Data and Interpretation. What have you learnt?. The delver into nature’s aims Seeks freedom and perfection; Let calculation sift his claims With faith and circumspection Goethe.
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What have you learnt?
Seeks freedom and perfection;
Let calculation sift his claims
With faith and circumspection
Goethe
Numerical approaches can never dispense … researchers from reflection on observations. Data analysis must be seen as an objective and nonexclusive approach to carry out indepth analysis of the data.
Legendre and Legendre
New hypotheses from reflection on observations. Data analysis must be seen as an objective and
General
Research Area
Specific problem
Sampling and
lab work
Data analysis and
interpretation
Conclusions
Unusable
data
Spatial heterogeneity is a functional characteristic of many systems and is not the result of random or noise generating processes.
Autocorrelation: The value of yj observed at site j is assumed to be the overall mean of the process (my) plus a weighted sum of the centered values (yi – my) at surrounding sites.
Yj = my +Sf(yimy) + ej
i2
i3
j
i1
i4
If there is no autocorrelation in the variable of interest, spatial variability may be the result of explanatory variables exhibiting spatial structure
Yj = my + f( explanatory variables) + ej
Correlograms from reflection on observations. Data analysis must be seen as an objective and
Variograms
Periodograms
Many tools exist for spatial analysisThe nature of the shapes of these graphical models are indicative of the nature of the processes that create spatial autocorrelation
Many research goals involve classifying objects that are sufficiently similar into useful or recognizable categories.
Multidimensional analysis
Partition a dataset into subsets
Subsets form a series of mutually exclusive cells
Many multivariate datasets have more dimensions than we can easily comprehend or manipulate in a meaningful way. There are a number of techniques to reduce the dimensionality of these datasets
Meaningful relationships are deduced from the relative positions of observation units in this reduced space
Similar to factor analysis, but for quantitative data.
Analysis generates new axes that capture the variance
General from reflection on observations. Data analysis must be seen as an objective and
Research Area
Specific problem
Sampling and
lab work
Data analysis and
interpretation
Conclusions
Unusable
data
+

B
Birth rate Population Death rate
R
+

+
+
Fractional
Birth Rate
Average
Lifetime
I have seen a number of papers that extrapolate to the globe based on one or two observations. They rarely get it right.
New hypotheses beyond statistical inferences to gain deeper insight into your data
General
Research Area
Specific problem
Sampling and
lab work
Data analysis and
interpretation
Conclusions
Unusable
data