Calculating Correlations and Sensitivity Coefficients

In summary, the conversation discusses a numerical simulation where an input parameter is randomly varied, resulting in variations in three output parameters. The output parameters have normal distributions and are correlated to each other. The individual is seeking advice on estimating the change in the mean of two of the output parameters based on a small change in the mean of the input parameter, taking into account the correlations. The suggested approach is to run the experiment again with a tweaked input parameter and compare the mean and standard deviation of the new outputs. The speaker also notes the importance of clear correlations in data analysis.
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I have a numerical simulation where I'm randomly varying an input parameter.

This results in variations in three output parameters: A, B and C. The output parameters can be assumed to have normal distributions, but are correlated to each other.

If I calculate the mean and standard deviation on the range of values of A, B and C is there any way I could estimate the change in the mean of B and C due to a small change in the mean of A, making some account of the correlations? I was thinking of an approach based on sensitivity coefficients, but I'm not sure that's appropriate.

Any help/advice would be very welcome! Thanks!
 
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It sounds to me like the only way you could make a valuable correlation would be if you ran your experiment again with slightly tweaked input parameter, giving you new outputs A', B', C'. Then I'd calculate mean and SD and whatever else you think is good for the new data, and then see the changes between correlated outputs (i.e. A vs A').

I have no idea about the order of magnitude for the relationship of the correlation, or if one could exist, but as an engineer who has often been presented with data that is "supposed to be useful", this is how I would define useful, meaning that the correlation between data is clear and not based on nested calculations if possible.
 

What is the purpose of calculating correlations and sensitivity coefficients?

The purpose of calculating correlations and sensitivity coefficients is to measure the strength and direction of the relationship between two variables. This can help scientists understand how changes in one variable may affect the other variable and make predictions about future outcomes.

How do you calculate a correlation coefficient?

To calculate a correlation coefficient, you need to use a statistical formula that takes into account the values of both variables and their deviations from their respective means. This formula produces a numerical value between -1 and 1, where a positive value indicates a positive correlation, a negative value indicates a negative correlation, and a value of 0 indicates no correlation.

What does a sensitivity coefficient tell us?

A sensitivity coefficient measures the magnitude of change in one variable in response to a change in another variable. It can help scientists understand how sensitive a system is to changes in certain variables and how different variables may interact with each other.

How do you interpret a correlation coefficient?

The interpretation of a correlation coefficient depends on its numerical value. A value of 1 or -1 indicates a perfect positive or negative correlation, respectively. A value close to 0 indicates a weak or non-existent correlation. The closer the value is to 0, the weaker the relationship between the two variables.

Can correlation coefficients be used to determine causation?

No, correlation coefficients only measure the strength and direction of a relationship between two variables. They cannot determine causation, as there may be other factors at play that are not accounted for in the calculation of the correlation coefficient.

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