The ratio of trend estimate to its standard deviation, called the t - ratio, is used as measure of
the statistically significance of the trend.
Not exact matches
The total variance in the data gives an upper limit to the errors, and using that upper limit we can compute a
statistically reliable estimate
of the
significance of the
trend.
I am especially interested in the mathematical details outlined in this sentence; «The total variance in the data gives an upper limit to the errors, and using that upper limit we can compute a
statistically reliable estimate
of the
significance of the
trend.»
First, Happer mentions statistical
significance, but global surface temperature
trends are rarely if ever
statistically significant (at a 95 % confidence level) over periods as short as a decade, even in the presence
of an underlying long - term warming
trend, because
of the natural variability and noise in the climate system.
However, none
of the
trends is
statistically significantly different from a Zero
trend, applying a 2 - sigma
significance threshold.
I asked for the evidence for this assertion, and I showed with some data sets that there are discernible
trends over the last 16 years in most
of those sets, which are not
statistically significant at a
significance level
of 95 %, though.
The absence
of a
statistically significant
trend (at a
significance level
of 5 per cent) means that if the null hypothesis true, there is at least a 5 per cent chance
of a Type 1 error.
There will never have been
statistically significant global warming is the last few years, because statistical
significance is heavily dependent on the amount
of data points and hence the length
of the record you are
trending.
Those scatter diagrams as presented simply show a lot
of scatter and I doubt that the
trend lines have any statistical
significance or that any features can be implied
statistically, but then I am not a statistician — in fact not even close.
This is nothing but an attempt to discredit the
significance of the
trend, something you disparage but which can be confirmed
statistically.
Whether a
trend is
statistically significant does not depend only on the number
of years, it depends also on the frequency
of data collection, the amount
of noise in the system (and the noise in the data collection system), the size
of the
trend (a smaller
trend will take longer to achieve
significance), and the amount
of autocorrelation in the data series.
I am getting hungry so later after breakfast I will get back to you to explain the
significance of the graphs with respect to pauses and from how far back you can determine when positive
trends are
statistically significant.
The lack
of statistical
significance in temperate
trends since 1998 is at least partly a statistical power issue - there is not enough data (since 98) to achieve a
statistically significant result, even if there has been warming.