10.1. Parallel Line Method
Balanced, symmetric or unbalanced assays can be analysed. The analysis is based on a regression of the response variable against the natural logarithm of the dose variable. A separate line is fitted on each preparation, subject to a constraint that they should be parallel. An assay is said to be balanced when:
1) there is an equal number of cases in each treatment group,
2) there is an equal number of dose groups for each preparation and
3) successive dose levels are the same for all preparations.
An assay fulfilling the first two conditions but having different dose levels for different preparations (yet having the same ratio of successive dose levels) will be called symmetric. Assays not fulfilling one or more of these conditions will be called asymmetric or unbalanced.
For validity tests, the following Analysis of Variance (ANOVA) options are available:
1) Completely randomised design
2) Randomised block design
3) Latin squares design
4) Twin and triple crossover designs
The unbalanced assays can only be analysed using the Completely Randomised Design option. All other options require symmetric or balanced assays. In most cases, the program will detect whether an assay is unbalanced, symmetric or balanced and apply the relevant algorithm automatically.
The data sets to be analysed according to European Pharmacopoeia (19972017) Parallel Line Method should be balanced.
10.1.1. Parallel Line Variable Selection
Once the data is arranged as described above, select Bioassay → Parallel Line Method from UNISTAT menus. A Variable Selection Dialogue will pop up.
Data columns available for selection are listed on the left. Variables are referred to by their column numbers, which are prefixed by a single letter representing the type of data. For instance, in the above example C1, C2 and C4 are numeric columns, whereas L3 means that column three contains Long Strings. Columns containing Short Strings (up to 8 characters) are prefixed by (S). Other data types that will probably not be used in bioassays are date (D) and time (T). If Column Labels have been entered, they will also appear in the list next to the column numbers.
The frame Select Data Type (at the top) displays options for the type of Analysis of Variance to be performed. The number of variables to be selected is different for these types of analyses. When the second option Randomised Block Design is selected, four variables will need to be selected.
The third and fourth options Latin Squares Design and Crossover Design require selection of five variables.
After selecting the analysis type, you will need to assign tasks to variables by sending them to the boxes on the right. To do this, highlight the variable on the left list and click on the desired task button (i.e. one of the command buttons in the middle of the dialogue). Likewise, you can deselect an already selected variable by highlighting it on the right list first and then clicking its task button.
When all variables are selected, click the [Next] button to proceed to Output Options Dialogue.
10.1.2. Parallel Line Output Options
Output options that have further options under them (i.e. they have further dialogues and windows to display) then an [Opt] button is placed to the left of their check boxes. When you click [Finish] without clicking on an [Opt] button first, the program will generate output with the default values. If you want to change the default values, you can click on the [Opt] button to display the further dialogues for this particular output option. Then you can either obtain this particular output option on its own by clicking [Finish], or click [Back] to display the Output Options Dialogue again and output all selected options together.
[Opt] buttons on this dialogue will allow you to choose from four different types of Normality Tests, five Homogeneity of Variance Tests, enter assigned potencies for test preparations and edit the plot of treatment means in UNISTAT’s Graphics Editor.
Data
This output option (which is available for all four bioassay analysis methods supported here) will enable the user to include a printout of the data used in the analysis as part of the output. This may be useful in fulfilling reporting and data integrity requirements.
Data
Preparations 
Response 
Dose 
Standard S 
300.0000 
0.2500 
Standard S 
310.0000 
0.2500 
Standard S 
330.0000 
0.2500 
Standard S 
289.0000 
1.0000 
Standard S 
221.0000 
1.0000 
Standard S 
267.0000 
1.0000 
Preparation T 
310.0000 
0.2500 
Preparation T 
290.0000 
0.2500 
Preparation T 
360.0000 
0.2500 
Preparation T 
230.0000 
1.0000 
Preparation T 
210.0000 
1.0000 
Preparation T 
280.0000 
1.0000 
Preparation U 
250.0000 
0.2500 
Preparation U 
268.0000 
0.2500 
Preparation U 
273.0000 
0.2500 
Preparation U 
236.0000 
1.0000 
Preparation U 
213.0000 
1.0000 
Preparation U 
283.0000 
1.0000 
10.1.2.1. Normality Tests for Bioassays
One of the basic assumptions of Parallel Line Method is that for each treatment group (i.e. a unique dosepreparation combination), observations are normally distributed.
If you still wish to use the classic ShapiroWilk (1965) and its accompanying overall normality tests as in earlier version of UNISTAT, then you can do so by entering the following line in Documents\Unistat10\Unistat10.ini file under the [Options] section:
OverallNormality=1
In classic ShapiroWilk test, observations are arranged in ascending order for each treatment group and then the following sum is found:
The test statistic for each sample is:
where S2 is the sum of squared differences from the mean, and a_{i} i = 1, …, k are the coefficients given by the authors.
If all sample sizes are between 7 and 20 (inclusive), an overall test of normality, which is based on the normal distribution, is also performed according to Shapiro & Wilk (1968).
First, the following ratio is calculated for each sample:
and:
where a, q and m are the coefficients for k degrees of freedom given by the authors in Shapiro & Wilk (1968).
The test statistic is defined as:
with a 1tail probability from the normal distribution.
10.1.2.2. Homogeneity of Variance Tests
Another basic assumption of Parallel Line Method is that variances for different treatment groups are not significantly different from each other.
Earlier versions of UNISTAT featured Bartlett’s chisquare test as recommended by European Pharmacopoeia (19972017), and Hartley’s F test. Here we provide three more homogeneity of variance tests. The computationally demanding Levene’s test is considered to be more powerful than other homogeneity of variance tests. For a detailed description of these tests see 7.4.2.1. Homogeneity of Variance Test Results.
10.1.2.3. Response Totals and Contrasts
These are the intermediate values calculated directly from raw data and they are used in computing all output statistics. Here we report these values in order to help the user with validating the final results.
First d (number of doses) rows of the table report the sums of all cases in each treatment group. Let:
represent the sum of cases for the j^{th} dose and the i^{th} preparation in the table.
The next row Total is the sum of these values over dose for each preparation:
The contrasts are then calculated for each preparation (i = 1, … , h) as follows:
No of doses 
Linear Contrast (L_{i}) 
Quadratic Contrast (Q_{i}) 
Cubic Contrast (J_{i}) 
2 
S_{2i} – S_{1I} 


