In sci.skeptic Claudius Denk <***@sbcglobal.net> wrote:
[...]
Post by Claudius DenkPost by Surfer- Global mean troposphere temperature has an upward trend
linehttp://pielkeclimatesci.files.wordpress.com/2010/08/0710_graf.jpg?w=5...
You must have a really good imagination to see anything significant in
this graph. I don't see it, but then maybe my imaginative abilities
are not as well developed as are yours.
[...]
Mostly blue on the left, mostly red on the right?
But, sure, judging things by eye is for people without numerical skills.
So let's do some time series analysis.
Here's the LOTI data for 1880-2010. For each month since Jun 1880 the
land+sea average global temperature is compared with the average temps
for the baseline period 1951-1980.
If you plot this out (judging things by eye again?) you can see ups
and downs as in the .jpg above -- and as in most of this type of data.
But a dispassionate time-series adjusted regression can spot a trend
if there is one.
We'll set the regression to throw out any points that are too far
(2 sigma) in either direction from the estimated line.
We'll adjust the confidence interval calculations to take into
account any auto-correlation (i.e. tendency for temps to stay high
year-on-year or stay low year-on-year).
We'll perform 2 methods to detect a trend. (a) TS estimate of slope
of trend line; (b) much more robust non-parametric test involving
comparing how often temp shows persistent increase year-on-year or
persistent decrease year-on-year.
Here's the data for any that want to check (the Puppeteer points his
eyes at each other at this point).
<http://data.giss.nasa.gov/work/modelEt/time_series/work/tmp.4_observLOTI_12_1880_2020_1951_1980-0/LTglb.txt>
#annual global mean anomalies vs 1951-1980
#year (12 month running mean)
#year Global_Mean
LOTI 1880.500000 -0.2870392203
LOTI 1880.583374 -0.2645724416
LOTI 1880.666626 -0.2594057918
LOTI 1880.750000 -0.2419331670
LOTI 1880.833374 -0.2229541987
LOTI 1880.916626 -0.2074880898
LOTI 1881.000000 -0.2043048292
LOTI 1881.083374 -0.1964165121
LOTI 1881.166626 -0.1936120242
LOTI 1881.250000 -0.1932898313
LOTI 1881.333374 -0.1950195283
LOTI 1881.416626 -0.2056796253
LOTI 1881.500000 -0.2045075744
LOTI 1881.583374 -0.2042157501
LOTI 1881.666626 -0.1837380528
LOTI 1881.750000 -0.1888128072
LOTI 1881.833374 -0.2099880725
LOTI 1881.916626 -0.2213578075
LOTI 1882.000000 -0.2220467031
LOTI 1882.083374 -0.2356183976
LOTI 1882.166626 -0.2390995473
LOTI 1882.250000 -0.2357863933
LOTI 1882.333374 -0.2439881116
LOTI 1882.416626 -0.2459754199
LOTI 1882.500000 -0.2695665359
LOTI 1882.583374 -0.2920927703
LOTI 1882.666626 -0.3194094896
LOTI 1882.750000 -0.3170636892
LOTI 1882.833374 -0.3069239855
LOTI 1882.916626 -0.3056268096
LOTI 1883.000000 -0.2877355516
LOTI 1883.083374 -0.2703407705
LOTI 1883.166626 -0.2773847878
LOTI 1883.250000 -0.2839022875
LOTI 1883.333374 -0.2806184590
LOTI 1883.416626 -0.2750584781
LOTI 1883.500000 -0.2534487844
LOTI 1883.583374 -0.2424502820
LOTI 1883.666626 -0.2275167108
LOTI 1883.750000 -0.2503300905
LOTI 1883.833374 -0.2686351538
LOTI 1883.916626 -0.2824572623
LOTI 1884.000000 -0.3008826971
LOTI 1884.083374 -0.3164333701
