UNISTAT - the ultimate Excel statistics add-in

Slope Ratio Method in Excel with UNISTAT

The UNISTAT statistics add-in extends Excel with Slope Ratio Method capabilities.

For further information visit UNISTAT User's Guide section 10.2. Slope Ratio Method.

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

Slope Ratio Method

Summary Statistics

Data variable: Response
Subsample selected by: Dose x Preparations
Quantile Method: Simple Average

Valid CasesMeanMedianVariance
0 x Blank 8 0.0232 0.0230 0.0000
0 x Standard S 0***
0 x Preparation T 0***
1 x Blank 0***
1 x Standard S 8 0.1351 0.1360 0.0000
1 x Preparation T 8 0.1200 0.1200 0.0000
2 x Blank 0***
2 x Standard S 8 0.2176 0.2180 0.0000
2 x Preparation T 8 0.1897 0.1900 0.0000
3 x Blank 0***
3 x Standard S 8 0.2996 0.2990 0.0000
3 x Preparation T 8 0.2554 0.2550 0.0000

Shapiro-Wilk Normality Test

Alpha = 0.05

Dose x PreparationsTest StatisticProbabilityPass/Fail
0 x Blank 0.8578 0.1143Pass
1 x Standard S 0.8969 0.2707Pass
2 x Standard S 0.8816 0.1952Pass
3 x Standard S 0.8269 0.0551Pass
1 x Preparation T 0.8599 0.1199Pass
2 x Preparation T 0.8042 0.0318**Fail**
3 x Preparation T 0.9255 0.4763Pass

Kolmogorov-Smirnov Normality Test

Alpha = 0.05

Dose x PreparationsTest Statistic* ProbabilityPass/Fail
0 x Blank 0.1964 0.2000Pass
1 x Standard S 0.2632 0.1076Pass
2 x Standard S 0.1970 0.2000Pass
3 x Standard S 0.3426 0.0063**Fail**
1 x Preparation T 0.2500 0.1494Pass
2 x Preparation T 0.3350 0.0086**Fail**
3 x Preparation T 0.2090 0.2000Pass

* Lilliefors probability = 0.2 means 0.2 or greater.

Cramer-von Mises Normality Test

Alpha = 0.05

Dose x PreparationsTest StatisticProbabilityPass/Fail
0 x Blank 0.0730 0.2229Pass
1 x Standard S 0.0832 0.1615Pass
2 x Standard S 0.0582 0.3577Pass
3 x Standard S 0.1351 0.0290**Fail**
1 x Preparation T 0.0863 0.1464Pass
2 x Preparation T 0.1404 0.0244**Fail**
3 x Preparation T 0.0608 0.3289Pass

Anderson-Darling Normality Test

Alpha = 0.05

Dose x PreparationsTest StatisticProbabilityPass/Fail
0 x Blank 0.4909 0.1530Pass
1 x Standard S 0.4529 0.1958Pass
2 x Standard S 0.3924 0.2868Pass
3 x Standard S 0.6980 0.0410**Fail**
1 x Preparation T 0.5178 0.1280Pass
2 x Preparation T 0.7702 0.0258**Fail**
3 x Preparation T 0.3484 0.3758Pass

Homogeneity of Variance Tests

For 7 groups defined by Dose x Preparations.
Alpha = 0.05

Test StatisticProbabilityPass/Fail
Bartlett’s Chi-square Test 9.7490 0.1356Pass
Bartlett-Box F Test 1.6372 0.1327Pass
Cochran’s C (max var / sum var) 0.2842 0.2667Pass
Hartley’s F (max var / min var) 6.2344*
Levene’s F Test 2.2108 0.0576Pass

Dixon’s Outlier Test

Alpha = 0.05
One-tailed tests

Dose x PreparationsDixon’s QTable QPass/Fail
0 x Blank Q(Min) 0.0000 0.5540Pass
Q(Max) 0.5000 0.5540Pass
1 x Standard S Q(Min) 0.3333 0.5540Pass
Q(Max) 0.2000 0.5540Pass
2 x Standard S Q(Min) 0.0000 0.5540Pass
Q(Max) 0.0000 0.5540Pass
3 x Standard S Q(Min) 0.0000 0.5540Pass
Q(Max) 0.3750 0.5540Pass
1 x Preparation T Q(Min) 0.3333 0.5540Pass
Q(Max) 0.0000 0.5540Pass
2 x Preparation T Q(Min) 0.0000 0.5540Pass
Q(Max) 0.0000 0.5540Pass
3 x Preparation T Q(Min) 0.2500 0.5540Pass
Q(Max) 0.2500 0.5540Pass

