0.0078125	Preparation T	0.3241	0.2523	0.3074	0.3408	0.3958
39	0.217	0.00390625	Preparation T	0.2301	0.1578	0.2113	0.2489	0.3023
40	0.125	0.001953125	Preparation T	0.1849	0.1115	0.1623	0.2074	0.2582
	Residuals	Standardised Residuals	Studentised Residuals
1	0.0059	0.1718	0.0064
2	-0.0487	-1.4169	-0.0518
3	-0.0503	-1.4642	-0.0554
4	0.0447	1.3000	0.0490
5	0.0230	0.6688	0.0249
6	-0.0547	-1.5911	-0.0580
** 7	0.0691	2.0089	0.0714
8	0.0013	0.0380	0.0013
9	0.0267	0.7758	0.0279
10	0.0047	0.1355	0.0050
11	0.0109	0.3173	0.0119
12	0.0263	0.7650	0.0280
13	0.0317	0.9214	0.0348
14	0.0317	0.9218	0.0347
** 15	-0.0770	-2.2405	-0.0835
16	0.0263	0.7654	0.0279
17	-0.0379	-1.1040	-0.0392
18	-0.0307	-0.8930	-0.0317
19	-0.0043	-0.1260	-0.0045
20	0.0437	1.2701	0.0465
21	0.0170	0.4959	0.0195
22	0.0023	0.0662	0.0024
23	-0.0443	-1.2878	-0.0478
24	-0.0097	-0.2809	-0.0107
25	0.0230	0.6687	0.0251
26	0.0195	0.5671	0.0210
27	-0.0127	-0.3699	-0.0133
28	0.0159	0.4631	0.0164
29	0.0119	0.3470	0.0124
30	-0.0069	-0.1996	-0.0072
31	-0.0130	-0.3768	-0.0148
32	0.0093	0.2698	0.0098
33	0.0047	0.1377	0.0051
34	0.0353	1.0283	0.0391
35	-0.0420	-1.2223	-0.0458
36	0.0125	0.3635	0.0134
37	-0.0137	-0.3990	-0.0143
38	0.0199	0.5795	0.0205
39	-0.0131	-0.3803	-0.0136
40	-0.0599	-1.7415	-0.0632

Responses marked by ‘**’ are outliers at 2 x Standard Deviation.

Effective Dose

	Dose	Standard Error	Lower 90%	Upper 90%
Standard S ED10	0.0191	0.0013	0.0169	0.0213
ED20	0.0393	0.0020	0.0359	0.0427
ED50	0.1348	0.0037	0.1285	0.1410
ED80	0.4624	0.0143	0.4383	0.4865
ED90	0.9510	0.0429	0.8786	1.0234
Preparation T ED10	0.0131	0.0009	0.0116	0.0146
ED20	0.0269	0.0014	0.0246	0.0293
ED50	0.0924	0.0026	0.0880	0.0967
ED80	0.3169	0.0098	0.3004	0.3334
ED90	0.6519	0.0292	0.6025	0.7013

Validity of Assay

Due To	Sum of Squares	DoF	Mean Square	F-Stat	Prob
Preparations	0.231	1	0.231	161.363	0.0000
Regression	41.963	3	13.988	9788.536	0.0000
Non-parallelism	0.002	3	0.001	0.489	0.6937
Non-linearity	0.011	12	0.001	0.619	0.8022
Treatments	42.206	19	2.221	1554.519	0.0000
Residual	0.029	20	0.001
Total	42.235	39	1.083
R-squared	0.999

ANOVA of Regression

Due To	Sum of Squares	DoF	Mean Square	F-Stat	Prob
Regression	42.193	4	10.548	8927.664	0.0000
Error	0.041	35	0.001
Total	42.235	39	1.083
R-squared	0.999

Measures of Variability

	Standard Deviation	Upper 95% Standard Deviation	Upper 95% GSD	Upper 95% %GCV	Upper 95% %CV
Total	0.0344	0.0429	1.0438	4.3838	4.2924

Potency

Assigned potency of Standard S: 0.4 IU/ml

	Estimated Potency	Lower 95%	Upper 95%
Preparation T	0.5835	0.5583	0.6099

	Relative Potency	Lower 95%	Upper 95%
Preparation T	145.89%	139.58%	152.48%

	Percent CI	Lower 95%	Upper 95%
Preparation T	100.00%	95.68%	104.52%