LOTI 1884.166626 -0.3137388825
LOTI 1884.250000 -0.3140973747
LOTI 1884.333374 -0.3127537072
LOTI 1884.416626 -0.3158432543
LOTI 1884.500000 -0.3215940297
LOTI 1884.583374 -0.3465836644
LOTI 1884.666626 -0.3558251858
LOTI 1884.750000 -0.3431555927
LOTI 1884.833374 -0.3428834081
LOTI 1884.916626 -0.3390768468
LOTI 1885.000000 -0.3462871611
LOTI 1885.083374 -0.3464398980
LOTI 1885.166626 -0.3501314819
LOTI 1885.250000 -0.3442657590
LOTI 1885.333374 -0.3411328495
LOTI 1885.416626 -0.3341733217
LOTI 1885.500000 -0.3137557805
LOTI 1885.583374 -0.3004218340
LOTI 1885.666626 -0.3119675815
LOTI 1885.750000 -0.3225693107
LOTI 1885.833374 -0.3075792193
LOTI 1885.916626 -0.2961017787
LOTI 1886.000000 -0.2881151736
LOTI 1886.083374 -0.2701530755
LOTI 1886.166626 -0.2660839558
LOTI 1886.250000 -0.2623470724
LOTI 1886.333374 -0.2681814730
LOTI 1886.416626 -0.2732165754
LOTI 1886.500000 -0.2914069891
LOTI 1886.583374 -0.3107959032
LOTI 1886.666626 -0.3193999827
LOTI 1886.750000 -0.3235819042
LOTI 1886.833374 -0.3423824310
LOTI 1886.916626 -0.3495471179
LOTI 1887.000000 -0.3391516805
LOTI 1887.083374 -0.3417507410
LOTI 1887.166626 -0.3477037251
LOTI 1887.250000 -0.3505294025
LOTI 1887.333374 -0.3551076949
LOTI 1887.416626 -0.3578089476
LOTI 1887.500000 -0.3665013015
LOTI 1887.583374 -0.3451480567
LOTI 1887.666626 -0.3399815559
LOTI 1887.750000 -0.3464401662
LOTI 1887.833374 -0.3381546736
LOTI 1887.916626 -0.3359285295
LOTI 1888.000000 -0.3369951248
LOTI 1888.083374 -0.3422552049
LOTI 1888.166626 -0.3357232809
LOTI 1888.250000 -0.3307074904
LOTI 1888.333374 -0.3052336872
LOTI 1888.416626 -0.2776562572
LOTI 1888.500000 -0.2609550357
LOTI 1888.583374 -0.2456672639
LOTI 1888.666626 -0.1956738234
LOTI 1888.750000 -0.1590766311
LOTI 1888.833374 -0.1303786635
LOTI 1888.916626 -0.1110890582
LOTI 1889.000000 -0.1015466750
LOTI 1889.083374 -0.1013996750
LOTI 1889.166626 -0.1042585969
LOTI 1889.250000 -0.1044155136
LOTI 1889.333374 -0.1202525869
LOTI 1889.416626 -0.1492130458
LOTI 1889.500000 -0.1587348580
LOTI 1889.583374 -0.1814049482
LOTI 1889.666626 -0.2266232371
LOTI 1889.750000 -0.2541835904
LOTI 1889.833374 -0.2839559913
LOTI 1889.916626 -0.3215562403
LOTI 1890.000000 -0.3429694474
LOTI 1890.083374 -0.3543447852
LOTI 1890.166626 -0.3646324575
LOTI 1890.250000 -0.3801426888
LOTI 1890.333374 -0.3743545115
LOTI 1890.416626 -0.3875130415
LOTI 1890.500000 -0.3844815493
LOTI 1890.583374 -0.3831771612
LOTI 1890.666626 -0.3934957385
LOTI 1890.750000 -0.3774314523
LOTI 1890.833374 -0.3733400404
LOTI 1890.916626 -0.3480086923
LOTI 1891.000000 -0.3347075582
LOTI 1891.083374 -0.3298490047
LOTI 1891.166626 -0.3159192204
LOTI 1891.250000 -0.3008930683
LOTI 1891.333374 -0.3037165999
LOTI 1891.416626 -0.2906368971
LOTI 1891.500000 -0.2741328776
LOTI 1891.583374 -0.2661935091
LOTI 1891.666626 -0.2308675498
LOTI 1891.750000 -0.2455904782
LOTI 1891.833374 -0.2566130459
LOTI 1891.916626 -0.2674593031
LOTI 1892.000000 -0.2668704689
LOTI 1892.083374 -0.2727688849
LOTI 1892.166626 -0.2806944847
LOTI 1892.250000 -0.2825532854
LOTI 1892.333374 -0.2835151851
LOTI 1892.416626 -0.2868277133
LOTI 1892.500000 -0.3130524457
LOTI 1892.583374 -0.3485340774