N = 8, Q(Min)=(X(2)-X(1))/(X(N-1)-X(1)), Q(Max)=(X(N)-X(N-1))/(X(N)-X(2))

Grubbs’ Outlier Test

Alpha = 0.05
One-tailed tests

Dose x PreparationsGrubbs’ GTable GPass/Fail
0 x Blank G(Min) 0.9001 2.0317Pass
G(Max) 1.9802 2.0317Pass
1 x Standard S G(Min) 1.6668 2.0317Pass
G(Max) 1.1617 2.0317Pass
2 x Standard S G(Min) 1.2706 2.0317Pass
G(Max) 1.1496 2.0317Pass
3 x Standard S G(Min) 0.9834 2.0317Pass
G(Max) 2.0137 2.0317Pass
1 x Preparation T G(Min) 1.8708 2.0317Pass
G(Max) 0.9354 2.0317Pass
2 x Preparation T G(Min) 1.5022 2.0317Pass
G(Max) 1.0730 2.0317Pass
3 x Preparation T G(Min) 1.3435 2.0317Pass
G(Max) 1.4849 2.0317Pass

G = Maximum deviation from mean / Standard Deviation

ESD Outlier Test

Alpha = 0.05
Two-tailed test
Number of outliers to test (ESD) = 2

Dose x PreparationsESD RiTable RiPass/Fail
0 x Blank (Max) 1 1.9802 2.1266Pass
0 x Blank (Max) 2 1.2702 2.0200Pass
1 x Standard S (Min) 1 1.6668 2.1266Pass
1 x Standard S (Min) 2 1.3736 2.0200Pass
2 x Standard S (Min) 1 1.2706 2.1266Pass
2 x Standard S (Min) 2 1.5667 2.0200Pass
3 x Standard S (Max) 1 2.0137 2.1266Pass
3 x Standard S (Max) 2 1.8750 2.0200Pass
1 x Preparation T (Min) 1 1.8708 2.1266Pass
1 x Preparation T (Min) 2 1.7008 2.0200Pass
2 x Preparation T (Min) 1 1.5022 2.1266Pass
2 x Preparation T (Min) 2 2.0000 2.0200Pass
3 x Preparation T (Max) 1 1.4849 2.1266Pass
3 x Preparation T (Min) 2 1.3093 2.0200Pass

Ri = Generalised Extreme Studentised Deviate

Slope Ratio Method

Slope Ratio Method

Separate Regression

InterceptSlopeR-squaredPass/Fail
Standard S 0.0530 0.0822 0.9989Pass
Preparation T 0.0530 0.0677 0.9992Pass

Common Regression

InterceptSlopeR-squaredPass/Fail
Standard S 0.0370 0.0891 0.9916Pass
Preparation T 0.0746

