[See notes on Statistical Inferencing, in relation to this analysis, here.
See here for follow-up Advanced Analysis. ]
The simplest form of relationship between two sets of figures (in this case vaccination rates and mortality rates) is a 'linear', or straight-line
relationship. This means it's represented by a straight line through the data plotted as X-Y points on a graph. A straight-line fit is based on
the idea that when X doubles, Y also doubles; when X is five times as much, Y is five times as much; etc (roughly, for real-life data - that's why
the X-Y points are scattered around the line). We'll do a linear relationship fit first, then show that an exponential graph fits the data even better.
The figures collected and listed by Dr Cunningham are copied below for your convenience, so that they can be cut-and-pasted into
a statistical analysis tool you can find here.
Simply copy-and-paste the column of figures headed 'X' (the percentage vaccination rates) into the box headed 'X Values' and the column
of figures headed 'Y' (the death rates per million) into the box headed 'Y Values'.
[Don't copy the X or Y, and be sure to copy all the numbers - preferably in one go.]
Look at these two graphs:
The first is a linear (straight-line) 'best fit' to the data, as used in our calculation above.
The second is a linear best-fit of logarithms
(to base 10) of death rates against vaccination percentages.
It's very clear, just by looking at them, that the second graph is a better straight-line fit than the first.
of the Y-axis data are a good straight-line fit to the X-values, this tells us that Y is exponentially
related to X.
In other words, our deaths-per-million show an exponential
increase in relation to increases in vaccination percentages.
So now we'll repeat our earlier test, but using the logarithms
of our deaths-per-million for our Y values.
Those logarithm values can be read off any student calculator: just press the 'log' button, enter the original Y-value, and you get the log Y-value.
For example, our first original Y-value was 28. So we press 'log', tap in '28', and press '='. We get the answer 1.44716 (when rounded).
This has all been done for you, in the Y-values below (though you can check them). You just have to copy-and-paste the X's and the Y's, as before.
As before paste both sets of 20 figures into the 'X Value' and 'Y Value'
then click on the 'Calculate R' button. This will produce the Pearson's Correlation Coefficient, as before:
this time it should give you a value of 0.8249, which is very
high for a set of 20 data pairs.
Scroll down past the calculations and you'll find it says:
"This is a strong positive correlation...".
To get a figure for statistical significance of this result, click on the link that says:
"Click here to calculate a p value". You'll be asked to input the R value (0.8249) and the number of data pairs (20) [You can also
choose a significance level if you like - if so, choose 0.01 - but we'd really need a 0.00001 option for the significance of this result!]
The calculator will tell you the probability of this R for 20 data pairs: <0.00001. That's less than 1 in 100,000 likelihood
that this result could happen by chance - in other words, a 99.999% probability that there's an exponential link between over-65s
influenza vaccination rate and Covid-19 death rate per million of population
This graph shows the calculated best-fit exponential line relating death rate to vaccination rate.
Now, we're always told to remember that "Correlation doesn't necessarily imply causation". We've shown that the link between these two
factors is very, very unlikely to be coincidence (it's significant at 4.25-sigma level, for those who are into stats, and that's pretty significant)
- it's very difficult to imagine what other factor could cause these two to be so strongly linked. (There will of course be other local factors
which would make this less than an absolute '+1' correlation).
We shouldn't forget, either, a previous finding reported in this study
showed 36% increase in risk of coronavirus (Prior to Covid-19) and 51% increased risk of another virus in those who'd been give influenza vaccine, compared to unvaccinated subjects.
This tends to reinforce the likelihood of the influenza vaccine being a causative, or at least contributory, factor for other illnesses.
The Bottom Line: There is very significant evidence that death rate from Covid-19 is exponentially linked to over-65s influenza vaccination rate, compared across Europe.