3 
S_{3i} – S_{1i} 
S_{1i} – 2S_{2i} + S_{3i} 

4 
3S_{4i} + S_{3i} – S_{2i} – 3S_{1i} 
S_{1i} – S_{2i} – S_{3i} + S_{3i} 
3S_{2i} – S_{1i} – S_{4i} – 3S_{3I} 
10.1.2.4. Validity of Assay
This output option displays an Analysis of Variance (ANOVA) table, which is used to test the Validity of Assay. Also, the residual sum of squares and its degrees of freedom are used in estimating the confidence limits for the Potency (see 10.1.2.7. Potency). The three basic tests performed are (i) significance of regression, (ii) parallelism and (iii) linearity. The table may have different entries in its rows depending on the number of doses and / or the ANOVA model employed.
The notation below is for balanced designs as given by European Pharmacopoeia (19972017). For unbalanced designs, the only difference is that the sums are taken up to the maximum number of observation in each treatment group. See 10.2. Slope Ratio Method, section Validity of Assay for a general unbalanced formulation.
Let us first define the three key entries of all ANOVA tables, namely, the Constant term:
which is the sum total of all cases divided by the total number of treatment groups, the Treatments term:
which is the sum of all squared treatment totals minus the constant term, and the Total term:
which is the sum of all squared cases minus the constant term. The rest of table entries are defined as follows:

Degrees of Freedom 
2dose 
3dose 
4dose 
Preparations 
h – 1 



Linear Regression 
1 



Nonparallelism 
h – 1 



Nonlinearity 
h for 3dose 2h for 4dose 



Quadratic Regression 
1 



Difference of Quadratics 
h – 1 



Residual 
h 



Treatments 
k – 1 
M 
M 
M 
Residual 

R 
R 
R 
Total 
nk – 1 
T 
T 
T 
The following relationships should always be true:
1) Degrees of freedom and sum of squares for the first four rows (i.e. Preparations, Linear Regression, Nonparallelism and Nonlinearity) should always add up to Treatments,
2) Quadratic Regression, Difference of Quadratics and their Residuals should always add up to Nonlinearity,
3) Treatments and their Residuals should always add up to Total.
10.1.2.5. Regression
10.1.2.6. Comparison of Slopes
If an assay with two or more test preparations is found to depart from parallelism significantly, then we ask the question which test preparation’s slope differs from the slope of the standard preparation. A Dunnett’s multiple comparison test is performed to answer this question.
European Pharmacopoeia (19972017) employs a slightly different algorithm, which is based on linear contrasts as a proxy for the slopes. The two approaches are identical and produce the same probability values. Although we report here the slopes test by default, the linear contrast test output can be displayed instead by entering the following line in Documents\Unistat10\Unistat10.ini file under the [Bioassay] section:
ParalEuroPharma=1
L_{1} is the linear contrast for the standard preparation,
L_{i} is the linear contrast for the i^{th} test preparation and
s^{2} is the residual mean square value from the ANOVA table (i.e. sum of squares for the overall residual term divided by its degrees of freedom)
The twotailed probability for the test statistic is generated using an algorithm developed by Charles Dunnett for α significance level, (h – 1) number of groups. The degrees of freedom is equal to that of the overall residual term of the ANOVA table.
10.1.2.7. Potency
By default, the program estimates the potency ratio and its confidence limits employing the generalised algorithm given in Finney (1978), which works with unbalanced, symmetric and balanced designs. Alternatively, the more restrictive algorithm for balanced assays (see European Pharmacopoeia 19972017) can be employed by entering the following line in Documents\Unistat10\Unistat10.ini file under the [Bioassay] section:
ParalEuroPharma=1
The logarithm of potency ratio is estimated for each test preparation, using the Common Regression slope b.
and:
where:
are the preparation means and A_{i} is the assumed potency of each test preparation. The estimated potency is the antilog of M, Exp(M).
The method of estimating the confidence interval for potency is based on Fieller’s Theorem (see Finney 1978, p. 80). Let us first define the correction factor g as:
The log of confidence limits for the potency ratio of each test preparation is defined as:
where the variance of M_{i} is:
Weights are computed after the estimated potency and its confidence interval are found:
and % Precision is:
According to European Pharmacopoeia (1997) the common slope b is calculated as:
Where:
Z = Log(dose_{i+1}) – Log(dose_{i}), i = 2, … , d
is the log of successive dose ratios. Also define a correction factor:
The log of the corrected potency estimate and its confidence intervals are computed as:
where:
The only difference from the default output here is reporting of C and H constants for validation purposes, where C = 1 / (1 – g).
If the data column [Dose] contains the actual dose levels administered in original dose units, we will obtain the estimated potency and its confidence limits in the same units. If, however, the [Dose] column contains unitless relative dose levels, then we may need to perform further calculations to obtain the estimated potency in original units. To do that you can enter assigned potency of the standard, assumed potency of each test preparation and predilutions for all preparations including the standard in a data column and select it as [Dilution] variable. UNISTAT will then calculate the estimated potency as described in section 10.0.2. Doses, Dilutions and Potency. Also see section 10.0.3. Potency Calculation Example.
10.1.2.8. Plot of Treatment Means
This option generates a Plot of Treatment Means against the log of dose. It provides a visual means of inspecting the data, enabling the user to notice immediately whether there is something substantially wrong with the data.
Clicking the [Opt] button situated to the left of the Plot of Treatment Means option will place the graph in UNISTAT’s Graphics Editor. Each preparation will be plotted as one data series, with as many points as the number of doses applied. A line of best fit will be drawn for each series, including the standard and all test preparations.
The plot can be further customised and annotated using the tools available under UNISTAT Graphics Window’s Edit menu.
10.1.3. Parallel Line Examples
The following Parallel Line Method examples are based on different Analysis of Variance methods. The data sets were entered into UNISTAT’s spreadsheet and the necessary data manipulations made by using UNISTAT spreadsheet functions (see 10.0.1. Data Preparation and 10.0.2. Doses, Dilutions and Potency). The final data sets were saved in two files; BIOPHARMA6 which contains examples from European Pharmacopoeia (2008, the 6^{th} edition) and BIOFINNEY containing examples from Finney (1978).
10.1.3.1. Completely Randomised Design with 2 Doses and 3 Preparations
Data is given in Table 5.1.1I. on p. 582 of European Pharmacopoeia (2008).
Open BIOPHARMA6 and select Bioassay → Parallel Line Method. From the Variable Selection Dialogue select the first option Completely Randomised Design and then select columns C1, C2 and L3 respectively as [Data], [Dose] and [Preparation]. Click [Next] to proceed to Output Options Dialogue. Click [All] to perform all tests in one go and click [Finish]. The following output is obtained:
Parallel Line Method
Completely Randomised Design
Normality Tests
Smaller probabilities indicate nonnormality.
* Lilliefors probability = 0.2 means 0.2 or greater.
DosexPreparations 
Valid Cases 
Mean 
Standard Deviation 
0.25 x Standard S 
10 
332.0000 
32.0416 
0.25 x Preparation T 
10 
323.9000 
26.9256 
0.25 x Preparation U 
10 
282.2000 
29.2339 
1 x Standard S 
10 
248.4000 
21.9960 
1 x Preparation T 
10 
244.0000 
26.8080 
1 x Preparation U 
10 
250.0000 
28.0119 
DosexPreparations 
ShapiroWilk Test 
Probability 
KolmogorovSmirnov Test 
* Probability 
0.25 x Standard S 
0.9565 
0.7451 
0.1538 
0.2000 
0.25 x Preparation T 
0.9471 
0.6348 
0.1429 
0.2000 
0.25 x Preparation U 
0.8940 
0.1878 
0.2235 
0.1639 
1 x Standard S 
0.9302 
0.4494 
0.2135 
0.2000 
1 x Preparation T 
0.9475 
0.6390 
0.1446 
0.2000 
1 x Preparation U 
0.9515 
0.6864 
0.1324 
0.2000 
DosexPreparations 
Cramervon Mises Test 
Probability 
AndersonDarling Test 
Probability 
0.25 x Standard S 
0.0331 
0.7759 
0.2218 
0.7658 
0.25 x Preparation T 
0.0333 
0.7721 
0.2311 
0.7326 
0.25 x Preparation U 
0.0895 
0.1360 
0.5030 
0.1549 
1 x Standard S 
0.0579 
0.3692 
0.3494 
0.3962 
1 x Preparation T 
0.0341 
0.7582 
0.2337 
0.7232 
1 x Preparation U 
0.0278 
0.8580 
0.2055 
0.8201 
Homogeneity of Variance Tests

