Practical data skills etc
Range
Range of a set of readings or calculated values is the smallest and largest values. The smallest value, the largest value and the difference should all be quoted with units.
Recording results to significant figures
Results should always be recorded to to the same number of significant figures. This number should be determined by the resolution of the device being used to measure the data or the uncertainty in measurement. E.g a length of string measured to be 60 cm using a ruler with mm graduations should be recorded at 600 mm, 60.0 cm -60.0 cm is to 3 significant figures , therefore = 0.600 m e.g 32cm is to 2 significant figures therefore 32cm = 0.32 m
History of theory etc
Scientific progress is made when experiment lane idence is found that supports a new theory or model E.g plum pudding model disproved by Rutherford scattering Wave theory of light disproved by photo electric effect Einstein Observation Hypothesis Experiment Results support hypothesis Predictions based on hypothesis Further experiments Theory
Valid conclusion
A conclusion supported by valid data obtained from an appropriate experimental design and based on sound reasoning.
Fair test
A fair test is one in which only the independent variable has been allowed to affect the dependent variable.
Sketch graph
A line graph not necessarily on a grid that shows the general shape of the relationship between two variables. It will not have any points plotted and Although the axes should be la bleed they may not be scaled.
Accuracy
A measurement is accurate if close to the true value value. It is likely to have been obtained using accurately calibrated instruments I the correct way and where no systematic error occur.
Repeatable
A measurement is repeatable if the original experimenter repeats the investigation using the same method and equipment and obtains the same results. It is the extent to which the measurements of s quantity remain consistent over repeated measurements of the same quantity under identical conditions. An experiment is repeatable if it yields consistent results of the same measurement. An experiment is not repeatable if repeated measurements give different results or if the scatter of measurements on a line graph is too great to establish the exact position of the line. - repeatability is higher when random errors are reduced. - the repeatability of data can be checked by carrying out repeat measurements and calculating a mean value. If no repeat readings are made, repeatability can be assessed by considering the pattern of points on a graph - if they show a consistent trend and points are close to a line of best fit then they can be considered repeatable.
Prediction
A prediction is a statement suggesting what will happen in the future, based on observation, experience of a hypothesis.
Hypothesis
A proposal intended to explain certain facts or observations
Prediction
A statement suggesting what will happen in the fututre/experiment based on observation, experience or a hypothesis
Nominal variable
A type of catergoric variable where there is no ordering of catergories- they have values but cannot be ordered e.g red flowers, pink flowers
Dependent variable
A variable is a physical quantity whose values changes as a result of change of value of the independent variable. It is measured by an investigator for each change in the independent variable.
Interval
The quantity between readings e.g a set of 11 readings equally spaced over a distance of 1 m would give an interval of 10 centimetres.
How do you calculate absolute uncertainty from repeat readings?
The uncertainty in a measurement is half the range (spread) from the lowest to the highest value obtained for a particular value of independent variable. Equation: Uncertainty = +-0.5 x ( highest value - lowest value ) Uncertainty had the same value as the quantity being measured. It is expressed +- attached to the mean value and should be to the same number of decimal places as the value e.g 1.2mm +- 0.1mm - may also be indicated by an error bar on a graph. - check should be made that the resolution of the measuring equipment is smaller than the uncertainty - if not then the resolution value should be used as the uncertainty E.g if a time is measured three times as 1.3, 1.4 and 1.5, what is the uncertainty? .... =+- 0.5 x (highest value - lowest value) = +-0.5(1.5-1.3) = +-0.1 mm E.g2 if. Distance is measured three times as 22,22,23 what is the uncertainty ?.... = +-0.5 x (highest value - lowest value) = +- 0.5(23-22) = +-0.5 mm - note that this should be written as +-1mm to give it the same number of decimal places as the data.
Absolute uncertainity
The uncertainty of a measurement gives the spread of values away from the average value. This is likely to include the accepted value. Uncertainty may be given a level of confidence. The interval within which the true value can be expected to lie with a given level of confidence or probability eg the temperature 20 genres +- 2 degrees at a confidence level of 95% Uncertainty results from limitations in procedures, equipment etc.
