Frank, W3LPL conducted two interesting experiments with WSPRlites on 20m from the US to Europe essentially. This article discusses the first test.
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 (19Hz in this case) feeding approximately the same power to the same antenna.
The first test uses two WSPRlites feeding the same antenna through a magic-T combiner producing a data set consisting of 900 pairs of SNR reports from Europe with only about 70 milliwatts from each WSPRlite at the antenna feed.
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 transmitter is approximately equal to that of the other, ie that the simultaneous difference observations should be close to zero in this scenario.
What of the distribution of the difference data?
Above is a frequency histogram of the distribution about the mean (0). Interpretation is frustrated by the discrete nature of the SNR statistic (1dB steps), it is asymmetric and a Shapiro-Wik test for normality gives a probability that it is normal p=1.4e-43.
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.
Nevertheless, we might expect that there is a relationship between the SNR reports for both transmitters, We might expect that SNR_W3GRF=SNR_W3LPL.
So, lets look at the data in a way that might expose such a relationship.
Above is a 3D plot of the observations which shows the count of spots for each combination of SNR due to the two transmitters. The chart shows us that whilst there were more spots at low SNR, the SNRs from both are almost always almost the same.
A small departure can be seen where a little ridge exists in front of the main data.
Lets look at in 2D. Continue reading W3LPL’s paired WSPRlite test – test 1