Test Statistic 
Probability 

Bartlett’s Chisquare Test 
1.2810 
0.9369 

BartlettBox F Test 
0.2575 
0.9362 

Cochran’s C (max var / sum var) 
0.2235 
1.0000 

Hartley’s F (max var / min var) 
2.1220 
0.0500 
p > 0.05 
Levene’s F Test 
0.3738 
0.8644 

Response Totals and Contrasts
Dose 
Standard S 
Preparation T 
Preparation U 
Total 
0.25 
3320.0000 
3239.0000 
2822.0000 

1 
2484.0000 
2440.0000 
2500.0000 

Total 
5804.0000 
5679.0000 
5322.0000 
16805.0000 
Linear Contrast 
836.0000 
799.0000 
322.0000 
1957.0000 
Validity of Assay
Due To 
Sum of Squares 
DoF 
Mean Square 
FStat 
Prob 
Constant 
4706800.417 
1 
4706800.417 


Preparations 
6256.633 
2 
3128.317 
4.086 
0.0223 
Linear Regression 
63830.817 
1 
63830.817 
83.377 
0.0000 
Nonparallelism 
8218.233 
2 
4109.117 
5.367 
0.0075 
Treatments 
78305.683 
5 
15661.137 


Residual 
41340.900 
54 
765.572 


Total 
119646.583 
59 
2027.908 


Separate Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard S 
248.4000 
60.3047 
13594.4000 
0.7199 
Preparation T 
244.0000 
57.6357 
12992.9000 
0.7107 
Preparation U 
250.0000 
23.2274 
14753.6000 
0.2600 
Common Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard S 
257.5833 
47.0559 
49559.1333 
0.5629 
Preparation T 
251.3333 



Preparation U 
233.4833 



Comparison of Slopes
Comparison 
Difference 
Standard Error 
q Stat 
Table q 
Preparation U – Standard S 
37.0773 
12.6231 
2.9372 
2.2713 
Preparation T – Standard S 
2.6690 
12.6231 
0.2114 
2.2713 
Comparison 
Probability 
Lower 95% 
Upper 95% 
Result 
Preparation U – Standard S 
0.0093 
8.4061 
65.7484 
** 
Preparation T – Standard S 
0.9678 
26.0022 
31.3401 

Potency

Estimated Potency 
Lower 95% 
Upper 95% 
Preparation T 
1.1420 
0.7836 
1.6869 
Preparation U 
1.6689 
1.1481 
2.5550 
G = 
0.0482 
C = 
1.0507 
Looking at the plot of treatment means we can see that Preparation U line is not parallel to Standard S and Preparation T lines. This can also be picked up from the nonparallelism test in Validity of Assay (0.0075), which is significant at 5% level. The Comparison of Slopes test also reports a significant difference between Preparation U and Standard S slopes.
This assay can still be useful by omitting Preparation U and performing the analysis for Standard S and Preparation U. In Excel AddIn Mode, you can simply select the block A1:C41 and repeat the analysis. In StandAlone Mode, you can define a Select Row column to omit these rows from the analysis, without actually deleting them from the spreadsheet. To do this, click somewhere on column 4, and select Data → Select Row option from UNISTAT’s spreadsheet menus. The colour of C4 will change. This indicates that all rows with a 0 entry in this column will be omitted from the subsequent analyses.
When the analysis is repeated without Preparation U, the following results are obtained:
Parallel Line Method
Rows 4160 Omitted
Selected by C4 Select
Completely Randomised Design
Normality Tests
Smaller probabilities indicate nonnormality.
* Lilliefors probability = 0.2 means 0.2 or greater.
DosexPreparations 
Valid Cases 
Mean 
Standard Deviation 
0.25 x Standard S 
10 
332.0000 
32.0416 
0.25 x Preparation T 
10 
323.9000 
26.9256 
1 x Standard S 
10 
248.4000 
21.9960 
1 x Preparation T 
10 
244.0000 
26.8080 
DosexPreparations 
ShapiroWilk Test 
Probability 
KolmogorovSmirnov Test 
* Probability 
0.25 x Standard S 
0.9565 
0.7451 
0.1538 
0.2000 
0.25 x Preparation T 
0.9471 
0.6348 
0.1429 
0.2000 
1 x Standard S 
0.9302 
0.4494 
0.2135 
0.2000 
1 x Preparation T 
0.9475 
0.6390 
0.1446 
0.2000 
DosexPreparations 
Cramervon Mises Test 
Probability 
AndersonDarling Test 
Probability 
0.25 x Standard S 
0.0331 
0.7759 
0.2218 
0.7658 
0.25 x Preparation T 
0.0333 
0.7721 
0.2311 
0.7326 
1 x Standard S 
0.0579 
0.3692 
0.3494 
0.3962 
1 x Preparation T 
0.0341 
0.7582 
0.2337 
0.7232 
Homogeneity of Variance Tests

