Cross-Over Report
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Database	D:\PublicaciónWEB\MiWEB\ehtpcp\trial1crossover.S0
Periods	ScoreP1,ScoreP2

Cross-Over Analysis Summary Section
					Lower 95,0% 	Upper 95,0% 
	Estimated	Standard	T Value	Prob	Confidence	Confidence
Parameter	Effect	Error	(DF=16)	Level	Limit	Limit
Treatment	8,83333	0,65617	13,46	0,0000	7,44232	10,22435
Period	0,50000	0,65617	0,76	0,4571	-0,89101	1,89101
Carryover	1,22222	1,43157	0,85	0,4058	-1,81256	4,25701

Interpretation of the Above Report
The two treatment means in a 2x2 cross-over study are significantly different at the 0,0500
significance level (the actual significance level was 0,0000). The design had 9 subjects in
sequence 1 (SESEF) and 9 subjects in sequence 2 (SEFSE). The average response to treatment SE
was 10,88889 and the average response to treatment SEF was 19,72222.

A preliminary test failed to reject the assumption of equal period effects at the 0,0500
significance level (the actual significance level was 0,4571). A preliminary test failed to
reject the assumption of equal carryover effects at the 0,0500 significance level (the actual
significance level was 0,4058).

Cross-Over Analysis Detail Section
				Least Squares	Standard	Standard
Seq.	Period	Treatment	Count	Mean	Deviation	Error
1	1	SE	9	10,33333	2,78388	0,92796
2	2	SE	9	11,44444	2,60342	0,86781
1	2	SEF	9	19,66667	1,41421	0,47140
2	1	SEF	9	19,77778	0,66667	0,22222
1	Difference	(SEF-SE)/2	9	4,66667	1,60078	0,53359
2	Difference	(SEF-SE)/2	9	-4,16667	1,14564	0,38188
1	Total	SE+SEF	9	30,00000	3,04138	1,01379
2	Total	SE+SEF	9	31,22222	3,03223	1,01074
.	.	SE	18	10,88889		0,63526
.	.	SEF	18	19,72222		0,26058
1	.	.	18	15,00000		
2	.	.	18	15,61111		
.	1	.	18	15,05556		0,47710
.	2	.	18	15,55556		0,49379

Interpretation of the Above Report
This report shows the means and standard deviations of various subgroups of the data. The least
squares mean of treatment SE is 10,88889 and of treatment SEF is 19,72222. Note that least
squares means are created by taking the simple average of their component means, not by taking
the average of the raw data. For example, if the mean of the 20 subjects in period 1 sequence 1
is 50.0 and the mean of the 10 subjects in period 2 sequence 2 is 40.0, the least squares mean
is (50.0 + 40.0)/2 = 45.0. That is, no adjustment is made for the unequal sample sizes. Also
note that the standard deviation and standard error of some of the subgroups are not
calculated.

	Cross-Over Report
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	ScoreP1,ScoreP2

Equivalence Based on the Confidence Interval of the Difference
	Lower	Lower 80,0% 	Upper 80,0% 	Upper	Equivalent	
	Equivalence	Confidence	Confidence	Equivalence	at the 10,0% 	
Test Type	Limit	Limit	Limit	Limit	Sign. Level?	
Shortest C.I.	-2,17778	7,95620	9,71047	2,17778	No
Westlake C.I.	-2,17778	-9,40070	9,40070	2,17778	No
Note: Westlake's k2 = -27,79 and k1 = 0,86.

Interpretation of the Above Report
Average bioequivalence of the two treatments has not been established at the 0,1000
significance level using the shortest confidence interval of the difference approach since both
confidence limits, 7,95620 and 9,71047, are not between the acceptance limits of -2,17778 and
2,17778. This experiment used a 2x2 cross-over design with 9 subjects in sequence 1 and 9
subjects in sequence 2.

