&gt;&quot;The null hypothesis would posit independent events with equal probability (the chance of an above-average and below-average year are equivalent).&quot;<p>Why should that be the null hypothesis? Is that a theory someone subscribes to? That would be a theory of no trends and no auto-correlation in temperature. I doubt you will find someone espousing such a theory, so why should we make something no one believes a null hypothesis? If you can find someone claiming that, I am interested in the reasoning.