Test Statistic 
Probability 

Bartlett’s Chisquare Test 
1.1985 
0.7534 

BartlettBox F Test 
0.4029 
0.7509 

Cochran’s C (max var / sum var) 
0.3475 
0.6641 

Hartley’s F (max var / min var) 
2.1220 
0.0500 
p > 0.05 
Levene’s F Test 
0.4381 
0.7271 

Response Totals and Contrasts
Dose 
Standard S 
Preparation T 
Total 
0.25 
3320.0000 
3239.0000 

1 
2484.0000 
2440.0000 

Total 
5804.0000 
5679.0000 
11483.0000 
Linear Contrast 
836.0000 
799.0000 
1635.0000 
Validity of Assay
Due To 
Sum of Squares 
DoF 
Mean Square 
FStat 
Prob 
Constant 
3296482.225 
1 
3296482.225 


Preparations 
390.625 
1 
390.625 
0.529 
0.4718 
Linear Regression 
66830.625 
1 
66830.625 
90.491 
0.0000 
Nonparallelism 
34.225 
1 
34.225 
0.046 
0.8308 
Treatments 
67255.475 
3 
22418.492 


Residual 
26587.300 
36 
738.536 


Total 
93842.775 
39 
2406.225 


Separate Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard S 
248.4000 
60.3047 
13594.4000 
0.7199 
Preparation T 
244.0000 
57.6357 
12992.9000 
0.7107 
Common Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard S 
249.3250 
58.9702 
26621.5250 
0.7151 
Preparation T 
243.0750 



Comparison of Slopes
Comparison 
Difference 
Standard Error 
q Stat 
Table q 
Preparation T – Standard S 
2.6690 
12.3983 
0.2153 
2.0281 
Comparison 
Probability 
Lower 95% 
Upper 95% 
Result 
Preparation T – Standard S 
0.8308 
22.4759 
27.8138 

Potency

Estimated Potency 
Lower 95% 
Upper 95% 
Preparation T 
1.1118 
0.8250 
1.5136 
G = 
0.0455 
C = 
1.0476 
In StandAlone Mode, do not forget to reset column 4, otherwise the Select Row function will be effective in subsequent procedures you run. To do this, click somewhere on column 4, and select Data → Select Row option again, or select Formula → Quick Formula from the menu and enter data. The colour of C4 will change back to its original value.
10.1.3.2. Completely Randomised Design with 5 Doses and 4 Preparations
Data is given in Table 5.1.4I. on p. 585 of European Pharmacopoeia (2008).
Open BIOPHARMA6 and select Bioassay → Parallel Line Method. From the Variable Selection Dialogue select the first option Completely Randomised Design and then select columns C15, C16 and L17 respectively as [Data], [Dose] and [Preparation]. Click [Next] to proceed to Output Options Dialogue. If you do not want to display all normality tests click on the [Opt] button situated to the left of Normality Tests option. Click [None] and then check the AndersonDarling Test and Report summary statistics boxes. Then click [Back] and [Finish] to display the following output:
Parallel Line Method
Completely Randomised Design
Normality Tests
Smaller probabilities indicate nonnormality.
DosexPreparations 
Valid Cases 
Mean 
Standard Deviation 
AndersonDarling Test 
Probability 
0.0625 x Standard S 
3 
3.0745 
0.0884 
0.2663 
0.3634 
0.125 x Standard S 
3 
2.3963 
0.0960 
0.2303 
0.4841 
0.25 x Standard S 
3 
1.8351 
0.0377 
0.1976 
0.5929 
0.5 x Standard S 
3 
1.1664 
0.1318 
0.3365 
0.2031 
1 x Standard S 
3 
0.6352 
0.0293 
0.1941 
0.6090 
0.0625 x Preparation T 
3 
2.3435 
0.0181 
0.4878 
0.0565 
0.125 x Preparation T 
3 
1.7891 
0.0628 
0.1896 
0.6303 
0.25 x Preparation T 
3 
1.0725 
0.0417 
0.2231 
0.5077 
0.5 x Preparation T 
3 
0.5503 
0.1416 
0.1896 
0.6304 
1 x Preparation T 
3 
0.1691 
0.1422 
0.2501 
0.4141 
0.0625 x Preparation U 
3 
2.5719 
0.1036 
0.3560 
0.1719 
0.125 x Preparation U 
3 
2.0017 
0.0710 
0.2307 
0.4827 
0.25 x Preparation U 
3 
1.3045 
0.0181 
0.3835 
0.1353 
0.5 x Preparation U 
3 
0.6183 
0.0912 
0.2070 
0.5544 
1 x Preparation U 
3 
0.0480 
0.0940 
0.1910 
0.6236 
0.0625 x Preparation V 
3 
2.4852 
0.0275 
0.4878 
0.0565 
0.125 x Preparation V 
3 
1.8745 
0.1040 
0.4518 
0.0768 
0.25 x Preparation V 
3 
1.1606 
0.0206 
0.3403 
0.1967 
0.5 x Preparation V 
3 
0.5539 
0.0713 
0.4738 
0.0637 
1 x Preparation V 
3 
0.0468 
0.0165 
0.4238 
0.0975 
Homogeneity of Variance Tests

Test Statistic 
Probability 
Bartlett’s Chisquare Test 
25.6778 
0.1394 
BartlettBox F Test 
1.3733 
0.1319 
Cochran’s C (max var / sum var) 
0.1514 
0.8834 
Hartley’s F (max var / min var) 
74.4176 

Levene’s F Test 
2.1145 
0.0230 
Response Totals and Contrasts
Dose 
Standard S 
Preparation T 
Preparation U 
Preparation V 
Total 
0.0625 
9.2236 




0.125 
7.1888 




0.25 
5.5054 




0.5 
3.4992 




1 
1.9055 




0.0625 

7.0305 



0.125 

5.3672 



0.25 

3.2176 



0.5 

1.6508 



1 

0.5072 



0.0625 


7.7158 


0.125 


6.0051 


0.25 


3.9135 


0.5 


1.8550 


1 


0.1439 


0.0625 



7.4555 

0.125 



5.6234 

0.25 



3.4819 

0.5 



1.6618 

1 



0.1404 

Total 
27.3225 
16.7590 
19.6333 
18.0822 
81.7970 
Validity of Assay
Due To 
Sum of Squares 
DoF 
Mean Square 
FStat 
Prob 
Constant 
111.513 
1 
111.513 