Average bioequivalence of the two treatments has not been established at the 0,1000
significance level using Westlake's confidence interval of the difference approach since both
confidence limits, -9,40070 and 9,40070, are not between the acceptance limits of -2,17778 and
2,17778. This experiment used a 2x2 cross-over design with 9 subjects in sequence 1 and 9
subjects in sequence 2.

	Cross-Over Report
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	ScoreP1,ScoreP2

Equivalence Based on the Confidence Interval of the Ratio
	Lower	Lower 80,0% 	Upper 80,0% 	Upper	Equivalent	
	Equivalence	Confidence	Confidence	Equivalence	at the 10,0% 	
Test Type	Limit	Limit	Limit	Limit	Sign. Level?	
Shortest C.I.	80,00000	173,06711	189,17778	120,00000	No
Westlake C.I.	80,00000	13,66704	186,33296	120,00000	No
Fieller's C.I.	80,00000	166,32973	198,06975	120,00000	No

Interpretation of the Above Report
Average bioequivalence of the two treatments has not been established at the 0,1000
significance level using the shortest confidence interval of the ratio approach since both
confidence limits, 173,06711 and 189,17778, are not between the acceptance limits of 80,00000
and 120,00000. This experiment used a 2x2 cross-over design with 9 subjects in sequence 1 and 9
subjects in sequence 2.

Average bioequivalence of the two treatments has not been established at the 0,1000
significance level using Westlake's confidence interval of the ratio approach since both
confidence limits, 13,66704 and 186,33296, are not between the acceptance limits of 80,00000
and 120,00000. This experiment used a 2x2 cross-over design with 9 subjects in sequence 1 and 9
subjects in sequence 2.

Average bioequivalence of the two treatments has not been established at the 0,1000
significance level using Fieller's confidence interval of the ratio approach since both
confidence limits, 166,32973 and 198,06975, are not between the acceptance limits of 80,00000
and 120,00000. This experiment used a 2x2 cross-over design with 9 subjects in sequence 1 and 9
subjects in sequence 2.

Equivalence Based on Schuirmann's Two One-Sided Hypothesis Tests
	Lower	Upper	10,0% 		Equivalent	
	Test	Test	Cutoff		at the 10,0% 	
Test Type	T Value	T Value	T Value	DF	Sign. Level?	
Schuirmann's 2 1-Sided Tests	16,78	10,14	1,34	16	No

Interpretation of the Above Report
Average bioequivalence of the two treatments was not established at the 0,1000 significance
level using Schuirmann's two one-sided t-tests procedure. The probability level of the t-test
of whether the treatment mean is not too much lower than the reference mean is 0,0000. The
probability level of the t-test of whether the treatment mean is not too much higher than the
reference mean is 1,0000. Since at least one of these values is greater than 0,1000, the null
hypothesis of average bioinequivalence was not rejected. This experiment used a 2x2 cross-over
design with 9 subjects in sequence 1 and 9 subjects in sequence 2.

	Cross-Over Report
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	ScoreP1,ScoreP2

Equivalence Based on Two One-Sided Wilcoxon-Mann-Whitney Tests
	Lower	Lower	Upper	Upper	Equivalent	
	Sum	Prob	Sum	Prob	at the 10,0% 	
Test Type	Ranks	Level	Ranks	Level	Sign. Level?	
2 1-Sided MW Tests	126,00	0,0002	126,00	0,9999	No

Interpretation of the Above Report
Average bioequivalence of the two treatments was not established at the 0,1000 significance
level using the nonparametric version of Schuirmann's two one-sided tests procedure which is
based on the Wilcoxon-Mann-Whitney test. The probability level of the test of whether the
treatment mean is not too much lower than the reference mean is 0,0002. The probability level
of the test of whether the treatment mean is not too much higher than the reference mean is
0,9999. Since at least one of these values is greater than 0,1000, the null hypothesis of
average bioinequivalence was not rejected. This experiment used a 2x2 cross-over design with 9
subjects in sequence 1 and 9 subjects in sequence 2.