LOTI 1892.666626 -0.3850739598
LOTI 1892.750000 -0.3734673858
LOTI 1892.833374 -0.3656685650
LOTI 1892.916626 -0.3703260124
LOTI 1893.000000 -0.3757945001
LOTI 1893.083374 -0.3590318263
LOTI 1893.166626 -0.3564615250
LOTI 1893.250000 -0.3594401479
LOTI 1893.333374 -0.3498216569
LOTI 1893.416626 -0.3299094141
LOTI 1893.500000 -0.3218286633
LOTI 1893.583374 -0.2969776392
LOTI 1893.666626 -0.2789469659
LOTI 1893.750000 -0.2818368077
LOTI 1893.833374 -0.2874177396
LOTI 1893.916626 -0.2821471095
LOTI 1894.000000 -0.2936539948
LOTI 1894.083374 -0.2993546724
LOTI 1894.166626 -0.2963675559
LOTI 1894.250000 -0.3040520847
LOTI 1894.333374 -0.3118915260
LOTI 1894.416626 -0.3268879354
LOTI 1894.500000 -0.3210047185
LOTI 1894.583374 -0.3209303021
LOTI 1894.666626 -0.3294200599
LOTI 1894.750000 -0.3334300518
LOTI 1894.833374 -0.3194440007
LOTI 1894.916626 -0.3164763749
LOTI 1895.000000 -0.2987016737
LOTI 1895.083374 -0.2979493737
LOTI 1895.166626 -0.2936100662
LOTI 1895.250000 -0.2734549940
LOTI 1895.333374 -0.2644051611
LOTI 1895.416626 -0.2424491644
LOTI 1895.500000 -0.2332325429
LOTI 1895.583374 -0.2115422040
LOTI 1895.666626 -0.1886577755
LOTI 1895.750000 -0.1896392554
LOTI 1895.833374 -0.1994296163
LOTI 1895.916626 -0.1872178018
LOTI 1896.000000 -0.1785040647
LOTI 1896.083374 -0.1664894372
LOTI 1896.166626 -0.1575461328
LOTI 1896.250000 -0.1531639099
LOTI 1896.333374 -0.1373832673
LOTI 1896.416626 -0.1392959952
LOTI 1896.500000 -0.1320005208
LOTI 1896.583374 -0.1236419305
LOTI 1896.666626 -0.1232021004
LOTI 1896.750000 -0.1087157428
LOTI 1896.833374 -0.8062408864E-01
LOTI 1896.916626 -0.6733881682E-01
LOTI 1897.000000 -0.6659699231E-01
LOTI 1897.083374 -0.6542234868E-01
LOTI 1897.166626 -0.6480225176E-01
LOTI 1897.250000 -0.6851546466E-01
LOTI 1897.333374 -0.7950954884E-01
LOTI 1897.416626 -0.8445990831E-01
LOTI 1897.500000 -0.8792933077E-01
LOTI 1897.583374 -0.7774527371E-01
LOTI 1897.666626 -0.8618669957E-01
LOTI 1897.750000 -0.1125146300
LOTI 1897.833374 -0.1297713667
LOTI 1897.916626 -0.1581225544
LOTI 1898.000000 -0.1637983173
LOTI 1898.083374 -0.1778985709
LOTI 1898.166626 -0.1907092035
LOTI 1898.250000 -0.1978401989
LOTI 1898.333374 -0.2121916413
LOTI 1898.416626 -0.2268027514
LOTI 1898.500000 -0.2411189228
LOTI 1898.583374 -0.2548599243
LOTI 1898.666626 -0.2619188428
LOTI 1898.750000 -0.2485789508
LOTI 1898.833374 -0.2395185679
LOTI 1898.916626 -0.2252092510
LOTI 1899.000000 -0.2324144691
LOTI 1899.083374 -0.2245644480
LOTI 1899.166626 -0.2112316936
LOTI 1899.250000 -0.2004254460
LOTI 1899.333374 -0.1785334945
LOTI 1899.416626 -0.1358452737
LOTI 1899.500000 -0.1308817714
LOTI 1899.583374 -0.1400587857
LOTI 1899.666626 -0.1032507718
LOTI 1899.750000 -0.7679914683E-01
LOTI 1899.833374 -0.7228151709E-01
LOTI 1899.916626 -0.6413201243E-01
LOTI 1900.000000 -0.4854213074E-01
LOTI 1900.083374 -0.4678838328E-01
LOTI 1900.166626 -0.4843966290E-01
LOTI 1900.250000 -0.4701300710E-01
LOTI 1900.333374 -0.4397628084E-01
LOTI 1900.416626 -0.6523643434E-01
LOTI 1900.500000 -0.5159040913E-01
LOTI 1900.583374 -0.4002730921E-01
LOTI 1900.666626 -0.4527903348E-01
LOTI 1900.750000 -0.4193184525E-01
LOTI 1900.833374 -0.3455120325E-01