Preparations 
4.475 
3 
1.492 
223.395 
0.0000 
Linear Regression 
47.584 
1 
47.584 
7125.912 
0.0000 
Nonparallelism 
0.019 
3 
0.006 
0.933 
0.4339 
Nonlinearity 
0.074 
12 
0.006 
0.926 
0.5307 
Treatments 
52.152 
19 
2.745 


Residual 
0.267 
40 
0.007 


Total 
52.419 
59 
0.888 


Separate Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard S 
0.5998 
0.8813 
0.0904 
0.9920 
Preparation T 
0.1355 
0.9037 
0.1208 
0.9898 
Preparation U 
0.0226 
0.9278 
0.0843 
0.9933 
Preparation V 
0.0714 
0.9211 
0.0459 
0.9963 
Common Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard S 
0.5621 
0.9085 
0.3600 
0.9925 
Preparation T 
0.1422 



Preparation U 
0.0495 



Preparation V 
0.0539 



Comparison of Slopes
Comparison 
Difference 
Standard Error 
q Stat 
Table q 
Preparation U – Standard S 
0.0466 
0.0304 
1.5296 
2.4415 
Preparation V – Standard S 
0.0398 
0.0304 
1.3074 
2.4415 
Preparation T – Standard S 
0.0224 
0.0304 
0.7365 
2.4415 
Comparison 
Probability 
Lower 95% 
Upper 95% 
Result 
Preparation U – Standard S 
0.3036 
0.0278 
0.1209 

Preparation V – Standard S 
0.4262 
0.0345 
0.1141 

Preparation T – Standard S 
0.8033 
0.0519 
0.0967 

Potency

Estimated Potency 
Lower 95% 
Upper 95% 
Preparation T 
2.1710 
2.0272 
2.3270 
Preparation U 
1.7581 
1.6435 
1.8820 
Preparation V 
1.9701 
1.8406 
2.1103 
G = 
0.0006 
C = 
1.0006 
All test preparations have an assumed potency of 20 μg protein/ml. Create a new column of data as follows and select it as [Dilution] variable.
1
1
20 μg protein/ml
1
20 μg protein/ml
1
20 μg protein/ml
For further information see section 10.0.2. Doses, Dilutions and Potency.
Parallel Line Method
Potency
Assumed potency of Preparation T: 20 Ö§ protein/ml
Assumed potency of Preparation U: 20 Ö§ protein/ml
Assumed potency of Preparation V: 20 Ö§ protein/ml

Estimated Potency 
Lower 95% 
Upper 95% 
Preparation T 
43.4197 
40.5448 
46.5397 
Preparation U 
35.1628 
32.8697 
37.6403 
Preparation V 
39.4018 
36.8126 
42.2058 
G = 
0.0006 
C = 
1.0006 
10.1.3.3. Randomised Block Design with 4 Doses and 2 Preparations
Data is given in Table 5.1.3.I on p. 585 of European Pharmacopoeia (2008).
Open BIOPHARMA6 and select Bioassay → Parallel Line Method. From the Variable Selection Dialogue select the second option Randomised Block Design and the select columns C10, C11, L12 and C13 respectively as [Data], [Dose], [Preparation] and [Row Factor]. Click [Next] to proceed to the Output Options Dialogue.
Parallel Line Method
Randomised Block Design
Normality Tests
Smaller probabilities indicate nonnormality.
* Lilliefors probability = 0.2 means 0.2 or greater.
DosexPreparations 
Valid Cases 
Mean 
Standard Deviation 
1 x Standard S 
5 
246.6000 
6.7305 
1 x Preparation T 
5 
237.4000 
6.4653 
1.5 x Standard S 
5 
203.0000 
6.1644 
1.5 x Preparation T 
5 
195.4000 
7.5033 
2.25 x Standard S 
5 
162.4000 
17.2714 
2.25 x Preparation T 
5 
150.4000 
5.5946 
3.375 x Standard S 
5 
107.4000 
5.7706 
3.375 x Preparation T 
5 
104.4000 
7.2319 
DosexPreparations 
ShapiroWilk Test 
Probability 
KolmogorovSmirnov Test 
* Probability 
1 x Standard S 
0.7977 
0.0777 
0.3237 
0.0942 
1 x Preparation T 
0.9171 
0.5116 
0.1982 
0.2000 
1.5 x Standard S 
0.7607 
0.0373 
0.3418 
0.0568 
1.5 x Preparation T 
0.9649 
0.8416 
0.2156 
0.2000 
2.25 x Standard S 
0.9904 
0.9809 
0.1729 
0.2000 
2.25 x Preparation T 
0.8523 
0.2018 
0.2660 
0.2000 
3.375 x Standard S 
0.8977 
0.3974 
0.2724 
0.2000 
3.375 x Preparation T 
0.9718 
0.8866 
0.2125 
0.2000 
DosexPreparations 
Cramervon Mises Test 
Probability 
AndersonDarling Test 
Probability 
1 x Standard S 
0.1018 
0.0770 
0.5636 
0.0681 
1 x Preparation T 
0.0413 
0.5834 
0.2658 
0.5150 
1.5 x Standard S 
0.1095 
0.0592 
0.6235 
0.0447 
1.5 x Preparation T 
0.0381 
0.6470 
0.2243 
0.6507 
2.25 x Standard S 
0.0238 
0.8949 
0.1660 
0.8710 
2.25 x Preparation T 
0.0666 
0.2535 
0.4027 
0.2095 
3.375 x Standard S 
0.0559 
0.3616 
0.3395 
0.3235 
3.375 x Preparation T 
0.0355 
0.6990 
0.2191 
0.6722 
Homogeneity of Variance Tests

Test Statistic 
Probability 

Bartlett’s Chisquare Test 
9.7854 
0.2011 

BartlettBox F Test 
1.4146 
0.1953 

Cochran’s C (max var / sum var) 
0.5000 
0.0039 

Hartley’s F (max var / min var) 
9.5304 
0.0500 
p > 0.05 
Levene’s F Test 
1.3017 
0.2813 

Response Totals and Contrasts
Dose 
Standard S 
Preparation T 
Total 
1 
1233.0000 
1187.0000 

