Hello everyone,
I would like to ask your opinion as to my interpretation of a one sided confidence limit in a particular situation. I use, as a basis for my discussion, the description provided on:
http://www.graphpad.com/guides/prism/6/statistics/index.htm?one_sided_confidence_intervals.htm
I have found that literature detailing one sided confidence limits is very thin on the ground.
Hypothetically, say I was conducting a 1-way ANOVA. I have 3 groups and one of my groups is the control. The omnibus F statistic is significant and so I decide to do a multiple comparisons Dunnett's test whereby I compare each of the 2 groups with the control. My alternative hypothesis is that each of the 2 group means is < the control mean.
Since our goal is to show that (group mean - control mean) tends to be a small number, we need to express the one-sided confidence interval as the upper limit only. Agreed?
For Dunnett's test, if our results were:
(group 1 - control): mean difference=34.56, s.e.=1.89, p=1.0
(group 2 - control): mean difference=12.63, s.e.=1.85, p=1.0
In this case, the 95% upper limits for the two comparisons are
(group 1 - control) = 38.35 (i.e. we are 95% sure that the difference "group 1-control" is no more than 38.35).
(group 2 -control) = 16.33 (i.e. we are 95% sure that the difference "group2 -control" is no more than 16.33).
Conversely, if my alternative hypothesis is that each of the 2 group means is > the control mean. Since our goal is to show that (group mean - control mean) tends to be a large number, we need to express the one-sided confidence interval as the lower limit only. Agreed?
For Dunnett's test, if our results were:
(group 1 - control): mean difference=34.56, s.e.=1.89, p < 0.0005
(group 2 - control): mean difference=12.63, s.e.=1.85, p < 0.0005
In this case, the 95% lower limits for the two comparisons are:
(group 1 - control) = 30.76 (i.e. we are 95% sure that the difference "group 1-control" is no less than 30.76).
(group 2 -control) = 8.94 (i.e. we are 95% sure that the difference "group2 -control" is no less than 8.94).
As regards calculation, if we take this latter example (alternative hypothesis is that each of the 2 group means is > the control mean) - we would simply calculate the 90% 2 sided confidence interval:
(group 1 - control): mean difference=34.56, s.e.=1.89, p < 0.0005, 90% CI: lower bound=30.76, upper bound=38.35
(group 2 - control): mean difference=12.63, s.e.=1.85, p < 0.0005, 90% CI: lower bound=8.94, upper bound=16.33
Since there is an additional 5% chance that group1-control is more than 38.35 and an additional 5% chance that group2-control is more than 16.33 then we can say that there is a 95% chance that group1-control is no less than 30.76 and there is a 95% chance that group2-control is no less than 8.94.
Many thanks for your views on this (and sorry that this email has been so long!).
Very best wishes,
Kim
Dr Kim Pearce PhD, CStat, Assoc. Fellow HEA
Senior Statistician
Haematological Sciences
Room MG261
Institute of Cellular Medicine
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Newcastle University
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