Data and interpretation
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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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Data and Interpretation

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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


Numerical approaches can never dispense … researchers from reflection on observations. Data analysis must be seen as an objective and non-exclusive approach to carry out in-depth analysis of the data.

Legendre and Legendre


Organization of this presentation

  • The scientific method – from the question to the answer and back again

  • Data analysis – beyond statistical inference (some tools)

  • From analysis to conclusions – modeling

  • Causal loop diagrams – a useful tool for beginning to explore modeling

  • Some practical things about drawing conclusions from data and models – fitting your data into what is already known, extrapolation and speculation

  • Updating theory and practice


New hypotheses

General

Research Area

Specific problem

Sampling and

lab work

Data analysis and

interpretation

Conclusions

Unusable

data


Analysis:Beyond statistical inference


Autocorrelation and spatial structure

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(yi-my) + ej

i2

i3

j

i1

i4


Spatial dependence

If there is no auto-correlation in the variable of interest, spatial variability may be the result of explanatory variables exhibiting spatial structure

Yj = my + f( explanatory variables) + ej


Correlograms

Variograms

Periodograms

Many tools exist for spatial analysis

The nature of the shapes of these graphical models are indicative of the nature of the processes that create spatial autocorrelation


Some applications

  • Biogeochemical cycles

  • Hydrology

  • Poverty dynamics

  • Vegetation structure


Mapping

  • Trend surface analysis - a regression approach

  • Interpolated maps – contour maps generated from a regular grid of measurements

  • Kriging – a geostatistical approach based on semivariance analysis


Classification

Many research goals involve classifying objects that are sufficiently similar into useful or recognizable categories.


Cluster analysis

Multidimensional analysis

Partition a dataset into subsets

Subsets form a series of mutually exclusive cells


Example of hierarchically nested partitions


Ordination in reduced space

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


Factor analysis

  • Frequently used in the social sciences

  • Aims at representing the covariance structure of the dataset in terms of a predetermined causal model


Principal components analysis

Similar to factor analysis, but for quantitative data.

Analysis generates new axes that capture the variance


General

Research Area

Specific problem

Sampling and

lab work

Data analysis and

interpretation

Conclusions

Unusable

data


Modeling

  • Conceptual models

  • Numerical models

    • Application models – based on laws and theories

    • Calculation tools – based on empirical relationships and correlations


Conceptual model


Modeling for a purpose

  • Throwaway models – used to improve the understanding of how a system is functioning in a specific study

  • Career models – Some scientists make a career out of one or a few models


Causal loop diagrams:A tool to help understand your system and begin to model it


Causal loop diagrams

  • Capturing your hypotheses about the causes of dynamics

  • Capturing mental models of individuals and teams

  • Understanding important feedbacks that may be operating in a system


What would happen if a variable were to change

+

-

B

Birth ratePopulationDeath rate

R

+

-

+

+

Fractional

Birth Rate

Average

Lifetime


Positive feedbacks of fire risk in Amazon basin


These an many other techniques can be useful in probing data beyond statistical inferences to gain deeper insight into your data


Beyond analysis of your data

  • What is known about your subject from other studies?

  • Don’t just compare your results to the results of others, synthesize what is known from other work and use the synthesis to put your new knowledge into context

  • Dig to understand what is different about your system and what novel knowledge you have generated


Speculation

  • Build your discussion on your data, not on speculation.

  • Clearly label speculation in your discussion

  • Speculation is never the basis for a conclusion


Extrapolation


Extrapolation


Extrapolation

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

General

Research Area

Specific problem

Sampling and

lab work

Data analysis and

interpretation

Conclusions

Unusable

data


Updating theory and practice

  • Science works incrementally

  • One paper is rarely sufficient to update theory or practice

  • Interpret your results appropriately, but do not over interpret them


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