1.5 
1015.0000 
977.0000 

2.25 
812.0000 
752.0000 

3.375 
537.0000 
522.0000 

Total 
3597.0000 
3438.0000 
7035.0000 
Linear Contrast 
2291.0000 
2220.0000 
4511.0000 
Quadratic Contrast 
57.0000 
20.0000 
77.0000 
Cubic Contrast 
87.0000 
10.0000 
77.0000 
Validity of Assay
Due To 
Sum of Squares 
DoF 
Mean Square 
FStat 
Prob 
Constant 
1237280.625 
1 
1237280.625 


Preparations 
632.025 
1 
632.025 
11.722 
0.0019 
Linear Regression 
101745.605 
1 
101745.605 
1887.111 
0.0000 
Nonparallelism 
25.205 
1 
25.205 
0.467 
0.4998 
Nonlinearity 
259.140 
4 
64.785 
1.202 
0.3321 
Quadratic Regression 
148.225 
1 
148.225 
2.749 
0.1085 
Quadratic Difference 
34.225 
1 
34.225 
0.635 
0.4323 
Residual 
76.690 
2 
38.345 


Treatments 
102661.975 
7 
14665.996 


Blocks(Rows) 
876.750 
4 
219.188 
4.065 
0.0101 
Residual 
1509.650 
28 
53.916 


Total 
105048.375 
39 
2693.548 


Separate Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard S 
248.5800 
113.0060 
1897.7400 
0.9651 
Preparation T 
238.5000 
109.5039 
747.8000 
0.9851 
Common Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard S 
247.5150 
111.2549 
2670.7450 
0.9744 
Preparation T 
239.5650 



Comparison of Slopes
Comparison 
Difference 
Standard Error 
q Stat 
Table q 
Preparation T – Standard S 
3.5022 
5.1221 
0.6837 
2.0484 
Comparison 
Probability 
Lower 95% 
Upper 95% 
Result 
Preparation T – Standard S 
0.4998 
6.9901 
13.9944 

Potency

Estimated Potency 
Lower 95% 
Upper 95% 
Preparation T 
1.0741 
1.0291 
1.1214 
G = 
0.0022 
C = 
1.0022 
Standard S has an assigned potency of 670 IU / mg, reconstitution of 16.7 mg / 25 ml and predilution of 1 ml / 40 ml. Sample 1 has a an assumed potency of 20,000 IU / vial, reconstitution of 1 vial / 40 ml and predilution of 1 ml / 40 ml. Create a new column of data as follows and select it as [Dilution] variable.
670 IU/mg
16.7 mg / 25 ml; 1 ml / 40 ml
20000 IU/vial
1 vial / 40 ml; 1 ml / 40 ml
For further information see section 10.0.2. Doses, Dilutions and Potency.
Parallel Line Method
Potency
Assigned potency of Standard S: 670 IU/mg
Predilution of Standard S: 16.7 mg / 25 ml; 1 ml / 40 ml
Assumed potency of Preparation T: 20000 IU/vial
Predilution of Preparation T: 1 vial / 40 ml; 1 ml / 40 ml

Estimated Potency 
Lower 95% 
Upper 95% 
Preparation T 
19228.4755 
18423.3508 
20075.1776 
G = 
0.0022 
C = 
1.0022 
10.1.3.4. Latin Squares Design with 3 Doses and 2 Preparations
Data is given in Table 5.1.2.II on p. 584 of European Pharmacopoeia (2008).
The entry and transformation of this data set is more complicated than the two previous examples. In order to assign the correct dose levels and preparation groups, information given in Table 5.1.2.I is essential. Ensure that the way the factor columns are created is understood well.
Open BIOPHARMA6 and select Bioassay → Parallel Line Method. From the Variable Selection Dialogue select the third option Latin Squares Design and then select columns C5, C6, L7, C8 and C9 respectively as [Data], [Dose], [Preparation], [Row Factor] and [Column Factor]. Click [Next] to proceed to Output Options Dialogue.
Parallel Line Method
Latin Squares Design
Normality Tests
Smaller probabilities indicate nonnormality.
* Lilliefors probability = 0.2 means 0.2 or greater.
DosexPreparations 
Valid Cases 
Mean 
Standard Deviation 
1 x Standard S 
6 
158.6667 
6.5929 
1 x Preparation T 
6 
156.1667 
4.7081 
1.5 x Standard S 
6 
176.5000 
5.3572 
1.5 x Preparation T 
6 
174.6667 
8.6641 
2.25 x Standard S 
6 
194.5000 
4.8477 
2.25 x Preparation T 
6 
195.5000 
4.0373 
DosexPreparations 
ShapiroWilk Test 
Probability 
KolmogorovSmirnov Test 
* Probability 
1 x Standard S 
0.8581 
0.1827 
0.3050 
0.0851 
1 x Preparation T 
0.8118 
0.0749 
0.2922 
0.1177 
1.5 x Standard S 
0.8965 
0.3536 
0.2038 
0.2000 
1.5 x Preparation T 
0.9757 
0.9284 
0.1639 
0.2000 
2.25 x Standard S 
0.9879 
0.9835 
0.1364 
0.2000 
2.25 x Preparation T 
0.8255 
0.0984 
0.3115 
0.0703 
DosexPreparations 
Cramervon Mises Test 
Probability 
AndersonDarling Test 
Probability 
1 x Standard S 
0.0849 
0.1450 
0.4756 
0.1438 
1 x Preparation T 
0.0886 
0.1276 
0.5470 
0.0901 
1.5 x Standard S 
0.0544 
0.3902 
0.3341 
0.3689 
1.5 x Preparation T 
0.0274 
0.8514 
0.1760 
0.8637 
2.25 x Standard S 
0.0210 
0.9388 
0.1514 
0.9165 
2.25 x Preparation T 
0.1046 
0.0740 
0.5613 
0.0818 
Homogeneity of Variance Tests

Test Statistic 
Probability 

Bartlett’s Chisquare Test 
3.7817 
0.5813 

BartlettBox F Test 
0.7637 
0.5760 

Cochran’s C (max var / sum var) 
0.3588 
0.2313 

Hartley’s F (max var / min var) 
4.6053 
0.0500 
p > 0.05 
Levene’s F Test 
1.5818 
0.1954 

Response Totals and Contrasts
Dose 
Standard S 
Preparation T 
Total 
1 
952.0000 
937.0000 

1.5 
1059.0000 
1048.0000 

2.25 
1167.0000 
1173.0000 

Total 
3178.0000 
3158.0000 
6336.0000 
Linear Contrast 
215.0000 
236.0000 
451.0000 
Quadratic Contrast 
1.0000 
14.0000 
15.0000 
Validity of Assay
Due To 
Sum of Squares 
DoF 
Mean Square 
FStat 
Prob 
Constant 
1115136.000 
1 
1115136.000 