Independent variable
The variable which is a physical quanitity for which values are changed/controlled or selected by the investigator. Changing the independent variable should result in a measurable change in the value of the dependent variable. Ideal number is 8 ( fewer is acceptable if equipment is restricted e.g only 5 wire diameters) Select an independent by doing a trial run Use biggest range as possible Must have equal intervals E.g measuring the resistance of a metre long wire suitable length values would be 100,200,300,400,500,600,700,800,900,1000 mm (100 and 200 can be omitted)
Tabulating data
There should be standard abbreviations e.g s for seconds, m for metres If a quantity is squared then the units should be squared e.g the units of velocity^2 appreciate (ms^-1)^2 = m^2s^-2. If the reciprocal of a quantity is needed on a results table then the units should be adjusted to suit e.g if value is 1/area (mm^2) then the units would be mm^-2 . Column headings need to include label and units separated by '/' Independent variable is In the left hand column. Units should only be in column headings.
Anomalies
These are values in a set of results which are judged. It to be part of the variation caused by random uncertainty.
Random error
These cause readings to be spread about the true value, due to results varying in an unpredictable way from one measurement to the next. Errors with no pattern or bias. Random errors are present when any measurement is made, and cannot be corrected.
Systematic error
These cause readings to differ from the true value by a consistent amount each time a measurement is made. Errors in measurement which show a pattern or bias or trend. Systematic error cannot be dealt with by simple repeats. If a systematic error is suspected, the date collection should be related using a different technique or a different set of equipment, and the results compared. An example of avoiding a systematic error is when using two crocodile clips with a length of wire I between, measure the length from the centre of the clips or from the same side of both.
True value
(Also called the accepted value) The true value of a measurement is the value of the most accurate measurement available eg speed of light (to three significant figures) = 3.00 x 10^8 ms^-1. It is the value that would be produced in an ideal experiment.
Name examples of random errors.
- human reaction time to start and stop a timer - measurement of random processes e.g radioactive decay. There will be s lower level of error (uncertainty) if time of measurement is longer or strength of a source is higher. - equipment variations e.g when investigating how high a cricket ball bounces, if it lands on the seam it will bounce differently. - environment variations e.g when measuring resistance of a wire in a room where temperature is variable -parallax errors (may also be systematic)
How to write up a 'planning practical' in an exam?
- name the equipment -describe how it will be set up (possibly with a diagram or circuit diagram If on electricity) - describe the independent, dependent and control variables, including how they will be measured (this involves the instrument used and technique) and the steps in the procedure used. -state how many readings will be made and that they will be recorded in a table. - state how many repeats will be done and that a mean average will be calculated. - describe the graph that will be plotted and how the results will be assessed - in relation to y=mx+c You might be asked on how you can make the experiment safe (state obvious risks and safety measures if relevant e.g take care when using ladders/ lifting heavy masses and use of safety clothing such as safety glasses) How could you reduce the percentage uncertainty / systematic (including zero) errors etc.
How many repeat readings should be taken in an experiment?
3 or more I.e an initial reading and two others. When measuring the wire diameter with a micrometer, a number of readings should be made around the wire and along the wire at different positions. An average would then be calculated.
Zero error
A zero error is a type of systematic error and airside when an instrument gives a non-zero reading for a true zero value of the quantity it measures. A positive zero error must be subtracted from all readings obtained with a particular instrument (negative error would need to be added to all readings) Any indication that a measuring system.p gives a false reading when the true value of a measured quantity is zero e.g the needle on an ammeter failing to return to zero when no current flows. A zero error may results in systematic uncertainty. And example is often found with micrometers which give a non - zero reading when they jaws are closed together. This could be due to wear on the jaws. Instruments to measure mass need to be set to zero prior to use e.g a top pan balance. An oh meters connected to very long leads which will have a significant resistance of their own would need to be set to zero with these leads connected.
Percentage uncertainty from a graph
Best y intercept - worst y intercept _____________________________________ X 100% Best y intercept
How could a parallel error be overcome"?
Can be avoided by lining up the eye with the marking in the scale to be read e.g when measuring he valine of a liquid in a measuring cylinder, the observers eye should be level with the part of the scale being read. A small distance between the scale and the thing being measured all reduces parallax error. A mirror next to the scale can also be used to ensure the scale is viewed from directly above.
