Readings
The values found from a single judgment when using a piece of equipment
Measurements
The values taken as the difference between the judgments of two values
Assessing uncertainty
Resolution of the instrument used
Manufacturer’s tolerance on instruments
Judgements that are made by the experimenter
The procedures adopted (e.g. Repeated readings)
Size of increments available
Uncertainty in a reading
At least plus or minus half of the smallest division
Uncertainty of a measurement
At least plus or minus one of the smallest divisions
Uncertainties in given values
E.g. Charge of an electron is given as 1.60x10^-19
Uncertainty is + or - 0.01x10^-19
Assume he uncertainty to be plus or minus 1 in the last significant digit
Repeated measurements
A method for reducing the uncertainty
Uncertainty in this case = half the range
Uncertainties from gradients
Percentage uncertainty = (best gradient - worst gradient) X 100 /best gradient
Error bars in physics
Plot data points at their
mean value
Calculate the range of data ignoring any anomalies
Add error bars with lengths equal to half the range
Variable and graph axis
X axis - independent variable (the variable that caused the observed effect) it isn’t affected by the other variable
Y axis - dependent variable (the variable that was effected by the independent variable)
Scientific ideas
The scientific community only accepts new ideas when they can be independently validated
This means others are able to reach the same conclusion
Uncertainties in using immersion heater experiment to calculate specific heat capacity
Temperature varies throughout - stir
Some of the input energy is use to raise the temperature of the heater and the container
Temperature will continue to rise after the heater has been turned off - find max temperature
Uncertainties in ammeter, voltmeter and thermometer
Combining uncertainties
If you are adding or subracting values you add the absolute uncertainties
If you are dividing or multiplying then you add the percentage uncertainties
If you are raising a number to a power then you multiply the percentage uncertainties by that power
Advantages of using data loggers
More accurate data
Higher sampling rate
Data can be displayed in real time
Random errors
These cause readings to be spread about the true value, due to results varying in an unpredictable way from one measurement to the next.
Random errors are present when any measurement is made, and cannot be corrected. The effect of random errors can be reduced by making more measurements and calculating a new mean.
Systematic errors
These cause readings to differ from the true value by a consistent amount each time a measurement is made.
Sources of systematic error can include the environment, methods of observation or instruments used.
Systematic errors cannot be dealt with by simple repeats. If a systematic error is suspected, the data collection should be repeated using a different technique or a different set of equipment, and the results compared.
Zero errors
Any indication that a measuring system gives a false reading when the true value of a measured quantity is zero, eg the needle on an ammeter failing to return to zero when no current flows.
A zero error may result in a systematic uncertainty.
Anomalies
These are values in a set of results which are judged not to be part of the variation caused by random uncertainty
Precision
Precise measurements are consistent, they fluctuate slightly about a mean value - this doesn’t indicate the value is accurate
The closeness of measurements to one another
Resolution
The smallest change in the quantity being measured (input) of a measuring instrument that gives a perceptible change in the reading
Accuracy
The level of conformity of a measurement to the actual value
How to determine if something is vertical ?
Use a plumb line
Use a spirit level
Reducing uncertainty
Take multiple readings / measurements
Longer time/distance/relevant variable - reduces percentage uncertainty
Percentage uncertainty in a y intercept
Same method as a gradient
Best intercept - worst intercept/best intercept x 100
Measurement error
The difference between a measured value and the true value
Evidence
Fair test
Hypothesis
Prediction
Data that has been shown to be valid
A test in which only the independent variable has been allowed to affect the dependent variable
A proposal intended to explain certain facts or observations
A statement suggesting what will happen in future, based on observation, experience or a hypothesis
Interval
The quantity between readings
e.g. a set of 11 readings equally spaced over 1 m would give an interval of 0.1 m
Repeatable
An experiment is repeatable if the original experimenter repeats the experiment using the same method and obtains the same results
Reproducible
A measurement is reproducible if the investigation is repeated by another person, or by using different equipment or techniques, and the same results are obtained
Uncertainty
The interval within which the true value can be expected to lie, with a given level of confidence or probability
Validity
Suitability of the investigative procedure to answer the question being asked
Valid conclusion
A conclusion supported by valid data, obtained from an appropriate experimental design and base on sound reasoning
Categoric variables
Have values that are labels
e.g. names of plants
Continuous variables
Can take on any values (infinite number of values)
Given magnitude by counting or by measurement
Control variables
A varaible which may, in addition ot the indepedent variable affect the outcome of the investigation and therefore has to be kept constant or monitored
Dependent variables
Independent variables
The variable of which the value is measured for each and every change in the independent variable - it is affected by the independent variable
The variable for which values are changed or selected by the experimenter - affects the dependent variable
Nominal variables
A type of categoric variable where there is no ordering of categories
Reliability
Reliable experiments produce consistent and stable results.
How does decreasing the time base of the oscilloscope reduce uncertainty?
Waveform will be stretched in the y axis
Resolution of the time axis increases
Increases the length/distance measured across the screen reduces percentage uncertainty in the reading of time
Validated evidence
Data collected from an experiment used to test a theory
The results of the experiment are consistent and deemed reliable - they are able to be replicated/independently validated
Things to consider when criticising data tables
Number of significant figures and consistency
Range of data used
Intervals used - are they consistent?
Number of values used
Number of repeats
Fundamental SI base units
mass - kilograms (kg)
time - seconds (s)
amount of substance - mol
temperature - kelvin (K)
length - metres (m)
electric current - amperes (A)
