Quantal Response Method in Excel with UNISTAT
The UNISTAT statistics add-in extends Excel with Quantal Response Method capabilities.
For further information visit UNISTAT User's Guide section 10.3. Quantal Response Method.
Here we provide a sample output from the UNISTAT Excel statistics add-in for data analysis.
Quantal Response Method
Valid Number of Cases: 8, 0 Omitted
Model selected: Logit
Regression Results
| Coefficient | Standard Error | Z-Statistic | 2-Tail Probability | Lower 90% | Upper 90% | |
|---|---|---|---|---|---|---|
| Common Slope | 4.1014 | 0.7983 | 5.1378 | 0.0000 | 2.7884 | 5.4145 |
| Intercept Standard S | -3.5122 | 0.7700 | -4.5615 | 0.0000 | -4.7786 | -2.2457 |
| Intercept Preparation T | -2.8919 | 0.6922 | -4.1776 | 0.0000 | -4.0305 | -1.7532 |
| Residual Variance | 0.5199 |
|---|---|
| Degrees of Freedom | 5 |
Case (Diagnostic) Statistics
| Response | Subject | Dose | Preparation | Estimated Response | Residuals | Standardised Residuals | Probability | |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 12 | 1 | Standard S | 0.3476 | -0.3476 | -0.4821 | 0.0290 |
| 2 | 3 | 12 | 1.6 | Standard S | 2.0419 | 0.9581 | 1.3288 | 0.1702 |
| 3 | 6 | 12 | 2.5 | Standard S | 6.7341 | -0.7341 | -1.0181 | 0.5612 |
| 4 | 10 | 11 | 4 | Standard S | 9.8764 | 0.1236 | 0.1714 | 0.8979 |
| 5 | 0 | 11 | 1 | Preparation T | 0.3186 | -0.3186 | -0.4419 | 0.0290 |
| ** 6 | 4 | 12 | 1.6 | Preparation T | 2.0419 | 1.9581 | 2.7157 | 0.1702 |
| ** 7 | 8 | 11 | 2.5 | Preparation T | 6.1729 | 1.8271 | 2.5341 | 0.5612 |
| 8 | 10 | 11 | 4 | Preparation T | 9.8764 | 0.1236 | 0.1714 | 0.8979 |
Cases marked by ‘**’ are outliers at 2 x Standard Deviation.
Effective Dose
| Effective Dose | Lower 95% | Upper 95% | Trim Entered | Trim Used | |
|---|---|---|---|---|---|
| Standard S ED50 | 2.3545 | 1.9176 | 2.9292 | ||
| Spearman-Karber | 2.3391 | 1.8891 | 2.8961 | 0.00% | 9.09% |
| Preparation T ED50 | 2.0240 | 1.6368 | 2.5114 | ||
| Spearman-Karber | 1.9703 | 1.5878 | 2.4450 | 0.00% | 9.09% |
Weighted ANOVA
| Sum of Squares | Chi-Square | DoF | Probability | |
|---|---|---|---|---|
| Preparations | 0.041 | 0.041 | 1 | 0.8401 |
| Regression | 26.397 | 26.397 | 1 | 0.0000 |
| Non-parallelism | 0.007 | 0.007 | 1 | 0.9351 |
| Non-linearity | 2.150 | 2.150 | 4 | 0.7081 |
| Standard S Non-linearity | 1.094 | 1.094 | 2 | 0.5787 |
| Preparation T Non-linearity | 1.057 | 1.057 | 2 | 0.5896 |
| Treatments | 28.595 | 28.595 | 7 | 0.0002 |
| Residual | ||||
| Total | 28.595 | 7 | ||
| R-squared | 0.925 |
Potency
| Estimated Potency | Lower 95% | Upper 95% | DoF | |
|---|---|---|---|---|
| Preparation T | 1.1633 | 0.8652 | 1.5793 | 0 |
