- #1
Master1022
- 611
- 117
- Homework Statement
- How to show that the occurrences of an event does not increase linearly over time?
- Relevant Equations
- Mean, standard deviation
Hi,
I think this is a simple question, but I just wanted to ask how I could go about showing this in a scientific manner. I will try to use an analogy later on which is, I hope, a simple way to understand what I am doing.
What I am trying to do:
I am trying to investigate whether the occurrences of an event increase linearly with time (i.e. if it happens 10 times in 1 month, then it will happen 20 times in 2 months).
What I have:
I have distribution data about the number of event occurrences for different time horizons (1 month, 2 months, ... , 6 months). From this distribution data, I can calculate all the common stats: mean, median, standard deviation, upper quartile, lower quartile, etc.
Why is it a distribution? Here is where I draw upon an analogy.
Let us imagine we want to measure the number of times some particles, in a box, collide in a certain time-frame. We can number the particles from 1 to ##n##, and then record over, for example, 1 minute, how many times they each bump into one another. Then we have a distribution from which we can calculate statistics. (Don't worry about any double counting here, that is not an issue in my problem, and this was just a simple analogy I made up in my head). Then we can run the experiment again for 2 minutes, 3 minutes, etc. and look at the distributions for each of the time horizons.
Now, returning to my problem:
What I am confused about:
1. What statistics should I be using to investigate this claim? If the data is normally distributed, should I be using the mean? Otherwise, should I be using the median?
- My data isn't normally distributed so I am leaning towards the median
- For example, we could look at the median (or mean) for 1 month and then look how the medians for later horizons compare to ##k \times ## 1 month.
2. What would be a nice way to visualize this?
- The idea I currently have is to visualize this is to have box plots (or even just points with error bars) to represent the median and LQ/UQ at each time horizon
- In background, I can have a simple linear trend line to represent what the median should look like if it were increasing linearly (basically just a line that passes through the integer multiples of the 1 month data).
I hope this makes sense and I would appreciate any insight or advice.
I think this is a simple question, but I just wanted to ask how I could go about showing this in a scientific manner. I will try to use an analogy later on which is, I hope, a simple way to understand what I am doing.
What I am trying to do:
I am trying to investigate whether the occurrences of an event increase linearly with time (i.e. if it happens 10 times in 1 month, then it will happen 20 times in 2 months).
What I have:
I have distribution data about the number of event occurrences for different time horizons (1 month, 2 months, ... , 6 months). From this distribution data, I can calculate all the common stats: mean, median, standard deviation, upper quartile, lower quartile, etc.
Why is it a distribution? Here is where I draw upon an analogy.
Let us imagine we want to measure the number of times some particles, in a box, collide in a certain time-frame. We can number the particles from 1 to ##n##, and then record over, for example, 1 minute, how many times they each bump into one another. Then we have a distribution from which we can calculate statistics. (Don't worry about any double counting here, that is not an issue in my problem, and this was just a simple analogy I made up in my head). Then we can run the experiment again for 2 minutes, 3 minutes, etc. and look at the distributions for each of the time horizons.
Now, returning to my problem:
What I am confused about:
1. What statistics should I be using to investigate this claim? If the data is normally distributed, should I be using the mean? Otherwise, should I be using the median?
- My data isn't normally distributed so I am leaning towards the median
- For example, we could look at the median (or mean) for 1 month and then look how the medians for later horizons compare to ##k \times ## 1 month.
2. What would be a nice way to visualize this?
- The idea I currently have is to visualize this is to have box plots (or even just points with error bars) to represent the median and LQ/UQ at each time horizon
- In background, I can have a simple linear trend line to represent what the median should look like if it were increasing linearly (basically just a line that passes through the integer multiples of the 1 month data).
I hope this makes sense and I would appreciate any insight or advice.