What Statistical Test Determines Concentricity in Spherical Geophysics Data?

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In summary, The conversation is about a geophysics project where the speaker is analyzing a data set with multiple lineations on a globe or sphere. They are trying to determine if the lineations can be described by concentric circles around a specific pole. The process involves rotating the data set, fitting a z-plane through each lineation, and calculating the sum of squares of residuals to find the best-fit pole. The speaker now wants to come up with a hypothesis or a goodness-of-fit test to determine if this is the best description for the lineations.
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I am doing a geophysics project where I am analyzing a number of lineations on a globe / sphere. That is, I have a data set with many (70 - 180) sets of data points that are grouped together in lineations. I am trying to determine if the lineations are best described by concentric circles about a specific pole. To do this for every longitude/latitude value on the sphere I rotate the entire data set so that the chosen axis of rotation is now the z-axis. I then fit a z-plane through each lineation, which amounts to averaging the z values for each lineation after rotation. I also calculate the sum of the squares of the residuals (z_i - <z>)^2 for each lineation. I then calculate the 'best fit' pole by choosing the pole which minimizes the sum of the squares of the residuals of each lineation with their respective best-fit plane.

Now I wish to come up with a hypothesis test or a goodness-of-fit test to determine if the lineations are best described by concentric circles about this pole (as opposed to two or three poles or something else altogether).

Any ideas? Thanks.
 
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Goodness of fit applies to the graduation of a probability distribution only.
 

Related to What Statistical Test Determines Concentricity in Spherical Geophysics Data?

1. What is a hypothesis test and why is it important in scientific research?

A hypothesis test is a statistical method used to determine whether there is a significant difference between two or more groups or variables. It is important in scientific research because it allows scientists to make data-driven conclusions and to test the validity of their hypotheses. This helps to ensure that research findings are reliable and accurate.

2. How do I know which hypothesis test to use for my data?

The type of hypothesis test to use depends on several factors, including the research question, the type of data being analyzed, and the number of groups or variables being compared. It is important to consult with a statistician or refer to statistical textbooks and guides to determine the most appropriate test for your specific research question and data.

3. Can I use any hypothesis test for my data?

No, not all hypothesis tests are suitable for all types of data. Some tests are designed for specific types of data, such as categorical or continuous data. It is important to understand the assumptions and limitations of each test before applying it to your data.

4. What is the difference between a parametric and non-parametric hypothesis test?

A parametric hypothesis test assumes that the data follows a normal distribution, while a non-parametric test does not make this assumption. Parametric tests are more powerful and sensitive, but they require the data to meet certain assumptions. Non-parametric tests are less powerful but can be used for data that do not meet the assumptions of parametric tests.

5. How do I interpret the results of a hypothesis test?

The results of a hypothesis test include a p-value, which indicates the probability of obtaining the observed results if the null hypothesis (the hypothesis that there is no significant difference between groups) is true. A p-value of less than 0.05 is typically considered statistically significant, meaning there is a low probability of obtaining the observed results by chance alone. However, it is important to also consider the effect size and the practical significance of the results when interpreting the findings of a hypothesis test.

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