Categoric variable
Catergoric variables are values that are labels eg names of plants or types material or colours of the spectrum or reading at week 1,2 etc
Significant numbers across power of 10
Changing the number of decimal places across a power of ten retains the number of significant figures but changes the accuracy. The same number of decimal places should therefore be generally used.
Continuous variable
Continuous variables can have values that can be given either a magnitude/quantity either by counting eg number of shrimp, number of cells or by measurement eg light intensity, flow rate
Evidence
Data that has been shown to be valid
How to record results from a stopwatch
If a stop watch display reads 01:34:23 this means 1 minute 34 seconds and 23 hundredths of a second. In a results table this should be recorded as 94.23 in the t/s column .
How do you reduce the uncertainty in readings when multiple instances are available
If measuring the quantity which is small e.g. thickness of paper the measurement was lower uncertainty can be obtained by measuring a multiple of the quantity e.g. thickness of 100 sheets of paper and calculating the thickness of one sheet and dividing it by 100 if one sheet of paper 0.1 mm thick is measured with a micrometre with (resolution +-0.01 mm )the uncertainty will be +-1mm. However if 100 sheets are measured (the total thickness is 10 mm) the uncertainty for each sheet will be +-0.01 mm /100 =+ -0.0001 mm . The same idea can be applied to oscillations of the pendulum, number of spins of the rotating object ,spacing of slits in the diffraction grating, wavelength of waves ,spacing of maxima on a diffraction pattern.
How do you workout the uncertainty if repeat readings are not made or repeat readings are all the same
If there are no repeat readings or repeat readings are all the same then certainty in a measurement relates to the resolution of the instrument the certainty is no smaller than plus or minus half the resolution of the instrument. Question1: if the smallest value of a voltmeter measures is 0.01 V then and it is used in an experiment where no repeat readings are made what is the uncertainty in the measurements? Answer :uncertainty equals plus or -0.01/2 equals plus or -0.005 V Question two : if the smallest value on a meter measures 0.01 mA and it is used in an experiment Where repeat readings are made as follows 0.04mA 0.04 mA and 0.04 mA what is the uncertainty in the measurements? Answer two: uncertainty = plus or -0.01 mA/2 equals plus -0.05 mA
Data
Information, either qualitative or quantitative that have been collected.
What should you comment on if you're evaluating results?
Might be a final calculation of a physical quantity or property(e.g resistivity) or a statement of the relationship established between two variables. Degree of accuracy therefore is s guide to number of sig fig in conclusion Mathematical links established by or verified between quantities should be stated in a 'relationship' conclusion. Evaluate to establish validity. Strengths of experimental evidence may include : -Reliability of data (suggest improvements where appropriate). You may need to consider the effect of the control variables if the experimental evidence is not as reliable as it should be. - discuss the methods Or proposed to eliminate or reduce any random or systematic errors describe the steps taken to deal with anomalous results -evaluate the accuracy of the results by considering the percentage uncertainties in the measurements. These can be compared to identify the most significant sources of error in the measurements which can then lead to discussion of how to reduce the most significant sources of error. -propose improvements to the strategy or experimental procedure is referring to the above discussion on validity as justification for the proposals -suggest further experimental work based on the strength of the conclusions. Strong conclusions could lead to prediction of how to test it.
Fair test
One in which only the independent variable affects the dependent variable
Control variable
One which may in addition to the independent variable, affect the outcome of the investigation and therefore has to be kept constant or at least monitered. The physical quantities are fixed by the experimenter as if they changed during the test may affect the dependent variable and if so results would not be valid (would not be a fair test)
Percentage uncertainty in a repeated measurement
Percentage uncertainty = uncertainty _____________ x 100% Mean value
Percentage uncertainty of a measurement
Percentage uncertainty = uncertainty _____________x 100% Value
Precision
Precise measurements are ones in which there is very little spread about the mean value. The precision of a measurement is high if repeated measurements are close together in value (small spread), however they mayn't be close to the true value. (Depends only on the extent of random errors and gives no indication of how close results are to the true value)
Situations where uncertainty may be increased
Sometimes other factors have a more significant affect on uncertainty and the resolution of the instrument if this is suspected then is best to record the full reading and then round to fewer significant figures to reflect this issue. When timing with the stopwatch capable of measuring to 0.01 seconds human reaction time (which may be up to 0.5 seconds in starting and stopping the stopwatch) will contribute significantly to uncertainty. If the time of the 10.39 seconds is displayed The uncertainty is more likely to be due to the reaction time of the experimenter- here the student should write should record the number but around it to 10.4 seconds or even 10 seconds later if a student measures the length of a piece of wire it is very difficult to hold the wire completely straight against the wall or it is kinked the uncertainty is likely to be higher than the +-1mm uncertainty of the ruler. -could be judged to be nearer +-2 or 3 mm.