LOTI 1900.916626 -0.4074757919E-01
LOTI 1901.000000 -0.4554763809E-01
LOTI 1901.083374 -0.5001511797E-01
LOTI 1901.166626 -0.5768522620E-01
LOTI 1901.250000 -0.7148895413E-01
LOTI 1901.333374 -0.9354954958E-01
LOTI 1901.416626 -0.1024901718
LOTI 1901.500000 -0.1171473190
LOTI 1901.583374 -0.1155539751
LOTI 1901.666626 -0.1116915345
LOTI 1901.750000 -0.1372789592
LOTI 1901.833374 -0.1560280025
LOTI 1901.916626 -0.1673339307
LOTI 1902.000000 -0.1794175655
LOTI 1902.083374 -0.1824641973
LOTI 1902.166626 -0.1886146367
LOTI 1902.250000 -0.1910230070
LOTI 1902.333374 -0.1970313340
LOTI 1902.416626 -0.2113285810
LOTI 1902.500000 -0.2260259539
LOTI 1902.583374 -0.2329125106
LOTI 1902.666626 -0.2317448705
LOTI 1902.750000 -0.2205458730
LOTI 1902.833374 -0.2344582677
LOTI 1902.916626 -0.2410008609
LOTI 1903.000000 -0.2569817305
LOTI 1903.083374 -0.2644364536
LOTI 1903.166626 -0.2740600109
LOTI 1903.250000 -0.2944988906
LOTI 1903.333374 -0.3189807236
LOTI 1903.416626 -0.3100824356
LOTI 1903.500000 -0.3060012162
LOTI 1903.583374 -0.3303214610
LOTI 1903.666626 -0.3724200726
LOTI 1903.750000 -0.3853571713
LOTI 1903.833374 -0.3848529160
LOTI 1903.916626 -0.3980813920
LOTI 1904.000000 -0.3829942644
LOTI 1904.083374 -0.3978652060
LOTI 1904.166626 -0.3993251622
LOTI 1904.250000 -0.3870683610
LOTI 1904.333374 -0.3854939342
LOTI 1904.416626 -0.3675279617
LOTI 1904.500000 -0.3565202355
LOTI 1904.583374 -0.3365268707
LOTI 1904.666626 -0.3446375728
LOTI 1904.750000 -0.3339640796
LOTI 1904.833374 -0.3242962360
LOTI 1904.916626 -0.3051163852
LOTI 1905.000000 -0.3041485548
LOTI 1905.083374 -0.2973368466
LOTI 1905.166626 -0.2735281885
LOTI 1905.250000 -0.2489298582
LOTI 1905.333374 -0.2340748012
LOTI 1905.416626 -0.2322801799
LOTI 1905.500000 -0.2261575311
LOTI 1905.583374 -0.2229665518
LOTI 1905.666626 -0.2026933581
LOTI 1905.750000 -0.2077642828
LOTI 1905.833374 -0.1812924445
LOTI 1905.916626 -0.1736800820
LOTI 1906.000000 -0.1651622206
LOTI 1906.083374 -0.1579279155
LOTI 1906.166626 -0.1587706208
LOTI 1906.250000 -0.1714507192
LOTI 1906.333374 -0.1669769287
LOTI 1906.416626 -0.1905267090
LOTI 1906.500000 -0.1832705438
LOTI 1906.583374 -0.1960975379
LOTI 1906.666626 -0.2086037099
LOTI 1906.750000 -0.2116245925
LOTI 1906.833374 -0.2445718944
LOTI 1906.916626 -0.2647938132
LOTI 1907.000000 -0.2874837518
LOTI 1907.083374 -0.3004579246
LOTI 1907.166626 -0.3403464854
LOTI 1907.250000 -0.3466707766
LOTI 1907.333374 -0.3549684584
LOTI 1907.416626 -0.3601937294
LOTI 1907.500000 -0.3871044517
LOTI 1907.583374 -0.3850499690
LOTI 1907.666626 -0.3664262295
LOTI 1907.750000 -0.3806443214
LOTI 1907.833374 -0.3770241439
LOTI 1907.916626 -0.3627473712
LOTI 1908.000000 -0.3368875086
LOTI 1908.083374 -0.3259939849
LOTI 1908.166626 -0.3004060686
LOTI 1908.250000 -0.2846394181
LOTI 1908.333374 -0.2864517570
LOTI 1908.416626 -0.2849734724
LOTI 1908.500000 -0.2831865549
LOTI 1908.583374 -0.2966278493
LOTI 1908.666626 -0.3072300255
LOTI 1908.750000 -0.3058762252
LOTI 1908.833374 -0.3155920804
LOTI 1908.916626 -0.3318843246
LOTI 1909.000000 -0.3522506356
LOTI 1909.083374 -0.3594977856
LOTI 1909.166626 -0.3489185870
LOTI 1909.250000 -0.3589918911
LOTI 1909.333374 -0.3515112400
