Scientific Variables & Data:

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1 Science Methods & Practice BES November 2, 29 : Types of variables & data and their attributes Scientific Data: Types, Attributes & Uncertainty Variable: Data: Variables: Examples Variables are categories of an attribute without ranking or numerical scale

2 Data: information about categoric variables Arctic Poppy (Papaver radicatum) can have yellow flowers or white flowers Habitat # Yellow flowers # White flowers Polar semidesert Polar desert 67 Statistical methods for such nominal data are unique so it is important to recognize the kind of data. Variables: Examples Variables are categories of an attribute with a meaningful ordered ranking Data: information using ordered variables Order Germinating Observed order of germination of alpine plant seeds in the early summer Mount Rainier Mount Baker Mount Hood First Aster alpigenus Silene acualis Aster alpigenus Second Epilobium alpina Aster alpigenus Smelowskia calycina Third Smelowskia calycina Epilobium alpina Epilobium alpina Fourth Silene acualis Smelowskia calycina P. davidsonii Five Penstemon davidsonii Penstemon davidsonii Silene acualis Data contains categories of an attribute with a meaningful ordered ranking Variables: examples values in numeric order Variables: size of the intervals between values is meaningful 2

3 Data: information using continuous variables Variables: Heig ght (ft) Height of Subalpine fir with Elevation values in numeric order size of the intervals between values is meaningful Moving beyond the textbook Variables are characterized by values in numeric order in discrete categories AND the size of the intervals between values is meaningful Height (ft) variables Original data that can assume any numerical value along a scale Height of Subalpine fir with Elevation Data Number of Pikas variables Moving beyond the textbook Derived data in which the original continuous or discontinuous variable is placed on a relative basis or derived from the combination of variables Pikas Derived Variables Variables in which the original data are normalized to allow meaningful comparisons Original, data Number of P What if these sites were of different size? y (# / m 2 ) Pika Density Derived, data Derived Variables Variables in which the original data are normalized to allow meaningful comparisons (per unit area, per unit time, etc.) Bioregion Number of grizzly bears Density of grizzly bears (# / km 2 ) North Cascades 4.2 Northern Rockies 26. Original, data Derived, data BOTH types of data answer important, but they each address DIFFERENT questions AND require different statistical approaches

4 Derived Accuracy & Precision Accuracy & Precision Accuracy Precision Accuracy Precision measured values are close to the actual value measured values are close to each other (repeatability) measured values are close to the actual value measured values are close to each other (repeatability) Accurate? Precise? Accuracy & Precision Is accuracy a good thing? An Example to illustrate issues of precision & accuracy Tree height can be measured with () a clinometer Is precision a good thing? 4

5 Precision & Accuracy Example Precision & Accuracy Tree height can be measured with () a clinometer or (2) calculated from an established relationship with DBH Measure Diameter at Breast Height (.5 m) above the ground - DBH 2 Establish DBH height relationship from set of trees Height DBH Calculate height of new trees from known DBH height relationship Results of a test of these two techniques using five forestry technicians measuring one tree Technician Clinometer DBH Regression Martha John Ed Alicia Barb AVERAGE STD DEV ft tall Which is more accurate? precise? The nature of precision Factors that contribute to variation in measurements Wind Speed (m/s) Wind Speed in Two Habitats Forest Field Minutes after Noon Which measurements are more precise? Real values of environmental parameters often vary in time & space Variability does not always equate with precision! I. Inherent variation in space and time. Sampling issues (next time). Human Error - perception 2. Instrument & Process Errors Factors that contribute to Variation in Measurements. Human Error - perception Variation from care in measurements Parallax Scale resolution 2. Instrument & process errors: selected issues Instrument maintenance calibration for accuracy What is CALIBRATION? Instrument operation for accuracy Instrument operation for precision 5

6 Measuring sunlight intensity sensor meter.45 mv Radiation (Watts m -2 ) Establishing the relationship & its limitations Electrical response (mv).45 mv sensor meter How do we get from electrical response to solar radiation intensity? Radiation (Watts m - 2 ) Danger of using an instrument outside of where it has been calibrated Sensor readout Actual value Electrical response (mv) Meter output Actual relationship sensor meter Factors that contribute to Variation in Measurements 2. Instrument & Process Errors Instrument maintenance: calibration for accuracy Instrument operation: standards to verify accuracy Standards of known value used as process / instrument check Sample Standard Instrument.45 mv NH 4 NO An Example of Standards Measuring NITROGEN in leaves Factors that contribute to Variation in Measurements 2. Instrument & Process Errors Instrument maintenance: calibration for accuracy Instrument operation: standards to verify accuracy Instrument operation: duplicate samples for precision Standards of known value used as process / instrument check Instrument Duplicate samples used as process / instrument check Instrument Sample Standard Multiple leaves from same tree Tissue samples from same leaf 6