The single sided ttest Null Hypothesis H 0

The single sided t-test Null Hypothesis H 0 : Albany temperatures anomalies from 1950 -1980 not different from 0. Alternative Hypothesis Ha : Temperature anomalies were negative* tcrit Calculated t t 0 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% Area under the curve gives the probability p(t< tcrit) *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.

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

TESTING A NULL HYPOTHESIS Hypothesis/Conclusio n Null hypothesis H 0 true Null hypothesis H 0 false Null hypothesis accepted Correct decision False decision (Type II error) Null hypothesis rejected False decision (Type I error) Correct decision

TEST FOR DIFFERENCES IN THE MEAN � H 0 : Here we would reject H 0 for the given p-value (α = 0. 05) Calculated test value Figure 5. 1 from Wilks “Statistical Methods in Atmospheric Sciences” (2006)

TEST FOR DIFFERENCES IN THE MEAN � H 0 : Here we would accept H 0 for the given p-value (α = 0. 05) Calculated test value Figure 5. 1 from Wilks “Statistical Methods in Atmospheric Sciences” (2006)

TESTING A NULL HYPOTHESIS Hypothesis/Conclusio n Null hypothesis H 0 true Null hypothesis H 0 false Null hypothesis accepted Correct decision False 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

A final remark on statistical hypothesis tests and decision making: Null Hypothesis: All edible! Null Hypothesis: No change in mean 5% significant, 1% not significant Error of second kind: Accept H 0 despite change In mean. © Dieter Sydow Hypholoma fasciculare Hypholoma capnoide

Climate Variability: El Niño - Southern Oscillation EL NIÑO REGION SST DEPARTURES (ANOMALIES) (OC) MEASURED IN DIFFERENT REGIONS OF THE TROPICAL PACIFIC

EFFECTS OF NAO ON WINTER TEMPERATURES 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) Source: http: //www. climate. gov/news-features/climate-current-events/winter-temperatures-influenced-north-atlanticoscillation-la (retrieved 2014 -04 -22)

PACIFIC NORTH AMERICAN PATTERN Positive Phase of the PNA Source: http: //www. nc-climate. ncsu. edu/climate/patterns/PNA. html

PACIFIC NORTH AMERICAN PATTERN Negative Phase of the PNA Source: http: //www. nc-climate. ncsu. edu/climate/patterns/PNA. html

TIME SERIES OF THE PNA INDEX