LOTI 1909.416626 -0.3351629674
LOTI 1909.500000 -0.3362783492
LOTI 1909.583374 -0.3175412714
LOTI 1909.666626 -0.3124439418
LOTI 1909.750000 -0.3058677614
LOTI 1909.833374 -0.2939391434
LOTI 1909.916626 -0.2762710750
LOTI 1910.000000 -0.2623834312
LOTI 1910.083374 -0.2449323982
LOTI 1910.166626 -0.2579781115
LOTI 1910.250000 -0.2602362633
LOTI 1910.333374 -0.2703239024
LOTI 1910.416626 -0.2858377695
LOTI 1910.500000 -0.2983848155
LOTI 1910.583374 -0.3156846464
LOTI 1910.666626 -0.3292639554
LOTI 1910.750000 -0.3426596224
LOTI 1910.833374 -0.3591892123
LOTI 1910.916626 -0.3705114126
LOTI 1911.000000 -0.3745774329
LOTI 1911.083374 -0.3784351647
LOTI 1911.166626 -0.3707291186
LOTI 1911.250000 -0.3631630838
LOTI 1911.333374 -0.3518798649
LOTI 1911.416626 -0.3374021947
LOTI 1911.500000 -0.3056381941
LOTI 1911.583374 -0.2788065970
LOTI 1911.666626 -0.2503005266
LOTI 1911.750000 -0.2401050925
LOTI 1911.833374 -0.2161459923
LOTI 1911.916626 -0.2060642242
LOTI 1912.000000 -0.2019743621
LOTI 1912.083374 -0.2264250517
LOTI 1912.166626 -0.2741774023
LOTI 1912.250000 -0.2950242460
LOTI 1912.333374 -0.3270427287
LOTI 1912.416626 -0.3411716819
LOTI 1912.500000 -0.3544026911
LOTI 1912.583374 -0.3666979969
LOTI 1912.666626 -0.3851347864
LOTI 1912.750000 -0.3876784444
LOTI 1912.833374 -0.3951779604
LOTI 1912.916626 -0.3989342153
LOTI 1913.000000 -0.4254081249
LOTI 1913.083374 -0.4143212140
LOTI 1913.166626 -0.3799566031
LOTI 1913.250000 -0.3622018993
LOTI 1913.333374 -0.3471803367
LOTI 1913.416626 -0.3368377388
LOTI 1913.500000 -0.3076281548
LOTI 1913.583374 -0.2813883126
LOTI 1913.666626 -0.2619502842
LOTI 1913.750000 -0.2462474108
LOTI 1913.833374 -0.2349800169
LOTI 1913.916626 -0.2158919722
LOTI 1914.000000 -0.1842430681
LOTI 1914.083374 -0.1766611785
LOTI 1914.166626 -0.1682290435
LOTI 1914.250000 -0.1631165743
LOTI 1914.333374 -0.1369271576
LOTI 1914.416626 -0.1332399100
LOTI 1914.500000 -0.1459093392
LOTI 1914.583374 -0.1584531367
LOTI 1914.666626 -0.1564395130
LOTI 1914.750000 -0.1525038779
LOTI 1914.833374 -0.1398409307
LOTI 1914.916626 -0.1417518407
LOTI 1915.000000 -0.1367123574
LOTI 1915.083374 -0.1230002418
LOTI 1915.166626 -0.1414299160
LOTI 1915.250000 -0.1327419728
LOTI 1915.333374 -0.1427819431
LOTI 1915.416626 -0.1325172633
LOTI 1915.500000 -0.1407100856
LOTI 1915.583374 -0.1382115632
LOTI 1915.666626 -0.1437764168
LOTI 1915.750000 -0.1587108374
LOTI 1915.833374 -0.1845599562
LOTI 1915.916626 -0.2135958076
LOTI 1916.000000 -0.2368515879
LOTI 1916.083374 -0.2541532218
LOTI 1916.166626 -0.2433175743
LOTI 1916.250000 -0.2711676061
LOTI 1916.333374 -0.2737989426
LOTI 1916.416626 -0.2974682152
LOTI 1916.500000 -0.3336951733
LOTI 1916.583374 -0.3533226252
LOTI 1916.666626 -0.3838029504
LOTI 1916.750000 -0.3938223124
LOTI 1916.833374 -0.3981635869
LOTI 1916.916626 -0.3985484242
LOTI 1917.000000 -0.3992471099
LOTI 1917.083374 -0.3824192584
LOTI 1917.166626 -0.3857887685
LOTI 1917.250000 -0.3784722090
LOTI 1917.333374 -0.3898594975
LOTI 1917.416626 -0.3830710948
LOTI 1917.500000 -0.3835049868
LOTI 1917.583374 -0.3905181885
LOTI 1917.666626 -0.3804565668
LOTI 1917.750000 -0.3643713593
LOTI 1917.833374 -0.3669557273
