How to test when series of data becomes not significant...

[labrookie]

Hello,
I am trying to figure out what test to use in order to solve a fairly basic concept. I am not sure if this is a cenvergence test or a significance test.

Example: Consider the following data

x y
1 30
2 22
3 18
4 12
5 10
6 9
7 8
8 6
9 5.5
10 5.8

I want to know at what x does the series of data start to become not significantly changing any more. If I simply know what type of test to be using, I think I am capable of solving my problem.

Thank you for your help!

[Dason]

I don't quite understand what you're trying to do. Could you try explaining it in a little more detail?

[labrookie]

Here is another example:

The more money I spend on a piece of equipment (x), the less number of errors will occur by the piece of equipment (y).

x y
$100 30
$200 22
$300 18
$400 12
$500 10
$600 9
$700 8
$800 6
$900 5.5
$1000 5.2

Statistically, when does it become not significant to spend any more money?

Hope this helps explain what I am trying to solve for! Thank you.

[Dason]

Nope - didn't really help much. Will you actually explain what you're trying to do? What do you mean by "not significant to spend any more money"? You didn't really clarify anything with that second post (at least not to me).

[Beejay dunga]

Try figure out what you really want to do, if to test for significant of beta and alpha or a and b in Y=a+bx+e, you can use t test that what I know can test on significance

[Dason]

Try figure out what you really want to do, if to test for significant of beta and alpha or a and b in Y=a+bx+e, you can use t test that what I know can test on significance

Except it doesn't sound like that's what they want to do at all. It sounds like they want something to do with some sort of change point model but they really haven't made it clear exactly what they're looking to do.

[jpkelley]

@ labrookie: Do you actually have a time series? In example #1, this is the indication. In your second example, it seems you moved towards a dataset where each y could realistically be independent of other y values (unlike in the time series). A change point test would indeed do the trick, though I have no experience. You seems that you need some baseline distribution by which to compare distributions of your dependent at each time step. The temporal non-independence precludes this.

@ everyone. Assuming there are enough time intervals and some measured variation along y, could labrookie model his time series data explicitly accounting for temporal autocorrelation and then compare distributions of y at successive time steps to the predicted distribution at t=0? Not sure if that made sense at all. It's late in the afternoon, and I'm taking a break from my dissertation to scan this site. Ugh. I've seen many peer-reviewed publications examine long-term changes in bird body or beak sizes by comparing each year's distribution to the 95% confidence intervals of the first year. Of course, this didn't take into account temporal autocorrelation, which may have effectively dampened some of their year-wise effects, so I'm wondering if adding a correlational structure to a model might be a solution...har, har...even if it's a terrible one.

@ labrookie...can you provide a simulated data set to show us the real nature of your data (how many intervals, if there are multiple measures of the dependent at each time step, etc.?

[trinker]

I'm not sure what labrookie's asking but the graph would be exponential decay. It sounds like a cost benifits analysis (way out of my field).

[labrookie]

Thanks for your help, everyone.

I thought it would be useful for me to make up a simple problem, but it sounds like it would be best to show the actual one:






As you cook a shrimp prawn, the color of the surface of the shrimp turns from an opaque/white color to a pink/red color. Using a colorimeter, I took measurements throughout the cooking process.

The colorimeter turns the color processed into a numeric value for analysis purposes.

Cook Time (min) Color Reading (C)
0.00 94.62
0.25 85.55
0.50 76.21
0.75 71.2
1.00 61.21
1.25 56.66
1.50 45.12
1.75 38.01
2.00 32.83
2.25 30.12
2.50 26.2
2.75 24.10
3.00 23.50
3.25 22.86
3.50 22.43
3.75 22.45
4.00 22.39


At what point in the cooking process is the shrimp prawn finished changing color?

(My initial thoughts are that the data points are significantly different from one another as the cooking process begins...and then at some point the data points are not significantly different from one another anymore. This would be the point where the prawn has finished changing color)

Thank you for your help - I hope this explanation is a little more clear.