Hi:
Sometimes we would like to demonstrate that the data has some
particular type of trend, e.g., monotone increase or decrease. How do
we demonstrate that this trend has statistical significance?
Thank you,
Cosine wrote:
Hi:
Sometimes we would like to demonstrate that the data has some
particular type of trend, e.g., monotone increase or decrease. How do
we demonstrate that this trend has statistical significance?
Thank you,
As a first step, you need to think about the context of whatever data
you have. In particular, you need to consider whether there is temporal >correlation/dependence present in addtition to whatever trend you might >postulate.
Also, you should think about whether a possible "trend"
should also include a possible change in variability instead-of or in >addition-to a change in location.
In the simplest case, you can just take a model-free approach whereby
you return to first-principles. Specifically: (a) find a numerical
measure of how much trend there is; (b) find the null distribution of
your numerical measure by evaluating the same numerical measure for
random permutations of the original data. It will be clear how the >assumptions needed for the validity of this relate to my first
paragraph.
In the more general case, you could resort to the usual thing of
building a full probabilistic model and testing via maximum likelihood.
Say we have five groups of subjects, and each receives different concentrations of medicine, from low to high.
At the endpoint, we measure the diameters of the lesion of each
subject and calculate the mean diameter of each group.
We expect a monotone decrease trend of the mean diameters of the
groups. But how do we demonstrate the significance?
Cosine wrote:
Say we have five groups of subjects, and each receives different
concentrations of medicine, from low to high.
At the endpoint, we measure the diameters of the lesion of each
subject and calculate the mean diameter of each group.
We expect a monotone decrease trend of the mean diameters of the
groups. But how do we demonstrate the significance?
As part of the first step in significance testing, you need to have a
null hypothesis as well as an alternative hypothesis.
There are two
obvious but distinct possibilities for one aspect of what might be
going on: in one the null hypothesis has an unspecified but varying
pattern, to be compared to a monotone pattern, while in the other the
null hypothesis has constant value, to be compared with a monotone
pattern.
On Sun, 8 Jan 2023 04:36:55 -0000 (UTC), "David Jones" <dajhawkxx@nowherel.com> wrote:
Cosine wrote:
Say we have five groups of subjects, and each receives different
concentrations of medicine, from low to high.
At the endpoint, we measure the diameters of the lesion of each
subject and calculate the mean diameter of each group.
We expect a monotone decrease trend of the mean diameters of the
groups. But how do we demonstrate the significance?
As part of the first step in significance testing, you need to have
a null hypothesis as well as an alternative hypothesis.
Or - you can have a situation where you want to provide a
precise assessment, where basic "significance" is assumed, and
readily established by any test.
Having 5 concentrations, without a Zero comparison, implies
that the questions (hypotheses) concern whether the lowest
dose (concentration) has much effect, or if there is continued
gain from increasing dose by each step.
A overall test:
Assuming that the doses here are judged (by the PI) to be
(in the relevant sense) equal intervals, a simple correlation
will show that increasing dose matters. This will be HIGHLY
significant, you hope.
(Also, the outcome should probably take into account the size
of the original lesion. Log of the Pre/Post ratio might be natural,
if lesions don't decrease to 0.)
If I had data like these, I would want to plot the Pre vs. Post
for the 5 doses, and figure out from the picture what there is
to describe. A strong linear trend of efficicay across dose (log concentration) with tiny contributions from the nonlinear ANOVA
components would be the outcome most convenient to describe.
There are two
obvious but distinct possibilities for one aspect of what might be
going on: in one the null hypothesis has an unspecified but varying pattern, to be compared to a monotone pattern, while in the other
the null hypothesis has constant value, to be compared with a
monotone pattern.
Rich Ulrich wrote:
On Sun, 8 Jan 2023 04:36:55 -0000 (UTC), "David Jones"
<dajhawkxx@nowherel.com> wrote:
Cosine wrote:
Say we have five groups of subjects, and each receives different
concentrations of medicine, from low to high.
At the endpoint, we measure the diameters of the lesion of each
subject and calculate the mean diameter of each group.
We expect a monotone decrease trend of the mean diameters of the
groups. But how do we demonstrate the significance?
As part of the first step in significance testing, you need to have
a null hypothesis as well as an alternative hypothesis.
Or - you can have a situation where you want to provide a
precise assessment, where basic "significance" is assumed, and
readily established by any test.
Having 5 concentrations, without a Zero comparison, implies
that the questions (hypotheses) concern whether the lowest
dose (concentration) has much effect, or if there is continued
gain from increasing dose by each step.
A overall test:
Assuming that the doses here are judged (by the PI) to be
(in the relevant sense) equal intervals, a simple correlation
will show that increasing dose matters. This will be HIGHLY
significant, you hope.
(Also, the outcome should probably take into account the size
of the original lesion. Log of the Pre/Post ratio might be natural,
if lesions don't decrease to 0.)
If I had data like these, I would want to plot the Pre vs. Post
for the 5 doses, and figure out from the picture what there is
to describe. A strong linear trend of efficicay across dose (log
concentration) with tiny contributions from the nonlinear ANOVA
components would be the outcome most convenient to describe.
There are two
obvious but distinct possibilities for one aspect of what might be
going on: in one the null hypothesis has an unspecified but varying
pattern, to be compared to a monotone pattern, while in the other
the null hypothesis has constant value, to be compared with a
monotone pattern.
The OP has been very unclear, so there seems also to be at least one
other possibility, where the null hypothesis is that there is a
monotone pattern, with the alternative hypothesis (that which one is
looking evidence might be happening) is that there is a change in
direction of the pattern as the dosage increases (but possibly just one >turning point).
| Sysop: | Keyop |
|---|---|
| Location: | Huddersfield, West Yorkshire, UK |
| Users: | 300 |
| Nodes: | 16 (3 / 13) |
| Uptime: | 190:15:37 |
| Calls: | 6,739 |
| Calls today: | 2 |
| Files: | 12,268 |
| Messages: | 5,366,708 |