# Thread: How can I determine if two graphs are statistically significantly different

1. ## How can I determine if two graphs are statistically significantly different

Hi, I'm working on a medical research project and need some stats help. I have limited statistical knowledge but I understand that basics. I need help with the following...

I have two graphs:

A: y = -0.000003x^3 + 0.000664x^2 - 0.028609x + 0.333098
B: y = -0.000003x^3 + 0.000781x^2 - 0.042135x + 0.627823

How can I determine if these two curves are statistically significantly different from one another?

2. ## Re: How can I determine if two graphs are statistically significantly different

Do they cross within your sample space? If so the slopes aren't parallel.

Can you provide some more background information on what you are doing? And is x^3 = to coefficient times (x*x*x), so it you are working with polynomials?

3. ## Re: How can I determine if two graphs are statistically significantly different

hi,
actually there is no such thing as a statistically significant difference in graphs. Are we talking about different models here?

regards

4. ## Re: How can I determine if two graphs are statistically significantly different

Originally Posted by rogojel
hi,
actually there is no such thing as a statistically significant difference in graphs. Are we talking about different models here?

regards
I think OP may be looking for a difference in functions, similar to the way you can test for differences in survival curves.

5. ## Re: How can I determine if two graphs are statistically significantly different

Originally Posted by ondansetron
I think OP may be looking for a difference in functions, similar to the way you can test for differences in survival curves.
For a statistical test you would need some random component. This would work if the two equations were the regression models of some phenomena in which case the question would also make sense, a bit reformulated, like is there significant difference hetween the two models? IMO this is the case for survival curves as well. In comparing two graphs, without this random component, there is no definition of statistical significance that could be applied.

regards

6. ## Re: How can I determine if two graphs are statistically significantly different

Originally Posted by rogojel
For a statistical test you would need some random component. This would work if the two equations were the regression models of some phenomena in which case the question would also make sense, a bit reformulated, like is there significant difference hetween the two models? IMO this is the case for survival curves as well. In comparing two graphs, without this random component, there is no definition of statistical significance that could be applied.

regards
Are you familiar with survival analysis techniques where a very descriptive initial, early step can involve a test of hypothesis that the survival functions in each of the k-groups are equal (specifically, Kaplan-Meier, if I recall)? It's similar to an ANOVA test of hypothesis (Ho: S(a)=S(b)=...=S(k)), but instead of means, you're dealing with survival functions.

Again, I don't think the OP literally meant comparing two graphs, but rather comparing functions. This is a common question and test of hypothesis covered in many survival analysis texts. I direct you to Hosmer and Lemeshow for a survival text if you're curious for a refence.

7. ## Re: How can I determine if two graphs are statistically significantly different

hi ondasetron,
how can you talk about a null and an alternative hypothesis, if you simply check whether f1(x)= f2(x) for x= x1,x2...etc?

regards

8. ## Re: How can I determine if two graphs are statistically significantly different

I was also thinking that, since the OP had undefined Xs in the function. But who really knows

9. ## The Following User Says Thank You to hlsmith For This Useful Post:

ondansetron (09-08-2017)

10. ## Re: How can I determine if two graphs are statistically significantly different

All good points. I think rogojel is being a little bit more meta. Yes, results are dependent on the model, which is wrong but. Informative. Survival curves analysis just compares two curves similarly to slopes in linear reg. Which we won't contest. Rogojel is still focusing on the premise behind sampling dist and that the model needs random variable for "statistical tests" to be used in comparing slopes, which we assume the OP has.

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