My R script merely finds the first time the temperature trend turns positive since last data point. My null hypothesis is when does the trend turn positive since the last data point. I'm not trying to be a smart ass, I'm just wanting to make clear I'm not making any grand claims, except that the most rigorous data, with the tightest confidence intervals (measured in fractions of K instead of multiple K's), says that nearly every model previous of the IPCC's 5th assessment was wrong. None of the models predicted a 2 decade lapse in warming. We don't know as much as we thought we knew.
[EDIT] I don't mean that the models were completely wrong, merely that they were missing some key variable to explain 19 years and 6 months of flat global temperature trends.
> My null hypothesis is when does the trend turn positive since the last data point. I'm not trying to be a smart ass
I'm sure you're not, and certainly you seem to be making a good faith effort to analyse the data, but I'm afraid you're just doing it wrong. You can't just keep testing up to x data points till you hit a significance level and then say "this proves x-1 doesn't show the trend".
Imagine you were measuring the height of waves on a beach as the tide comes in. After 20 measurements, you can see a significant height difference, showing the tide is indeed rising. Now imagine if your stated conclusion was, "the tide hasn't been coming in for the last 19 waves".
It would be ridiculous, right? That's pretty much what you're doing here. If adding more data makes your conclusion worse, you're doing it wrong.
The correct way to test this is to say, "30 years of data shows a rising trend. Is the past 19 years significantly different to this?". Then your null hypothesis is that the trend remains the same and when you add more data your conclusion (either way) becomes stronger.
Since you've shown enough interest to create an R script to test this data, I sincerely hope you'll have enough interest now to test it properly and share what you find. Good luck!
Thank you for the great response, certainly good stuff to think about. But I think I did not make myself clear. The RSS trop data shows there is a 1.2K/century trend. My interest was in "the pause" over the last ~20 years.
So the metaphor becomes, imagine you were told the tide was coming in at a steady rate and that CO2 was causing it. Then for 19.5 years CO2 continued to grow at a steady rate, but the tide didn't come any closer during that period. That is certainly interesting in an of itself; and needs an explanation.
You made yourself clear. To follow the metaphor, if the increase in tidal levels over the past 19.5 years were significantly different to the increase in tidal levels over (say) the past 30 years then it needs an explanation.
If they were not, then the simple explanation is that 19.5 years is not enough data to draw any conclusions. That's just how it works. You can't draw a conclusion from a lack of data.
EDIT: Forgot to say: at the moment, what you are trying to show is that there has been no significant warming over the past 19 years. Your null hypothesis is that there has been no warming over the past 19 years. When what you're trying to show is the same as your null hypothesis, you're doing something wrong.
If merpnderp were to say the null hypothesis is that the longer-term trend (1.2K/century as stated) should continue as expected even into recent decades (or perhaps "correct" the data for that relationship because we're assuming it's not up for debate), then the data for the past ~20 years would show a departure from that hypothesis, would it not? In that case, the point being shown is different from the null hypothesis, and may be significant. Am I missing something?
Nope, you're missing nothing. That's absolutely correct. The problem (from merpnderp's point of view) is that the data for the past ~20 years doesn't differ significantly from the 30 year (or longer) trend. It's using the lack of significance to mean something significant which is the root of the error.
[EDIT] I don't mean that the models were completely wrong, merely that they were missing some key variable to explain 19 years and 6 months of flat global temperature trends.