| Relative Potency | Lower 95% | Upper 95% | |
|---|---|---|---|
| Preparation T | 116.33% | 86.52% | 157.93% |
| Percent CI | Lower 95% | Upper 95% | |
|---|---|---|---|
| Preparation T | 100.00% | 74.38% | 135.77% |
| G | 0.1455 |
|---|---|
| C | 1.1703 |
Quantal Response Method
Valid Number of Cases: 8, 0 Omitted
Model selected: Probit
Regression Results
| Coefficient | Standard Error | Z-Statistic | 2-Tail Probability | Lower 90% | Upper 90% | |
|---|---|---|---|---|---|---|
| Common Slope | 2.4011 | 0.4170 | 5.7582 | 0.0000 | 1.7152 | 3.0869 |
| Intercept Standard S | -2.0504 | 0.4086 | -5.0176 | 0.0000 | -2.7226 | -1.3783 |
| Intercept Preparation T | -1.7208 | 0.3829 | -4.4945 | 0.0000 | -2.3506 | -1.0911 |
| Residual Variance | 0.4781 |
|---|---|
| Degrees of Freedom | 5 |
Case (Diagnostic) Statistics
| Response | Subject | Dose | Preparation | Estimated Response | Residuals | Standardised Residuals | Probability | |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 12 | 1 | Standard S | 0.2419 | -0.2419 | -0.3499 | 0.0202 |
| 2 | 3 | 12 | 1.6 | Standard S | 2.1395 | 0.8605 | 1.2445 | 0.1783 |
| 3 | 6 | 12 | 2.5 | Standard S | 6.7138 | -0.7138 | -1.0323 | 0.5595 |
| 4 | 10 | 11 | 4 | Standard S | 9.8935 | 0.1065 | 0.1541 | 0.8994 |
| 5 | 0 | 11 | 1 | Preparation T | 0.2218 | -0.2218 | -0.3207 | 0.0202 |
| ** 6 | 4 | 12 | 1.6 | Preparation T | 2.1395 | 1.8605 | 2.6907 | 0.1783 |
| ** 7 | 8 | 11 | 2.5 | Preparation T | 6.1543 | 1.8457 | 2.6692 | 0.5595 |
| 8 | 10 | 11 | 4 | Preparation T | 9.8935 | 0.1065 | 0.1541 | 0.8994 |
Cases marked by ‘**’ are outliers at 2 x Standard Deviation.
Effective Dose
| Effective Dose | Lower 95% | Upper 95% | Trim Entered | Trim Used | |
|---|---|---|---|---|---|
| Standard S ED50 | 2.3489 | 1.9291 | 2.8956 | ||
| Spearman-Karber | 2.3391 | 1.8891 | 2.8961 | 0.00% | 9.09% |
| Preparation T ED50 | 2.0477 | 1.6716 | 2.5166 | ||
| Spearman-Karber | 1.9703 | 1.5878 | 2.4450 | 0.00% | 9.09% |
Weighted ANOVA
| Sum of Squares | Chi-Square | DoF | Probability | |
|---|---|---|---|---|
| Preparations | 0.066 | 0.066 | 1 | 0.7969 |
| Regression | 33.975 | 33.975 | 1 | 0.0000 |
| Non-parallelism | 0.001 | 0.001 | 1 | 0.9743 |
| Non-linearity | 1.921 | 1.921 | 4 | 0.7502 |
| Standard S Non-linearity | 0.851 | 0.851 | 2 | 0.6533 |
| Preparation T Non-linearity | 1.070 | 1.070 | 2 | 0.5856 |
| Treatments | 35.964 | 35.964 | 7 | 0.0000 |
| Residual | ||||
| Total | 35.964 | 7 | ||
| R-squared | 0.947 |
Potency
| Estimated Potency | Lower 95% | Upper 95% | DoF | |
|---|---|---|---|---|
| Preparation T | 1.1471 | 0.8640 | 1.5368 | 0 |
| Relative Potency | Lower 95% | Upper 95% | |
|---|---|---|---|
| Preparation T | 114.71% | 86.40% | 153.68% |