LOTI 1917.916626 -0.3713503480
LOTI 1918.000000 -0.3612268865
LOTI 1918.083374 -0.3685966134
LOTI 1918.166626 -0.3936119080
LOTI 1918.250000 -0.3833328784
LOTI 1918.333374 -0.3537890315
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LOTI 1995.750000 0.3200929761
LOTI 1995.833374 0.3100895584
LOTI 1995.916626 0.3210239112
LOTI 1996.000000 0.3041326106
LOTI 1996.083374 0.2973635793
LOTI 1996.166626 0.3063247800
LOTI 1996.250000 0.3100617826
LOTI 1996.333374 0.2885059714
LOTI 1996.416626 0.2871877253
LOTI 1996.500000 0.2934322953
LOTI 1996.583374 0.2935825586
LOTI 1996.666626 0.2804166377
LOTI 1996.750000 0.2911760211
LOTI 1996.833374 0.2940318584
LOTI 1996.916626 0.3028585911
LOTI 1997.000000 0.3328912556
LOTI 1997.083374 0.3197345734
LOTI 1997.166626 0.3083647192
LOTI 1997.250000 0.3177514076
LOTI 1997.333374 0.3457960188
LOTI 1997.416626 0.3634203672
LOTI 1997.500000 0.3825819790
LOTI 1997.583374 0.4045383036
LOTI 1997.666626 0.4467202425
LOTI 1997.750000 0.4543276131
LOTI 1997.833374 0.4737372696
LOTI 1997.916626 0.5032517910
LOTI 1998.000000 0.5192593336
LOTI 1998.083374 0.5539480448
LOTI 1998.166626 0.5779045224
LOTI 1998.250000 0.5801445842
LOTI 1998.333374 0.5702176094
LOTI 1998.416626 0.5589799285
LOTI 1998.500000 0.5542870164
LOTI 1998.583374 0.5431619883
LOTI 1998.666626 0.5251235366
LOTI 1998.750000 0.4995376468
LOTI 1998.833374 0.4731709659
LOTI 1998.916626 0.4363355637
LOTI 1999.000000 0.4054751992
LOTI 1999.083374 0.3780059218
LOTI 1999.166626 0.3500004113
LOTI 1999.250000 0.3389944434
LOTI 1999.333374 0.3336953521
LOTI 1999.416626 0.3219966590
LOTI 1999.500000 0.3086466491
LOTI 1999.583374 0.2899633646
LOTI 1999.666626 0.2833445966
LOTI 1999.750000 0.3020571768
LOTI 1999.833374 0.3256017566
LOTI 1999.916626 0.3314893842
LOTI 2000.000000 0.3331597447
LOTI 2000.083374 0.3342891037
LOTI 2000.166626 0.3410858214
LOTI 2000.250000 0.3441580832
LOTI 2000.333374 0.3310964108
LOTI 2000.416626 0.3289524615
LOTI 2000.500000 0.3199721277
LOTI 2000.583374 0.3381243944
LOTI 2000.666626 0.3289325535
LOTI 2000.750000 0.3345920742
LOTI 2000.833374 0.3270110190
LOTI 2000.916626 0.3474135995
LOTI 2001.000000 0.3545602560
LOTI 2001.083374 0.3707930148
LOTI 2001.166626 0.3790234923
LOTI 2001.250000 0.3931757510
LOTI 2001.333374 0.4163171649
LOTI 2001.416626 0.4493446648
LOTI 2001.500000 0.4739433229
LOTI 2001.583374 0.5014572740
LOTI 2001.666626 0.5264521837
LOTI 2001.750000 0.5538262129
LOTI 2001.833374 0.5677855015
LOTI 2001.916626 0.5728142858
LOTI 2002.000000 0.5738685131
LOTI 2002.083374 0.5784193277
LOTI 2002.166626 0.5783999562
LOTI 2002.250000 0.5794250369
LOTI 2002.333374 0.5836792588
LOTI 2002.416626 0.5703246593
LOTI 2002.500000 0.5586030483
LOTI 2002.583374 0.5534768701
LOTI 2002.666626 0.5375267863
LOTI 2002.750000 0.5072289705
LOTI 2002.833374 0.5009176135
LOTI 2002.916626 0.4966633320
LOTI 2003.000000 0.4904974997
LOTI 2003.083374 0.4833981097
LOTI 2003.166626 0.4986106753
LOTI 2003.250000 0.5079582334
LOTI 2003.333374 0.5226535201
LOTI 2003.416626 0.5215522647
LOTI 2003.500000 0.5470480323
LOTI 2003.583374 0.5363866091
LOTI 2003.666626 0.5499585271
LOTI 2003.750000 0.5575102568
LOTI 2003.833374 0.5594354868
