Analyzing Data for Correlation for Academic Research

[24forChromium]

I hope this is the right place to post this, please move if you think it's needed.

I want to ask how do I extrapolate a correlation from a bunch of numbers. I did and experiment on gyroscopes, and have three kinds of data, w1, w3 and F_t, the later two can be used to calculate L3 and T_g. My theory is: T_g = L3 * w1.

Now, how do I prove or disprove this theoretical correlation with these data? I know that I can plot the theoretical values and the actual values on the same graph and say "look, they look like they are matching.", but how can I do this in a academically sophisticated way? Where can I learn to do this professionally? How should I evaluate the methods and the results?

 

[Simon Bridge]

I want to ask how do I extrapolate a correlation from a bunch of numbers.

Depends on the numbers and what sort of correlation you are trying to demonstrate (or, more usually, disprove).

I did and experiment on gyroscopes, and have three kinds of data, w1, w3 and F_t, the later two can be used to calculate L3 and T_g. My theory is: T_g = L3 * w1.

All this is meaningless unless you say what the symbols mean. It would also help to explain the experiment.

Now, how do I prove or disprove this theoretical correlation with these data? I know that I can plot the theoretical values and the actual values on the same graph and say "look, they look like they are matching.", but how can I do this in a academically sophisticated way? Where can I learn to do this professionally? How should I evaluate the methods and the results?

With each data point, you should have an estimate of the uncertainty in the measurement (or propagated uncertainties due to underlying measurement uncertainties). Your graph should use error bars - when the theoretical curve goes through all error bars you can say that there is a good match between theory and data ... however, it is better to use some form of regression analysis (i.e. least squares) to work out the important parameters and see if they agree (within stated error limits) with the theoretical value for the same parameter.

 

[24forChromium]

All this is meaningless unless you say what the symbols mean. It would also help to explain the experiment.

Well I didn't think anyone would be interested. Since you asked, it's an experiment on how does the combination of angular momentum and velocity of precession affect the torque generated by a gyroscope. w1 is the angular velocity of precession. w3 is the gyroscope's rotational velocity (used to find its angular momentum L3) F_t is the tension force detected in a string. This string is used to pull the gyroscope up in a horizontal position, but its "task" will be alleviated if the gyroscope creates a torque to help "share its labour". Therefore, this tension force was used to find the torque generated by the gyroscope, which is T_g.

If you want to know the specifics of the experimental construction, just let me know.

With each data point, you should have an estimate of the uncertainty in the measurement (or propagated uncertainties due to underlying measurement uncertainties). Your graph should use error bars - when the theoretical curve goes through all error bars you can say that there is a good match between theory and data ... however, it is better to use some form of regression analysis (i.e. least squares) to work out the important parameters and see if they agree (within stated error limits) with the theoretical value for the same parameter.

Are there websites or online classes that I can access to learn about these? I am expected to write a long analysis for the experiment, just plotting the data and using mathematics may not be enough, although some regression analysis certainty would come handy.

 

[Svein]

I want to ask how do I extrapolate a correlation from a bunch of numbers. I did and experiment on gyroscopes, and have three kinds of data, w1, w3 and F_t, the later two can be used to calculate L3 and T_g. My theory is: T_g = L3 * w1.

Look up "chi square test" and "null hypothesis".

 

[Simon Bridge]

Tg and w1 are things you measure... the theory is that a plot of Tg vs w1 will be a straight line that passes through the origin... so you need to test the data for "goodness of fit" to a line.
The slope of the line tells you L3... which is what you wanted to calculate.
Work out the slope by least squares regression.
...

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