Observations and Measurements

The Nature of Observation

• Subjective vs. Objective

• Qualitative vs. Quantitative

Subjective vs. Objective

• “I can tell he’s lying.”• “His galvanic skin response changed

significantly when he said that.”• Both are valid• Both are useful• Objective measures usually have more

credibility because they are more reproducible

Qualitative vs. Quantitative

• “It’s really hot outside.”

• “The outside thermometer indicates 35 ºC.”• Both are valid

• Both are useful

• Quantitative measures, like objective measures, are considered more credible.

Combinations

• Subjective Qualitative:– “Sure is hot!”

• Objective Qualitative:– “The engine light is on.”

• Subjective Quantitative:– “I estimated her speed to be 55 mph.”

• Objective Quantitative:– “RADAR indicated she was traveling at 54 mph.

Quantification: Precision vs. Accuracy

• Precision:– Scale of measurement– Limited by the instrument

• Accuracy:– Correctness of measurement– Also limited by the instrument

• How precise is the meter stick above?– 0.1 cm (or 0.001 m)– How did we determine this?

• How accurate is it?

Precise but inaccurate Accurate but imprecise

Precise and accurate

Significant Figures

• Significant Figures indicate the precision with which a measurement has been made– e.g. 1.3 meters has 2 significant digits,

indicating that the measurement device could measure tenths of meters, but not hundredths

• But there can be ambiguity; e.g.– Given 112,000 miles, how many of the digits

are significant?– Are any of the zeroes “real”?

Scientific Notation

• Scientific Notation removes the ambiguity:– 1.12 x 105 miles has 3 significant digits– 1.120 x 105 miles has 4 significant digits, and

indicates one of the zeroes was “real”• i.e. we know that it isn’t 1.121 x 105 miles

• but we don’t know whether it might be 1.1201 x 105 miles or 1.1202 x 105 miles

Reporting Results• We never report a result with more

significant digits than the LEAST significant of the measurements that went into it; e.g.– (1.2 x 102 m)(2.15 x 100m) = 2.6 x 102 m2

• Some quantities have infinite precision:– If the problem says to “double” something, we

assume the 2 used to multiply has infinite SFigs– Counts have infinite SFigs

• Use all in calculation, then round