Choosing the right statistical function

[Stibbz]

I was wondering which statistical function would be the best to use when
trying to see if their is a relationship between temperature and glacier
length change.

I have used the CORREL function to try and assess there correlation but will
this give me bad answers as there isn't a straight line relationship between
the two!?!?

 

[Dave Curtis]

Hi,

Presumably you have tried plotting the data on an x-y chart and tried adding
any of the non-linear trendlines?

Dave

 

[Dana DeLouis]

I'm trying to picture the relationship around the 31-33 degree F range :>)

Just kidding...
Dana DeLouis

 

[Stibbz]

No I haven't used any of the non-linear trendlines as I am unsure on which
one is appropriate to use

 

[Dave Curtis]

I agree there's a danger of drawing erroneous conclusions, just because your
data happens to fit part of, say a fourth order polynomial.
Is therebno published data on a theoretical relationship between the two
variables?
Why not post a sample your data?

Dave

 

[Stibbz]

Ok here's some sample data for you to look at

Glacier length change data
Year Aquila
1896 -2
1897
1898 10
1899
1900 -12
1901
1902
1903 -16
1904 -9
1905 -8
1906
1907 -14
1908
1909
1910
1911 4
1912
1913
1914 -4
1915
1916
1917 -3
1918
1919 -13
1920
1921 -34
1922
1923 4
1924 -6
1925 50
1926 -34
1927
1928 -9
1929
1930 -16
1931 14
1932 -13
1933
1934
1935
1936
1937 -6
1938 2
1939 0
1940 11
1941 -3
1942 -7
1943 -2
1944 -6
1945 -105
1946
1947 -18
1948
1949 -22
1950
1951 -6
1952 -8
1953 -6
1954 -4
1955 -14
1956 -18
1957 -22
1958 22
1959 -21
1960 7
1961 -23
1962 -8
1963 -7
1964 -14
1965 -15
1966 6
1967 1
1968 -1
1969 -33
1970 -16
1971
1972
1973
1974
1975
1976 0
1977 0
1978 -15
1979 0
1980 4
1981 -9
1982 21
1983 18
1984
1985 -5
1986 -19
1987
1988 -3
1989 -6
1990 -12
1991
1992 -17
1993 -8
1994 -14
1995 -11
1996 -17
1997 -29
1998 -71
1999 -23.4
2000 -14
2001 -18.8
2002 -77.1
2003 -76.8
2004 -1.8
2005 -13.8
2006 -26.1

Temperature Data
1896 8.33
1897 9.34
1898 9.56
1899 9.76
1900 9.78
1901 8.62
1902 8.84
1903 8.98
1904 9.74
1905 9.03
1906 9.32
1907 9.00
1908 8.75
1909 8.46
1910 9.13
1911 10.06
1912 8.93
1913 9.52
1914 9.01
1915 9.32
1916 9.21
1917 8.41
1918 9.32
1919 9.05
1920 10.05
1921 10.24
1922 9.01
1923 9.88
1924 9.13
1925 9.39
1926 9.84
1927 9.63
1928 10.38
1929 9.28
1930 10.18
1931 9.17
1932 9.33
1933 9.19
1934 10.16
1935 9.78
1936 9.82
1937 10.16
1938 9.63
1939 9.33
1940 8.85
1941 8.94
1942 9.53
1943 10.55
1944 9.77
1945 10.52
1946 10.15
1947 11.08
1948 10.32
1949 10.82
1950 10.64
1951 9.83
1952 10.14
1953 9.92
1954 9.62
1955 9.94
1956 8.72
1957 9.68
1958 9.80
1959 10.40
1960 9.93
1961 10.77
1962 9.27
1963 8.70
1964 10.02
1965 9.03
1966 10.22
1967 9.88
1968 9.56
1969 9.33
1970 9.54
1971 9.49
1972 9.41
1973 9.34
1974 10.02
1975 9.89
1976 9.99
1977 10.07
1978 9.23
1979 9.92
1980 9.05
1981 9.78
1982 10.60
1983 10.47
1984 9.74
1985 9.36
1986 10.03
1987 10.07
1988 10.71
1989 10.90
1990 10.98
1991 10.36
1992 10.79
1993 10.28
1994 11.84
1995 10.85
1996 9.99
1997 10.94
1998 10.83
1999 10.71
2000 11.37
2001 11.07
2002 11.54
2003 11.77
2004 11.18
2005 10.69
2006 11.18

 

[Dave Curtis]

Hi,

OK, here's my first attempt.
First I deleted all the rows for which you have no length change data.
Then, with years in column A starting in A2
with length change in column B starting in B2
with temperature in Column C starting in C2.
I assumed an original arbitrary length of 1000
so the length of the glacier over the years is given in D2 by

=1000+SUM($B$2:B2)

and copied down.

A x y plot of temp against this length gives a big group of points, and a
linear trendline slopes downwards with an R-squared of about 0.4.


Are we getting anywhere?

Dave

 

[Herbert Seidenberg]

Excel 2007
Correlation Chart
I believe, I believe!
http://www.mediafire.com/file/nyljg4oydzi/03_11_09.xlsx

 

[Stibbz]

Yeah that looks pretty good to me thanks!

Hi,

OK, here's my first attempt.
First I deleted all the rows for which you have no length change data.
Then, with years in column A starting in A2
with length change in column B starting in B2
with temperature in Column C starting in C2.
I assumed an original arbitrary length of 1000
so the length of the glacier over the years is given in D2 by

=1000+SUM($B$2:B2)

and copied down.

A x y plot of temp against this length gives a big group of points, and a
linear trendline slopes downwards with an R-squared of about 0.4.


Are we getting anywhere?

Dave

 

[David J. Braden]

Ugh!
Surely there are lags in glacial-length change with respect to
temperatures?!? Tossing out the missing temps sounds like a bad approach
to me; getting the data, or working out a model to fill in the missing
points, would make a lot more sense to me. PLUS, "Temperature" of
what?!? Average ambient air at a predetermined height above the glacier
over it's length? What about the other temperatures that come into play,
as well as the precipitation over the course of the year, as well as the
amount of sunlight hitting the glacier (amount sunlight reaching the
Earth's surface has decreased markedly over this time period due to
increased particulate matter)? Seems to me you need to explore for more
explanatory variables, and try a different approach to fill in for
missing data.

Dave