Residual Variance 0.0187
Degrees of Freedom 53

Case (Diagnostic) Statistics

ResponseDosePreparationsEstimated ResponseResidualsStandardised Residuals
1 0.022 0Blank 0.0370-0.0150-1.8524
2 0.024 0Blank 0.0370-0.0130-1.6049
3 0.024 0Blank 0.0370-0.0130-1.6049
4 0.026 0Blank 0.0370-0.0110-1.3575
5 0.023 0Blank 0.0370-0.0140-1.7287
6 0.022 0Blank 0.0370-0.0150-1.8524
7 0.022 0Blank 0.0370-0.0150-1.8524
8 0.023 0Blank 0.0370-0.0140-1.7287
9 0.133 1Standard S 0.1261 0.0069 0.8571
10 0.133 1Standard S 0.1261 0.0069 0.8571
11 0.131 1Standard S 0.1261 0.0049 0.6097
12 0.136 1Standard S 0.1261 0.0099 1.2283
13 0.137 1Standard S 0.1261 0.0109 1.3520
14 0.136 1Standard S 0.1261 0.0099 1.2283
15 0.138 1Standard S 0.1261 0.0119 1.4758
16 0.137 1Standard S 0.1261 0.0109 1.3520
17 0.215 2Standard S 0.2152-0.0002-0.0216
18 0.215 2Standard S 0.2152-0.0002-0.0216
19 0.216 2Standard S 0.2152 0.0008 0.1021
20 0.218 2Standard S 0.2152 0.0028 0.3496
21 0.22 2Standard S 0.2152 0.0048 0.5971
22 0.22 2Standard S 0.2152 0.0048 0.5971
23 0.219 2Standard S 0.2152 0.0038 0.4733
24 0.218 2Standard S 0.2152 0.0028 0.3496
25 0.299 3Standard S 0.3043-0.0053-0.6528
26 0.299 3Standard S 0.3043-0.0053-0.6528
27 0.299 3Standard S 0.3043-0.0053-0.6528
28 0.297 3Standard S 0.3043-0.0073-0.9003
29 0.297 3Standard S 0.3043-0.0073-0.9003
30 0.305 3Standard S 0.3043 0.0007 0.0896
31 0.299 3Standard S 0.3043-0.0053-0.6528
32 0.302 3Standard S 0.3043-0.0023-0.2816
33 0.12 1Preparation T 0.1115 0.0085 1.0482
34 0.119 1Preparation T 0.1115 0.0075 0.9245
35 0.118 1Preparation T 0.1115 0.0065 0.8008
36 0.12 1Preparation T 0.1115 0.0085 1.0482
37 0.12 1Preparation T 0.1115 0.0085 1.0482
38 0.121 1Preparation T 0.1115 0.0095 1.1720
39 0.121 1Preparation T 0.1115 0.0095 1.1720
40 0.121 1Preparation T 0.1115 0.0095 1.1720
41 0.188 2Preparation T 0.1861 0.0019 0.2369
42 0.188 2Preparation T 0.1861 0.0019 0.2369
43 0.19 2Preparation T 0.1861 0.0039 0.4844
44 0.19 2Preparation T 0.1861 0.0039 0.4844
45 0.19 2Preparation T 0.1861 0.0039 0.4844
46 0.191 2Preparation T 0.1861 0.0049 0.6081
47 0.191 2Preparation T 0.1861 0.0049 0.6081
48 0.19 2Preparation T 0.1861 0.0039 0.4844
49 0.254 3Preparation T 0.2606-0.0066-0.8218
50 0.253 3Preparation T 0.2606-0.0076-0.9456
51 0.255 3Preparation T 0.2606-0.0056-0.6981
52 0.258 3Preparation T 0.2606-0.0026-0.3269
53 0.257 3Preparation T 0.2606-0.0036-0.4507
54 0.257 3Preparation T 0.2606-0.0036-0.4507
55 0.255 3Preparation T 0.2606-0.0056-0.6981
56 0.254 3Preparation T 0.2606-0.0066-0.8218

Validity of Assay

Due ToSum of SquaresDoFMean SquareF-StatProbPass/Fail
Constant 1.759 1 1.759
Regression 0.410 2 0.205 57206.122 0.0000Pass
Blanks 0.003 1 0.003 911.134 0.0000Pass
Intercept 0.000 1 0.000 0.001 0.9771**Fail**
Non-linearity 0.000 2 0.000 3.214 0.0488**Fail**
Standard S Non-linearity 0.000 1 0.000 0.093 0.7616
Preparation T Non-linearity 0.000 1 0.000 6.334 0.0152
Treatments 0.413 6 0.069
Residual 0.000 49 0.000
Total 0.413 55 0.008

Potency

Estimated PotencyLower 95%Upper 95%DoF
Preparation T 0.8368 0.8315 0.8421 49

Relative PotencyLower 95%Upper 95%
Preparation T 83.68% 83.15% 84.21%

Percent CILower 95%Upper 95%
Preparation T 100.00% 99.37% 100.64%

G 0.0000
C 1.0000

Slope Ratio Method