| Percent CI | Lower 95% | Upper 95% | |
|---|---|---|---|
| Preparation T | 100.00% | 75.32% | 133.97% |
| G | 0.1131 |
|---|---|
| C | 1.1275 |
Quantal Response Method
Valid Number of Cases: 8, 0 Omitted
Model selected: Gompit
Regression Results
| Coefficient | Standard Error | Z-Statistic | 2-Tail Probability | Lower 90% | Upper 90% | |
|---|---|---|---|---|---|---|
| Common Slope | 2.5897 | 0.4390 | 5.8988 | 0.0000 | 1.8676 | 3.3119 |
| Intercept Standard S | -2.7331 | 0.5077 | -5.3838 | 0.0000 | -3.5681 | -1.8981 |
| Intercept Preparation T | -2.4148 | 0.4926 | -4.9018 | 0.0000 | -3.2251 | -1.6045 |
| Residual Variance | 0.8846 |
|---|---|
| Degrees of Freedom | 5 |
Case (Diagnostic) Statistics
| Response | Subject | Dose | Preparation | Estimated Response | Residuals | Standardised Residuals | Probability | |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 12 | 1 | Standard S | 0.7554 | -0.7554 | -0.8031 | 0.0629 |
| 2 | 3 | 12 | 1.6 | Standard S | 2.3660 | 0.6340 | 0.6741 | 0.1972 |
| 3 | 6 | 12 | 2.5 | Standard S | 6.0265 | -0.0265 | -0.0282 | 0.5022 |
| 4 | 10 | 11 | 4 | Standard S | 9.9574 | 0.0426 | 0.0453 | 0.9052 |
| 5 | 0 | 11 | 1 | Preparation T | 0.6924 | -0.6924 | -0.7362 | 0.0629 |
| 6 | 4 | 12 | 1.6 | Preparation T | 2.3660 | 1.6340 | 1.7373 | 0.1972 |
| ** 7 | 8 | 11 | 2.5 | Preparation T | 5.5243 | 2.4757 | 2.6322 | 0.5022 |
| 8 | 10 | 11 | 4 | Preparation T | 9.9574 | 0.0426 | 0.0453 | 0.9052 |
Cases marked by ‘**’ are outliers at 2 x Standard Deviation.
Effective Dose
| Effective Dose | Lower 95% | Upper 95% | Trim Entered | Trim Used | |
|---|---|---|---|---|---|
| Standard S ED50 | 2.4939 | 2.0013 | 3.0379 | ||
| Spearman-Karber | 2.3391 | 1.8891 | 2.8961 | 0.00% | 9.09% |
| Preparation T ED50 | 2.2054 | 1.7528 | 2.6850 | ||
| Spearman-Karber | 1.9703 | 1.5878 | 2.4450 | 0.00% | 9.09% |
Weighted ANOVA
| Sum of Squares | Chi-Square | DoF | Probability | |
|---|---|---|---|---|
| Preparations | 0.074 | 0.074 | 1 | 0.7854 |
| Regression | 32.588 | 32.588 | 1 | 0.0000 |
| Non-parallelism | 0.168 | 0.168 | 1 | 0.6818 |
| Non-linearity | 3.560 | 3.560 | 4 | 0.4688 |
| Standard S Non-linearity | 0.935 | 0.935 | 2 | 0.6265 |
| Preparation T Non-linearity | 2.625 | 2.625 | 2 | 0.2692 |
| Treatments | 36.390 | 36.390 | 7 | 0.0000 |
| Residual | ||||
| Total | 36.390 | 7 | ||
| R-squared | 0.898 |
Potency
| Estimated Potency | Lower 95% | Upper 95% | DoF | |
|---|---|---|---|---|
| Preparation T | 1.1308 | 0.8479 | 1.5235 | 0 |
| Relative Potency | Lower 95% | Upper 95% | |
|---|---|---|---|
| Preparation T | 113.08% | 84.79% | 152.35% |
| Percent CI | Lower 95% | Upper 95% | |
|---|---|---|---|
