1. 0 Null Hypothesis H 0 : Albany temperatures anomalies from 1950-1980 not different from 0. Alternative Hypothesis H a : Temperature anomalies were negative* *Note that we formed anomalies with respect to the 1981-2010 climatology. Thus we test if 1950-1980 was significantly cooler than the 1981-2010. t Area under the curve gives the probability p(t< t crit ) t crit We reject the null hypothesis if the calculated t-value falls into the tail of the distribution. The p-value is chosen usually chosen to be small 0.1 0.05 0.01 are typical –p-values. We then say: “We reject the null-hypothesis at the level of significance of 10% (5%) (1%)” Calculated t

2. 0 Null Hypothesis H 0 : Albany temperatures anomalies from 1950-1980 not different from 0. Alternative Hypothesis H a : Temperature anomalies were different from zero t t crit Calculated t We cannot reject H 0 at the two-sided significance level of ‘p’-percent (e.g. 5%)

3. Hypothesis/ConclusionNull hypothesis H 0 trueNull hypothesis H 0 false Null hypothesis acceptedCorrect decisionFalse decision (Type II error) Null hypothesis rejected False decision (Type I error) Correct decision

4.  H 0 : Here we would reject H 0 for the given p-value (α = 0.05) Figure 5.1 from Wilks “Statistical Methods in Atmospheric Sciences” (2006) Calculated test value

5.  H 0 : Here we would accept H 0 for the given p-value (α = 0.05) Figure 5.1 from Wilks “Statistical Methods in Atmospheric Sciences” (2006) Calculated test value

6. Hypothesis/ConclusionNull hypothesis H 0 trueNull hypothesis H 0 false Null hypothesis acceptedCorrect decisionFalse decision (Type II error) Probability of this type of error is usually hard to quantify ( β‘beta’) Null hypothesis rejected False decision (Type I error) Probability of this error is given by the p-value ( α ‘alpha’) Correct decision

7. 5% significant, 1% not significant Error of second kind: Accept H0 despite change In mean. Null Hypothesis: No change in mean Null Hypothesis: All edible! Hypholoma fasciculare © Dieter Sydow Hypholoma capnoide A final remark on statistical hypothesis tests and decision making:

8. Climate Variability: El Niño - Southern Oscillation (SST: Sea Surface Temperature)

9. Source: http://www.climate.gov/news-features/climate-current-events/winter-temperatures-influenced-north-atlantic- oscillation-lahttp://www.climate.gov/news-features/climate-current-events/winter-temperatures-influenced-north-atlantic- oscillation-la (retrieved 2014-04-22) A negative phase of the NAO (Weaker Island Low and weaker Azores High) causes cooler than normal winter temperature. But other modes of variability affect the NA winter climate (Polar vortex, blocking events etc.) “This latest cold outbreak was one case where they [the Arctic Oscillation and NAO] were not in strong alignment; in early January 2014, the NAO index was near zero.” Quote from http://www.climate.gov/news-features/event- tracker/how-polar-vortex-related-arctic-oscillation (retrieved 2014-04-22)http://www.climate.gov/news-features/event- tracker/how-polar-vortex-related-arctic-oscillation

10. Positive Phase of the PNA Source: http://www.nc-climate.ncsu.edu/climate/patterns/PNA.html

11. Negative Phase of the PNA Source: http://www.nc-climate.ncsu.edu/climate/patterns/PNA.html