Preparations 
11.111 
1 
11.111 
0.535 
0.4730 
Linear Regression 
8475.042 
1 
8475.042 
408.108 
0.0000 
Nonparallelism 
18.375 
1 
18.375 
0.885 
0.3581 
Nonlinearity 
5.472 
2 
2.736 
0.132 
0.8773 
Quadratic Regression 
3.125 
1 
3.125 
0.150 
0.7022 
Quadratic Difference 
2.347 
1 
2.347 
0.113 
0.7402 
Treatments 
8510.000 
5 
1702.000 


Blocks(Rows) 
412.000 
5 
82.400 
3.968 
0.0116 
Blocks(Columns) 
218.667 
5 
43.733 
2.106 
0.1069 
Residual 
415.333 
20 
20.767 


Total 
9556.000 
35 
273.029 


Separate Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard S 
158.6389 
44.1879 
478.3611 
0.8895 
Preparation T 
155.7778 
48.5040 
573.1111 
0.8901 
Common Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard S 
157.7639 
46.3460 
1069.8472 
0.8879 
Preparation T 
156.6528 



Comparison of Slopes
Comparison 
Difference 
Standard Error 
q Stat 
Table q 
Preparation T – Standard S 
4.3160 
4.5883 
0.9407 
2.0860 
Comparison 
Probability 
Lower 95% 
Upper 95% 
Result 
Preparation T – Standard S 
0.3581 
5.2551 
13.8871 

Potency

Estimated Potency 
Lower 95% 
Upper 95% 
Preparation T 
0.9763 
0.9112 
1.0456 
G = 
0.0107 
C = 
1.0108 
Standard S has an assigned potency of 4855 IU/mg and reconstitution of 25.2 mg / 24.5 ml. Preparation T has an assumed potency of 5600 IU/mg and reconstitution of 21.4 mg / 23.95 ml. Create a new column of data as follows and select it as [Dilution] variable.
4855 IU/mg
25.2 mg / 24.5 ml
5600 IU/mg
21.4 mg / 23.95 ml
For further information see section 10.0.2. Doses, Dilutions and Potency.
Parallel Line Method
Potency
Assigned potency of Standard S: 4855 IU/mg
Predilution of Standard S: 25.2 mg / 24.5 ml
Assumed potency of Preparation T: 5600 IU/mg
Predilution of Preparation T: 21.4 mg / 23.95 ml

Estimated Potency 
Lower 95% 
Upper 95% 
Preparation T 
5456.3665 
5092.3689 
5843.3620 
G = 
0.0107 
C = 
1.0108 
10.1.3.5. Twin Crossover Design
Data is given in Table 5.1.5II. on p. 586 of European Pharmacopoeia (2008).
Open BIOPHARMA6 and select Bioassay → Parallel Line Method. From the Variable Selection Dialogue select the fourth option Crossover Design and select columns C18, C19, L20, C21 and C22 respectively as [Data], [Dose], [Preparation], [Row Factor] and [Column Factor]. Click [Next] to proceed to Output Options Dialogue and then click [Finish]. The following output is obtained:
Parallel Line Method
Crossover Design
Normality Tests
Smaller probabilities indicate nonnormality.
* Lilliefors probability = 0.2 means 0.2 or greater.
DosexPreparations 
Valid Cases 
Mean 
Standard Deviation 
1 x Standard 
16 
101.1875 
30.5160 
1 x Test 
16 
91.5625 
26.4448 
2 x Standard 
16 
68.1250 
18.8428 
2 x Test 
16 
77.5625 
29.8060 
DosexPreparations 
ShapiroWilk Test 
Probability 
KolmogorovSmirnov Test 
* Probability 
1 x Standard 
0.9507 
0.5009 
0.1380 
0.2000 
1 x Test 
0.9229 
0.1876 
0.1453 
0.2000 
2 x Standard 
0.9112 
0.1216 
0.1901 
0.1220 
2 x Test 
0.9278 
0.2253 
0.1260 
0.2000 
DosexPreparations 
Cramervon Mises Test 
Probability 
AndersonDarling Test 
Probability 
1 x Standard 
0.0470 
0.5319 
0.2966 
0.5482 
1 x Test 
0.0542 
0.4284 
0.4079 
0.3070 
2 x Standard 
0.0806 
0.1890 
0.4974 
0.1809 
2 x Test 
0.0636 
0.3197 
0.4091 
0.3049 
Homogeneity of Variance Tests

Test Statistic 
Probability 
Bartlett’s Chisquare Test 
3.7999 
0.2839 
BartlettBox F Test 
1.2736 
0.2815 
Cochran’s C (max var / sum var) 
0.3240 
0.6856 
Hartley’s F (max var / min var) 
2.6228 

Levene’s F Test 
2.1683 
0.1011 
Response Totals and Contrasts
Dose 
Standard 
Test 
Total 
Days: 1 



1 
765.0000 
719.0000 

2 
557.0000 
579.0000 

Total 
1322.0000 
1298.0000 
2620.0000 
Days: 2 



1 
854.0000 
746.0000 

2 
533.0000 
662.0000 

Total 
1387.0000 
1408.0000 
2795.0000 
Preparations 



Total 
2709.0000 
2706.0000 
5415.0000 
Linear Contrast 



Days: 1 
208.0000 
140.0000 
348.0000 
Days: 2 
321.0000 
84.0000 
405.0000 
Total 
529.0000 
224.0000 
753.0000 
Validity of Assay
Due To 
Sum of Squares 
DoF 
Mean Square 
FStat 
Prob 
Constant 
458159.7656 
1 
458159.7656 


Nonparallelism 
1453.5156 
1 
1453.5156 
1.0638 
0.3112 
DaysxPreparations 
31.6406 
1 
31.6406 
0.0232 
0.8801 
DaysxLinear Regression 
50.7656 
1 
50.7656 
0.0372 
0.8485 
Error Between 
38258.8125 
28 
1366.3862 


Blocks(Rows) 
39794.7344 
31 
1283.7011 


Preparations 
0.1406 
1 
0.1406 
0.0010 
0.9747 
Linear Regression 
8859.5156 
1 
8859.5156 
64.5324 
0.0000 
Days 
478.5156 
1 
478.5156 
3.4855 
0.0724 
DaysxNonparallelism 
446.2656 
1 
446.2656 
3.2506 
0.0822 
Error Within 
3844.0625 
28 
137.2879 


