01-20-24, 01:49 PM

From HERE

Re: Fig 2

Variance of a Gaussian distribution is an indirect indicator of the certainty of the value of the average. See the attached photo. With the wide range of data values shown in Fig. 2 (which is used to calculate the variance) the variance of the distribution is high, meaning that the certainty of the value of the GAT is low.

I believe this is one reason that climate science is so adamant about not using the variance of measurement data as the required partner for making sense of an average. Every statistics textbook I have collected over the years say you *must* have both the average and the variance to understand a Gaussian distribution. If the distribution is not Gaussian then you must use a different set of statistical descriptors such as the 5-number descriptor.

As you add random variables into your data set the variance increases, e.g. combining Southern Hemisphere temperature data with Northern Hemisphere data. This happens whether you use absolute temps or anomalies since anomalies inherit the variances of the components used to find the anomalies. Var(X+Y) = Var(X-Y) = Var(X) + Var(Y).

There *is* a reason why climate science ignores variances in their statistical analyses and try to get by using only the average. That way they can pretend their averages are 100% accurate and therefore their anomalies are 100% accurate. In fact, I’ve never seen a climate science paper analyze whether the various temperature data sets are even Gaussian at all! My guess is that they are multi-modal (e.g. SH vs NH would be just like the heights of Shetland ponies combined with the heights of quarter horses) meaning the average is pretty much meaningless in physical terms.

lo_hi_variance

Re: Fig 2

Variance of a Gaussian distribution is an indirect indicator of the certainty of the value of the average. See the attached photo. With the wide range of data values shown in Fig. 2 (which is used to calculate the variance) the variance of the distribution is high, meaning that the certainty of the value of the GAT is low.

I believe this is one reason that climate science is so adamant about not using the variance of measurement data as the required partner for making sense of an average. Every statistics textbook I have collected over the years say you *must* have both the average and the variance to understand a Gaussian distribution. If the distribution is not Gaussian then you must use a different set of statistical descriptors such as the 5-number descriptor.

As you add random variables into your data set the variance increases, e.g. combining Southern Hemisphere temperature data with Northern Hemisphere data. This happens whether you use absolute temps or anomalies since anomalies inherit the variances of the components used to find the anomalies. Var(X+Y) = Var(X-Y) = Var(X) + Var(Y).

There *is* a reason why climate science ignores variances in their statistical analyses and try to get by using only the average. That way they can pretend their averages are 100% accurate and therefore their anomalies are 100% accurate. In fact, I’ve never seen a climate science paper analyze whether the various temperature data sets are even Gaussian at all! My guess is that they are multi-modal (e.g. SH vs NH would be just like the heights of Shetland ponies combined with the heights of quarter horses) meaning the average is pretty much meaningless in physical terms.

lo_hi_variance

“A theory that is not refutable by any conceivable event is non-scientific.” – Karl Popper

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