LOTI 2003.916626 0.5457716584
LOTI 2004.000000 0.5397373438
LOTI 2004.083374 0.5149759054
LOTI 2004.166626 0.4974953234
LOTI 2004.250000 0.4854559898
LOTI 2004.333374 0.4790748358
LOTI 2004.416626 0.4931302667
LOTI 2004.500000 0.4799817204
LOTI 2004.583374 0.4942241311
LOTI 2004.666626 0.4868121147
LOTI 2004.750000 0.4967460930
LOTI 2004.833374 0.5060160756
LOTI 2004.916626 0.5215128660
LOTI 2005.000000 0.5439230204
LOTI 2005.083374 0.5740800500
LOTI 2005.166626 0.5853979588
LOTI 2005.250000 0.6034425497
LOTI 2005.333374 0.6149129868
LOTI 2005.416626 0.6133242249
LOTI 2005.500000 0.6217342615
LOTI 2005.583374 0.6038072109
LOTI 2005.666626 0.6038013101
LOTI 2005.750000 0.5935218930
LOTI 2005.833374 0.5809197426
LOTI 2005.916626 0.5709815621
LOTI 2006.000000 0.5666434765
LOTI 2006.083374 0.5545851588
LOTI 2006.166626 0.5589477420
LOTI 2006.250000 0.5480116010
LOTI 2006.333374 0.5360572338
LOTI 2006.416626 0.5367087126
LOTI 2006.500000 0.5438236594
LOTI 2006.583374 0.5773862004
LOTI 2006.666626 0.5809700489
LOTI 2006.750000 0.5841441751
LOTI 2006.833374 0.5999441743
LOTI 2006.916626 0.6145035028
LOTI 2007.000000 0.6136848330
LOTI 2007.083374 0.6234223247
LOTI 2007.166626 0.6159473062
LOTI 2007.250000 0.6113790274
LOTI 2007.333374 0.6079616547
LOTI 2007.416626 0.5952960253
LOTI 2007.500000 0.5697643757
LOTI 2007.583374 0.5088769794
LOTI 2007.666626 0.4785093069
LOTI 2007.750000 0.4805369973
LOTI 2007.833374 0.4598188400
LOTI 2007.916626 0.4438244104
LOTI 2008.000000 0.4277707040
LOTI 2008.083374 0.4282906055
LOTI 2008.166626 0.4130594134
LOTI 2008.250000 0.4160292447
LOTI 2008.333374 0.4166229069
LOTI 2008.416626 0.4246318638
LOTI 2008.500000 0.4310206175
LOTI 2008.583374 0.4639549851
LOTI 2008.666626 0.4813087285
LOTI 2008.750000 0.4664338827
LOTI 2008.833374 0.4708602726
LOTI 2008.916626 0.4818562567
LOTI 2009.000000 0.5064594746
LOTI 2009.083374 0.5149075985
LOTI 2009.166626 0.5303887129
LOTI 2009.250000 0.5411190987
LOTI 2009.333374 0.5453741550
LOTI 2009.416626 0.5540969372
LOTI 2009.500000 0.5646377802
LOTI 2009.583374 0.5782875419
LOTI 2009.666626 0.6019529700
LOTI 2009.750000 0.6334959865
LOTI 2009.833374 0.6555088162
LOTI 2009.916626 0.6643188596
LOTI 2010.000000 0.6608605385
LOTI 2010.083374 0.6494707465
LOTI 2010.166626 0.6494237781
LOTI 2010.250000 0.6420695782
Here's the output from the regression:
avx 1943.502319
sdx 36.897190 (= 1.898490% of avx)
rangex 1880.500000..2009.666626 (= 6.646075% of avx)
avy -0.030250
sdy 0.232463 (= -768.462007% of avy)
rangey -0.425408..0.601953 (= -3396.186527% of avy)
533 (35.6%) points > 1 \sigma
40 (2.7%) points > 2 \sigma
y = 0.00544583*x + -10.6142
sdx 1426.41
rss 20.331
se 0.116577
r 0.864378
limits for beta at 90.0% CI
tc = 1.64586 at 1496 d.f.
beta in 0.00544583 +- 0.000134513 = [0.00531132, 0.00558034]
T-tests on beta:
H0 beta == 0.000000 against H1 beta != 0.000000
calculated t = 66.6337 at 1496 d.f.
|t| > tc (1.64586 2-sided); reject H0
H0 beta == 0.000000 against H1 beta > 0.000000
t > tc (1.28212 right tail); reject H0
Probabilities:
P(beta!=0.000000) = 1.000000
P(beta>0.000000) = 1.000000
limits for alpha at 90.0% CI
tc = 1.64586 at 1496 d.f.
