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)