| Preparation T | 100.00% | 74.98% | 134.73% |
| G | 0.1179 |
|---|---|
| C | 1.1336 |
Quantal Response Method
Valid Number of Cases: 8, 0 Omitted
Model selected: LogLog
Regression Results
| Coefficient | Standard Error | Z-Statistic | 2-Tail Probability | Lower 90% | Upper 90% | |
|---|---|---|---|---|---|---|
| Common Slope | 2.7740 | 0.5369 | 5.1670 | 0.0000 | 1.8909 | 3.6571 |
| Intercept Standard S | -1.8175 | 0.4346 | -4.1818 | 0.0000 | -2.5323 | -1.1026 |
| Intercept Preparation T | -1.4621 | 0.4035 | -3.6233 | 0.0003 | -2.1258 | -0.7983 |
| Residual Variance | 0.5492 |
|---|---|
| Degrees of Freedom | 5 |
Case (Diagnostic) Statistics
| Response | Subject | Dose | Preparation | Estimated Response | Residuals | Standardised Residuals | Probability | |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 12 | 1 | Standard S | 0.0254 | -0.0254 | -0.0343 | 0.0021 |
| 2 | 3 | 12 | 1.6 | Standard S | 2.2558 | 0.7442 | 1.0043 | 0.1880 |
| 3 | 6 | 12 | 2.5 | Standard S | 7.3909 | -1.3909 | -1.8769 | 0.6159 |
| 4 | 10 | 11 | 4 | Standard S | 9.6438 | 0.3562 | 0.4807 | 0.8767 |
| 5 | 0 | 11 | 1 | Preparation T | 0.0233 | -0.0233 | -0.0315 | 0.0021 |
| ** 6 | 4 | 12 | 1.6 | Preparation T | 2.2558 | 1.7442 | 2.3536 | 0.1880 |
| 7 | 8 | 11 | 2.5 | Preparation T | 6.7750 | 1.2250 | 1.6530 | 0.6159 |
| 8 | 10 | 11 | 4 | Preparation T | 9.6438 | 0.3562 | 0.4807 | 0.8767 |
Cases marked by ‘**’ are outliers at 2 x Standard Deviation.
Effective Dose
| Effective Dose | Lower 95% | Upper 95% | Trim Entered | Trim Used | |
|---|---|---|---|---|---|
| Standard S ED50 | 2.1975 | 1.8240 | 2.7530 | ||
| Spearman-Karber | 2.3391 | 1.8891 | 2.8961 | 0.00% | 9.09% |
| Preparation T ED50 | 1.9332 | 1.6008 | 2.4240 | ||
| Spearman-Karber | 1.9703 | 1.5878 | 2.4450 | 0.00% | 9.09% |
Weighted ANOVA
| Sum of Squares | Chi-Square | DoF | Probability | |
|---|---|---|---|---|
| Preparations | 0.001 | 0.001 | 1 | 0.9704 |
| Regression | 28.438 | 28.438 | 1 | 0.0000 |
| Non-parallelism | 0.142 | 0.142 | 1 | 0.7064 |
| Non-linearity | 1.168 | 1.168 | 4 | 0.8834 |
| Standard S Non-linearity | 1.040 | 1.040 | 2 | 0.5945 |
| Preparation T Non-linearity | 0.128 | 0.128 | 2 | 0.9381 |
| Treatments | 29.749 | 29.749 | 7 | 0.0001 |
| Residual | ||||
| Total | 29.749 | 7 | ||
| R-squared | 0.956 |
Potency
| Estimated Potency | Lower 95% | Upper 95% | DoF | |
|---|---|---|---|---|
| Preparation T | 1.1367 | 0.8574 | 1.5093 | 0 |
| Relative Potency | Lower 95% | Upper 95% | |
|---|---|---|---|
| Preparation T | 113.67% | 85.74% | 150.93% |
| Percent CI | Lower 95% | Upper 95% | |
|---|---|---|---|
| Preparation T | 100.00% | 75.43% | 132.78% |
| G | 0.1351 |
|---|---|
| C | 1.1562 |
