What statistical test can I do to analyse this data?

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elephantalkali
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#1
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#1
I have tested the bone stiffness of 6 bones, lets say for simplicity that they are:

Bone 1: 20 (n/mm)
Bone 2: 45 (n/mm)
Bone 3: 14 (n/mm)
Bone 4: 45 (n/mm)
Bone 5: 34 (n/mm)
Bone 6: 19 (n/mm)

Can I do anything with this data apart from drawing a bar chart? nothing I can do find out if there is a statically significant difference between the values


Edit:

We conducted an experiment to test different factors that could affect a external fixation construct (see pic)
Each bone was differnt to the other, we adjusted things like how close the pins were to the fracture, how many parallel rods we had.
Currently the only data I have is load (n) and extension (mm) - I worked out stiffness from here.
Can I do any stats to show that one bone model is better /worse than other?
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Gregorius
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#2
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#2
(Original post by elephantalkali)
I have tested the bone stiffness of 6 bones, lets say for simplicity that they are:

Bone 1: 20 (n/mm)
Bone 2: 45 (n/mm)
Bone 3: 14 (n/mm)
Bone 4: 45 (n/mm)
Bone 5: 34 (n/mm)
Bone 6: 19 (n/mm)

Can I do anything with this data apart from drawing a bar chart? nothing I can do find out if there is a statically significant difference between the values

For the data you have (a very small sample size) pretty much the best you can do is to produce summary statistics - the mean bone stiffness and its standard error. This, if the sample was homogeneous in some way (that is, a random sample drawn from some well-defined population of bones), would allow you to estimate the population mean bone stiffness and to give that estimate some 95% confidence intervals.

Also, again provided that this is a random sample drawn from some well-defined population of bones, you have just enough data to do a statistical test that asks whether the mean bone stiffness is some particular pre-defined value or not (provided that the pre-defined value was not hypothesized after having looked at the data!) However you would (with this small sample size) have to use a specialized technique (bootstrapped t-test, for example) to do so - and may need some expert advice.

I will add that this is a bit of an odd question, as it is all topsy-turvy from a scientific point of view. An appropriate procedure would be something like this:

1) Ask a scientific question about bone stiffness; for example, do two different types of bone differ in stiffness?

2) Calculate how many observations would be needed to detect a particular difference in stiffness between the two groups.

3) Do the statistical test (a t-test in this case, or some relative) and draw the conclusions.
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Spandy
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#3
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Are you familiar with coding in R (or matlab?). If yes, I would suggest that you run a code for bootstrapping on this data set a large number of times, then, I believe that by scatter-plotting the resultant data, I believe we can safely conclude that bones (1,3,6) belong to a separate class from (2,4,5) (But then, the dataset is too small to be certain)

You can also try estimating its https://en.wikipedia.org/wiki/Maximum_likelihood, but honestly, I personally can't really visualise any random variable which satisfies.

I would say, data is insufficient to make a powerful argument.
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Gregorius
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#4
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(Original post by Spandy)
Are you familiar with coding in R (or matlab?). If yes, I would suggest that you run a code for bootstrapping on this data set a large number of times, then, I believe that by scatter-plotting the resultant data, I believe we can safely conclude that bones (1,3,6) belong to a separate class from (2,4,5) (But then, the dataset is too small to be certain)
The big question here is: "bootstrapping what?" If it was pre-specified that bones 1,3,6 were thought to be of a different class than bones 2,4,5 then you might just get away with this (but you would still have statisticians the world over sucking air through their teeth and shaking their heads).

If you decide to test a difference between (1,3,6) and (2,4,5) on the basis of having seen the data then any statistical test would have no validity. i.e. Don't do it!
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Spandy
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#5
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(Original post by Gregorius)
The big question here is: "bootstrapping what?" If it was pre-specified that bones 1,3,6 were thought to be of a different class than bones 2,4,5 then you might just get away with this (but you would still have statisticians the world over sucking air through their teeth and shaking their heads).

If you decide to test a difference between (1,3,6) and (2,4,5) on the basis of having seen the data then any statistical test would have no validity. i.e. Don't do it!
Ah, my bad...
I am not really a statistician (nyet anyway). Bootstrapping was taught in class only earlier this week. I guess a freshman can get a first-time pass?
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Gregorius
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#6
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(Original post by Spandy)
Ah, my bad...
I am not really a statistician (nyet anyway). Bootstrapping was taught in class only earlier this week. I guess a freshman can get a first-time pass?
Sure

Bootstrapping is seriously good and should be used in all circumstances except when it shouldn't.
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elephantalkali
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#7
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#7
(Original post by Gregorius)
For the data you have (a very small sample size) pretty much the best you can do is to produce summary statistics - the mean bone stiffness and its standard error. This, if the sample was homogeneous in some way (that is, a random sample drawn from some well-defined population of bones), would allow you to estimate the population mean bone stiffness and to give that estimate some 95% confidence intervals.

Also, again provided that this is a random sample drawn from some well-defined population of bones, you have just enough data to do a statistical test that asks whether the mean bone stiffness is some particular pre-defined value or not (provided that the pre-defined value was not hypothesized after having looked at the data!) However you would (with this small sample size) have to use a specialized technique (bootstrapped t-test, for example) to do so - and may need some expert advice.

I will add that this is a bit of an odd question, as it is all topsy-turvy from a scientific point of view. An appropriate procedure would be something like this:

1) Ask a scientific question about bone stiffness; for example, do two different types of bone differ in stiffness?

2) Calculate how many observations would be needed to detect a particular difference in stiffness between the two groups.

3) Do the statistical test (a t-test in this case, or some relative) and draw the conclusions.

Thank you
Sorry I don't think I've given enough information in my question.

We conducted an experiment looking at external fixation and factors that could influence the stiffness of the external fixation construct (see picture).
We changed things like how close the perpendicular pins were to the fracture, how close the parallel rods were to the fracture, whether we had one or two rods.

So all 6 bones are different with one or more of these things adjusted

My question is whether I can look at say bone 1 (that has pins far away from fracture) and say that it was worse than bone 2 (where pins were close to the fracture). I can see that bone 2 has higher stiffness but can I do statistic to say whether this difference was significant?
or do i not have enough data.

We collected data on load (n) and extension (mm) so I worked out stiffness from there.
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Gregorius
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#8
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#8
(Original post by elephantalkali)
Thank you
Sorry I don't think I've given enough information in my question.

We conducted an experiment looking at external fixation and factors that could influence the stiffness of the external fixation construct (see picture).
We changed things like how close the perpendicular pins were to the fracture, how close the parallel rods were to the fracture, whether we had one or two rods.

So all 6 bones are different with one or more of these things adjusted

My question is whether I can look at say bone 1 (that has pins far away from fracture) and say that it was worse than bone 2 (where pins were close to the fracture). I can see that bone 2 has higher stiffness but can I do statistic to say whether this difference was significant?
or do i not have enough data.
OK, so the quick answer is that bone 1 is clearly worse than bone 2!

But I suspect that this is not really what you're interested in. What would really be interesting is an experiment that allowed you to generalize from what you see from your sample to the underlying population (of all bones of this type, presumably) allowing you to conclude that particular factors were associated with stiffness and to estimate how much they were associated. This would allow you to predict (with an estimate of uncertainty) how stiff future configurations would be.

To do this you would need replication of configurations in order to estimate the random variation (between bone to bone, for example) associated with the process in the same configuration.

It is quite possible that variation between samples with the same configuration may be tiny - and that you can therefore make conclusions from a very small sample. But you have to do that experiment first!
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