Equivalence Based on Anderson and Hauck's Hypothesis Test
				Equivalent
			Prob	at the 10,0% 
Test Type	Pr(-TL)	Pr(TU)	Level	Sign. Level?
Anderson and Hauck's Test	0,0000	1,0000	1,0000	No

Interpretation of the Above Report
Average bioequivalence of the two treatments was not established at the 0,1000 significance
level using Anderson and Hauck's test procedure. The actual probability level of the test was
1,0000. This experiment used a 2x2 cross-over design with 9 subjects in sequence 1 and 9
subjects in sequence 2.

Plot of Sequence-by-Period Means

	Cross-Over Report
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Interpretation of the Sequence-by-Period Means
The sequence-by-period means plot shows the mean responses on the vertical axis and the periods
on the horizontal axis. The lines connect like treatments. If there is no period, carryover, or
interaction effects, two horizontal lines will be displayed. The distance between these lines
represents the magnitude of the treatment effect. The tendency for both lines to slope up or
down represents period and carryover effects. The tendency for the lines to cross represents
period-by-treatment interaction. This is also a type of carryover effect.

Plot of Subject Profiles

Interpretation of the Profile Plot
The profile plot displays the raw data for each subject. The response variable is shown along
the vertical axis. The two sequences are shown along the horizontal axis. The data for each
subject is depicted by two points connected by a line. The subject's response to the reference
formulation is shown first followed by their response to the treatment formulation. Hence, for
sequence 2, the results for the first period are shown on the right and for the second period
on the left. This plot used to develop a 'feel' for your data. You should view it first as a
tool to check for outliers (points and subjects that are very different from the majority).
Note that outliers should be removed from the analysis if a reason can be found for their
deletion. Of course, the first step is to double-check the values to determine if a typing
error might have caused them. Also, look for subjects whose lines exhibit a very different
pattern from the rest of the subjects in that sequence. Again, this might be a signal of some
type of data-recording or data-entry error. The profile plot allows you to assess the
consistency of the responses to the two treatments across subjects. You may also be able to
evaluate the degree to which the variation is equal in the two sequences.

	Cross-Over Report
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	ScoreP1,ScoreP2

Plot of Sums and Differences

Interpretation of the Sums and Differences Plot
The sums and differences plot shows the sum of each subject's two responses on the horizontal
axis and the difference between each subject's two responses on the vertical axis. Dot plots of
the sums and differences have been added above and to the right of the scatter plot,
respectively. Each point represents the sum and difference of a single subject. Different
plotting symbols are used to denote the subject's sequence. A horizontal line has been added at
zero to provide an easy reference from which to determine if a difference is positive (favors
treatment R) or negative (favors treatment T). The degree to which the plotting symbols tend to
separate along the horizontal axis represents the size of the carryover effect. The degree to
which the plotting symbols tend to separate along the vertical axis represents the size of the
treatment effect. Outliers are easily found on this plot. Outlying subjects should be reviewed
for data-entry errors and for special conditions that might have caused the responses to be
unusual. Outliers should not be removed from an analysis just because they are different. A
compelling reason should be found for their removal and the removal should be well documented.

Period Plot

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	ScoreP1,ScoreP2

Interpretation of the Period Plot
The Period Plot displays a subject's period 1 response on the horizontal axis and their period
2 response on the vertical axis. The plotting symbol is the sequence number. The plot is used
to find outliers and other anomalies.

Probability Plots

Interpretation of the Probability Plots
These plots show the differences (P1-P2) on the vertical axis and values on the horizontal axis
that would be expected if the differences were normally distributed. The first plot shows the
differences for sequence 1 and the second plot shows the differences for sequence 2. If the
assumption of normality holds, the points should fall along a straight line. The degree to
which the points are off the line represents the degree to which the normality assumption does
not hold. Since the normality of these differences is assumed by the t-test used to test for a
difference between the treatments, these plots are useful in assessing whether that assumption
is valid. If the plots show a pronounced pattern of non-normality, you might try taking the
square roots or the logs of the responses before beginning the analysis.