Total 
53423.2344 
63 
847.9878 


Separate Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard 
101.1875 
47.6991 
19294.1875 
0.3119 
Test 
91.5625 
20.1977 
23815.8750 
0.0618 
Common Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard 
96.4219 
33.9484 
44563.5781 
0.1658 
Test 
96.3281 



Comparison of Slopes
Comparison 
Difference 
Standard Error 
q Stat 
Table q 
Test – Standard 
27.5014 
8.4520 
3.2538 
2.0484 
Comparison 
Probability 
Lower 95% 
Upper 95% 
Result 
Test – Standard 
0.0030 
10.1882 
44.8146 
** 
Potency

Estimated Potency 
Lower 95% 
Upper 95% 
Test 
1.0028 
0.8354 
1.2041 
G = 
0.0650 
C = 
1.0695 
Although the plot of treatment means and the Comparison of Slopes test seem to indicate deviation from parallelism, the nonparallelism test in Validity of Assay (0.3112) is not significant at 5% level.
Standard and Test preparations are equipotent. Test preparation has an assumed potency of 40 units per millilitre. Create a new column of data as follows and select it as [Dilution] variable.
1
1
40 unit/ml
1
For further information see section 10.0.2. Doses, Dilutions and Potency.
Parallel Line Method
Potency
Assumed potency of Test: 40 unit/ml

Estimated Potency 
Lower 95% 
Upper 95% 
Test 
40.1106 
33.4162 
48.1646 
G = 
0.0650 
C = 
1.0695 
10.1.3.6. Triple Crossover Design
Table 10.3.1. on p. 205 from Finney, D. J. (1978) is an example with three dose levels and two preparations.
Open BIOFINNEY and select Bioassay → Parallel Line Method. From the Variable Selection Dialogue select the fourth option Crossover Design and select columns C15, C16, S17, C18 and C19 respectively as [Data], [Dose], [Preparation], [Row Factor] and [Column Factor]. Click [Next] to proceed to Output Options Dialogue. Click on the [Opt] button situated to the left of Normality Tests option and check the ShapiroWilk Test and Report summary statistics boxes. Then click [Back] and [Finish].
Parallel Line Method
Crossover Design
Normality Tests
Smaller probabilities indicate nonnormality.
DosexPreparations 
Valid Cases 
Mean 
Standard Deviation 
ShapiroWilk Test 
Probability 
0.5 x Standard 
10 
3.7120 
0.1946 
0.9485 
0.6508 
1.25 x Test 
10 
4.0700 
0.3391 
0.9285 
0.4330 
1 x Standard 
10 
3.2550 
0.7950 
0.9026 
0.2341 
2.5 x Test 
10 
3.4630 
0.5483 
0.9046 
0.2459 
2 x Standard 
10 
3.3970 
0.4072 
0.9038 
0.2408 
5 x Test 
10 
3.2780 
0.3720 
0.9058 
0.2532 
Homogeneity of Variance Tests

Test Statistic 
Probability 

Bartlett’s Chisquare Test 
18.0814 
0.0028 

BartlettBox F Test 
3.6473 
0.0027 

Cochran’s C (max var / sum var) 
0.4548 
0.0035 

Hartley’s F (max var / min var) 
16.6848 
0.0100 
p < 0.01 
Levene’s F Test 
6.6315 
0.0001 

Response Totals and Contrasts
Dose 
Standard 
Test 
Total 
Days: 1 



1 
18.7200 
19.8100 

2 
14.6900 
19.0100 

3 
17.0300 
16.1400 

Total 
50.4400 
54.9600 
105.4000 
Days: 2 



1 
18.4000 
20.8900 

2 
17.8600 
15.6200 

3 
16.9400 
16.6400 

Total 
53.2000 
53.1500 
106.3500 
Preparations 



Total 
103.6400 
108.1100 
211.7500 
Linear Contrast 



Days: 1 
1.6900 
3.6700 
5.3600 
Days: 2 
1.4600 
4.2500 
5.7100 
Total 
3.1500 
7.9200 
11.0700 
Quadratic Contrast 



Days: 1 
6.3700 
2.0700 
4.3000 
Days: 2 
0.3800 
6.2900 
5.9100 
Total 
5.9900 
4.2200 
10.2100 
Validity of Assay
Due To 
Sum of Squares 
DoF 
Mean Square 
FStat 
Prob 
Constant 
747.3010 
1 
747.3010 


Nonparallelism 
0.5688 
1 
0.5688 
1.6032 
0.2176 
Quadratic Regression 
0.8687 
1 
0.8687 
2.4484 
0.1307 
DaysxPreparations 
0.3481 
1 
0.3481 
0.9810 
0.3318 
DaysxLinear Regression 
0.0031 
1 
0.0031 
0.0086 
0.9267 
DaysxQuadratic Difference 
1.9026 
1 
1.9026 
5.3624 
0.0294 
Error Between 
8.5153 
24 
0.3548 


Blocks(Rows) 
12.2066 
29 
0.4209 


Preparations 
0.3330 
1 
0.3330 
4.7403 
0.0395 
Linear Regression 
3.0636 
1 
3.0636 
43.6087 
0.0000 
Days 
0.0150 
1 
0.0150 
0.2141 
0.6477 
Quadratic Difference 
0.0261 
1 
0.0261 
0.3716 
0.5478 
DaysxNonparallelism 
0.0164 
1 
0.0164 
0.2335 
0.6333 
DaysxQuadratic Regression 
0.0216 
1 
0.0216 
0.3075 
0.5844 
Error Within 
1.6861 
24 
0.0703 


Total 
17.3685 
59 
0.2944 


Separate Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard 
3.4547 
0.2272 
8.1200 
0.0576 
Test 
4.1272 
0.5713 
5.2830 
0.3725 
Common Regression

Intercept 
Slope 
Residual SS 
Rsquared 
Standard 
3.4547 
0.3993 
13.9718 
0.1798 
Test 
3.9695 



Comparison of Slopes
Comparison 
Difference 
Standard Error 
q Stat 
Table q 
Test – Standard 
0.3441 
0.1209 
2.8455 
2.0639 
Comparison 
Probability 
Lower 95% 
Upper 95% 
Result 
Test – Standard 
0.0089 
0.5937 
0.0945 
** 
Potency

Estimated Potency 
Lower 95% 
Upper 95% 
Test 
0.2754 
0.1783 
0.3923 
G = 
0.0977 
C = 
1.1083 