alpha in -10.6142 +- 0.261473 = [-10.8757, -10.3528]
r2 = 0.745411
calculated Spearman corr = 0.870068
Testing:
H0: vars are independent
|r| > rc (0.432000 2-sided) at 1%; reject H0
Durbin-Watson d = 0.017697
d < dL (1.441109): Positive auto-corr at 5%
Here an explanation what that means:
In method (a) the model found is anomaly = a + b*year where b is
0.00544583. I.e. for each 100 years there appears to be .5 C
increase in anomalous temperature above baseline.
The T value for this estimate is 66 at 1400 degrees of freedom.
This boils down to saying there is almost no chance (approx 1 in 1000)
this increasing trend is due to chance alone.
Further, the r2 value indicates that 100-74.5% = 26% of the year-to-year
deviations in temperature anomaly are NOT explained by passage of time.
There are effects other than a simple increase over time, but together
they account for only 1/4 of what appears to be a persistent increase
over time. (Some of these other effects are (a) sunspots or
other variation in solar output; (b) volcanic eruptions that normally
produce approx 5-year periods of slight global cooling).
For method (b) (Spearman correlation) the probability the ordering
of the temperature anomalies is so similar (i.e. min temp anomaly tend
to be at start; max temp anaomaly tend to be at end of period)
is around 1 chance in 100. At 99% confidence we can say there is
an upward trend in anomalous temperature readings.
Having the 2 methods determine the same pattern increases the probability
the data shows a real trend, not just a chance effect that may "go away"
with more data over coming years.
Now, given we have estiblished there is an increasing trend, we could
ask -- does the trend stay the same over time?
Let's take just the data for the past 20 years and see whether there is
still a statistically significant trend. (None of this "by eye" stuff).
avx 2000.201172
sdx 5.854342 (= 0.292688% of avx)
rangex 1990.000000..2010.250000 (= 1.012398% of avx)
avy 0.412967
sdy 0.146199 (= 35.402116% of avy)
rangey 0.091196..0.664319 (= 138.781585% of avy)
89 (37.2%) points > 1 \sigma
2 (0.8%) points > 2 \sigma
y = 0.0196376*x + -38.8661
sdx 91.189
rss 1.99751
se 0.0918059
r 0.786359
limits for beta at 90.0% CI
tc = 1.65132 at 237 d.f.
beta in 0.0196376 +- 0.00166249 = [0.0179751, 0.0213001]
T-tests on beta:
H0 beta == 0.000000 against H1 beta != 0.000000
calculated t = 19.5056 at 237 d.f.
|t| > tc (1.65132 2-sided); reject H0
H0 beta == 0.000000 against H1 beta > 0.000000
t > tc (1.28514 right tail); reject H0
Probabilities:
P(beta!=0.000000) = 1.000000
P(beta>0.000000) = 1.000000
limits for alpha at 90.0% CI
tc = 1.65132 at 237 d.f.
alpha in -38.8661 +- 3.32533 = [-42.1914, -35.5408]
r2 = 0.627726
calculated Spearman corr = 0.771690
Testing:
H0: vars are independent
|r| > rc (0.432000 2-sided) at 1%; reject H0
Durbin-Watson d = 0.033817
d < dL (1.665418): Positive auto-corr at 5%
Explanation of numbers:
Both the (b) Spearman test (at 99% confidence) and (a) LS T-test (at >99%
confidence) show an increasing trend. The r2 shows there are more
effects in this short period than for the dataset as a whole.
Now the effects of other things like volcanic erupts or variations
in solar radiation account for approx 100-62.7 = 36% of the variation in
year-to-year temp anomaly. I.e. the year-on-year trend still swamps
all other effects combined 2:1.
And the model estimated by (a) show a trend of almost 2 deg per C
of anomalous warming.
This same kind of thing can be done to relate (e.g.) a suspected
connection between CO2 levels and anomalous warming. Rather than
just assume that a trend exists over time we can nail it to a suspected
cause, if required. If we can estimate what the variation
in anomalous temp vs CO2 concentration, and we can estimate how
this concentration is expected to change over time (perhaps not
linearly) then we can better estimate any change in anomalous temp.
Of course, maybe there *is* no statistically significant link. :)
But the analysis has been done, and we sure there is such a link
in the data, confirming the hypothesis that increasing CO2 levels
is influencing the observed anomalous temp increase.
--
R Kym Horsell <***@kymhorsell.com>
If your ideas are any good you'll have to ram them down people's throats.
-- Howard Aiken