1. ## Sampling question

Hi.

I want to estimate the height of a building between floors 1 and 10. But I can only use stairs and can only sample 10 steps from say 431 stairs between floors 1 and 10. Each floor doesn't exactly have the same number of steps... but I know how many are in each floor. Say I have sampled these correctly, what would be next logical step?

What do you suggest? Do you suggest me to find the average of these sample steps and multiple it by 431 steps to get an estimate height? and maybe get a 95% confidence interval on the point estimate?

Do you have any other suggestions? i.e. any other statistical methods I can use? bootstrap method?

2. ## Re: Sampling question

Hey lpd.

Just to clarify what you are doing, are you doing ten "trials" where you are trying to sample the number of "steps" between a single floor by counting the number of steps between successive floors? Also do you assume all floors have roughly the same height (but not necessarily the same number of steps)?

3. ## Re: Sampling question

Originally Posted by chiro
Hey lpd.

Just to clarify what you are doing, are you doing ten "trials" where you are trying to sample the number of "steps" between a single floor by counting the number of steps between successive floors? Also do you assume all floors have roughly the same height (but not necessarily the same number of steps)?
I guess the question is to estimate the height of the building between floors 1 and 10. And I am allowed to measure up to 10 steps between these floors.

I don't think we can make the assumptions that all the floors have the same height. Because some floors are in fact higher up than others...

4. ## Re: Sampling question

This seems to me a little ambiguous: can you give for example state a few records of data that you measure (so a few rows of data with all the columns for each row) and then describe what those numbers refer to (steps, metres, whatever and if they are positive and negative please say what the reference point: i.e. what the origin refers to).

5. ## Re: Sampling question

Originally Posted by chiro
This seems to me a little ambiguous: can you give for example state a few records of data that you measure (so a few rows of data with all the columns for each row) and then describe what those numbers refer to (steps, metres, whatever and if they are positive and negative please say what the reference point: i.e. what the origin refers to).
Some of the steps includes (in CM)
22.15
21.14
21.99
20.58
20.42
20.19
20.75
20.25
20.43
22.49

and a random generator was used to generate those steps that was measured. There is no reference point as we were not given it. We were just told to measure 10 steps and then estimate the height between floors 1 and 10.

6. ## Re: Sampling question

So do you have an idea using either rule of thumb, an educated guess, or some other thing to estimate the building?

You are going to have to use assumption of how many steps there are for the height of a building and there are many ways to go about it.

7. ## Re: Sampling question

Originally Posted by chiro
So do you have an idea using either rule of thumb, an educated guess, or some other thing to estimate the building?

You are going to have to use assumption of how many steps there are for the height of a building and there are many ways to go about it.
I guess what I was planning to do is to find the mean of the sample that I found. Then multiply it by the number of steps between floors 1 and 10.

Is that an okay approach? Or what other approach do you suggest?

8. ## Re: Sampling question

Absolutely if you have this information then this would be a great approach.

You should however get a confidence interval for the height of the building rather than just a simple point estimate: You can use the properties of variance and expectation for this.

For example if the variance of one step size is v then the variance for n steps is n*v if we assume that every step is independent from the others.

9. ## Re: Sampling question

Originally Posted by chiro
Absolutely if you have this information then this would be a great approach.

You should however get a confidence interval for the height of the building rather than just a simple point estimate: You can use the properties of variance and expectation for this.

For example if the variance of one step size is v then the variance for n steps is n*v if we assume that every step is independent from the others.
Im not quite sure what you mean by the variance of one step size... I just used a statistical program to help me find a confidence interval...

10. ## Re: Sampling question

Well basically you can can get the variance for the distribution of the sample mean given these observations and this will give the variance of one particular step.

But if you are looking at many steps, you need to consider how the variance changes and this means that you multiply the variance by the number of steps.

The mean will be multiplied in the same way but the variance will grow larger and larger to take into account the cumulative effects of adding more and more steps (since they could be either a bit smaller or a bit larger). The effect won't be too big but it will be noticeable and if you have lots of steps, it will make a difference.