Frank, W3LPL conducted two interesting experiments with WSPRlites on 20m from the US to Europe essentially.

The first experiment was a calibration run if you like to explore the nature of simultaneous WSRP SNR reports for two transmitters using different call signs on slightly different frequencies simultaneously feeding approximately the same power to the same antenna.

This article is about the second test which he describes:

The second test uses a WSPRlite directly feeding the same stacked Yagis, and the second WSPRlite feeding nearly identical stacked Yagis that point directly through the other stack located four wavelengths directly in front. Power at each antenna was about 140 milliwatts for each WSPRlite.

The data for the test interval was extracted from DXplorer, and the statistic of main interest is the paired SNR differences, these are the differences in a report from the same station of the two signals in the same measurement WSPR interval.

There is an immediate temptation of compare the average difference, it is simple and quick. But, it is my experience that WSPR SNR data are not normally distributed and applying parametric statistics (ie statistical methods that depend on knowledge of the underlying distribution) is seriously flawed.

We might expect that whilst the observed SNR varies up and down with fading etc, that the SNR measured due to one antenna relative to the other depends on their gain in the direction of the observer. Even though the two identical antennas point in the same direction for this test, the proximity of one antenna to the other is likely to affect their relative gain in different directions.

What of the distribution of the difference data?

Above is a frequency histogram of the distribution about the mean (4.2). Each of the middle bars (0.675σ) should contain 25% of the 815 observations (204). It is clearly grossly asymmetric and is most unlikely to be normally distributed. A Shapiro-Wik test for normality gives a probability that it is normal p=4.3e-39.

So lets forget about parametric statistics based on normal distribution, means, standard deviation, Student’s t-test etc are unsound for making inferences because they depend on normality. Continue reading W3LPL’s paired WSPRlite test – test 2