Testing when a series becomes not significantly different anymore

[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!

 

[Stephen Tashi]

If this is a real world problem, you might get an answer if you describe the problem.

The information you have given so far doesn't pose a question that has any mathematical answer. Applying statistics involves making enough assumptions so that the mathematical problem is "well posed".

 

[labrookie]

Thanks! Here is the real word situation:

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 94.62
.25 85.55
.50 76.21
.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.

 

[Stephen Tashi]

The first thing to settle is what you are trying to accomplish. For example, if you are preparing food to be eaten then presumably the goal is to use color as a guide to how long the food should be cooked. The goal would be to have the food be "done". On the other hand, if you only intend to photograph the food (and not eat it) then perhaps goal is to cook it till it is pink as possible.

If you are only interested in color, you have to decide what "significantly different" means in this problem. From your data, the colorometer gives a reading to two decimal points. Do you consider "22.73" to be "significantly different" than "22.74". What are the physical units for these readings?

 

[pmsrw3]

You can't be serious -- this is a "real world situation"? Who uses a colorimeter to determine when their prawns are done? :-O

Anyway, the question as you ask it doesn't have an objective answer. There's no way to know, without a lot more information, when the color changing process has really "finished", or when the changes are no longer "significant". And in reality, it's likely that the color continues to change indefinitely -- it just slows way, way down.

I would just plot the data and see where the curve appears to go flat.

 

[Stephen Tashi]

And in reality, it's likely that the color continues to change indefinitely -- it just slows way, way down.

My guess is that eventually the color would change from pink to brown. Is the goal to attain the "max pink"?

labrookie will have to tell us what he is doing.

I can't resist imagining some things.

Case 1: The goal is to write a cook book and state directions for cooking shrimp prawn of the form "Cook the prawn at 375 F for X minutes or until the prawn turn a dark pink". We want to know what number to use for X

Case 2:The goal is to designing an home appliance, the Shrimp-O-matic, which will automatically cook shrimp prawn. It will use a colorometer to determine when the shrimp are done.

Case 3: The goal is to determine how various diets affect the cooking time of shrimp prawn raised on a aqua-farm. To do this the lab needs to standardize their testing procedure so ti produces an objective measurement for cooking time. Hence we desire to make the measurement with a colorometer rather than have various lab technicians make subjective judgments.