Why/ how could systematic errors occur
Sourced of systematic error can include: - the environment - methods of observation or instruments used e.g calibration error (e.g zero error), -from incorrect use or reading of instruments (e,g parrallax errors), --poorly set up or calibrated equipment or -be caused by another factor changing the quantity in an unknown or unrecognised manner.
Validity
Suitability of the investigative procedure to answer the question being asked. For example, am investigation to find out if the rate of a chemical reaction depended upon the concentration of one of the reactants would not be valid pride cure if the temperature of the reactants was not controlled.
Measurement error
The difference between a measured value and the true value.
How can random errors be reduced?
The effect of random errors can be reduced by making more measurements and calculating a new mean. A larger magnitude of measurement will also tend to have smaller random error.
Reproducible
The extent to which the measurement of a quantity remain consistent when repeated by a different person, equipment or technique. A measurement is reproducible if the investigation is repeated by another person or by using different equipment or techniques the same results are obtained.
Calibration
The marking of a scale on a measuring instrument. This involves establishing the relationship between indications of a measuring is turning and standard or reference quantity values, which must be applied e.g a temperature scale can be marked on a thermometer In melting ice to see whether it reads 0 degrees and marking 100 degrees in boiling water in order to check if it has been calibrated correctly.
Parallax error
This is an error in reading an instrument employing a scale and pointer because the observers eye and pointer are not in line perpendicular to the plane of the scale. This would generally read to a random error, however if the observer is always in the same incorrect position could lead to a systematic error.
Resolution
This is the smallest change in the quantity being measured (input ) of a measuring instrument that gives a perceptible change in the reading. Of an instrument it is the smallest non-zero reading that can be measured using the instrument. If a stopwatch display reads 01:34:23 it's resolution is 0.01 I.e its smallest non zero readings is 0.01s. This can be written as -+ 0.01 s Resolution of a metre ruler with 1mm divisions is +- 1mm = +- 0.001 m. The resolution of a voltmeter which can measure to 1/100v is +-0.@1 V.
The number of significant figures to use to record squared values
This should be the same as the initial values. E.g if the average time is 1.26 s then The average time ^2 = (1.26)^2 = 1.5876 s^2. This should be recorded as 1.59s^2 E.g2 if the average time is 1.1 s then average time^2 = (1.1)^2 =1.21 s^2. This should be recorded as 1.2s^2
Number of decimal places to record average values
This should be to the same number of decimal places ass the individual values taken . E.g if three times have been measured as 1.22s , 1.30 s and 1.26 s, then the average is 1.2633333 s but this should be recorded as 1.26 s E.g2 if three times have been measured as 1.34 s, 1.29 s and 1.27 s then the average is 1.35 but this should be written as 1.30.
How to reduce uncertainty
Use a higher precision apparatus / higher sensitivity Calibration - measure known value - if there is a difference between measured and you can use this to correct the inaccuracy of the apparatus and so reduce your systematic error repeated measurements : by repeating the measurements several times and averaging you reduced the random un certainty in your result. The more measurements you averages over, the less error you're likely to have
When will uncertainty occur at both ends of a measurement?
When measuring the length, time and angle etc the uncertainty will occur at both ends of the measurement in this case the total uncertainty will be 2 x +- half the resolution of the instrument = +-the resolution of the instrument. Example: if 1 metre ruler has 1 mm scale divisions and repeat readings are made as follows 0.112 m 0.112 m and 0.112 m what is the uncertainty in the measurements? Answer the uncertainty equals + -0.001 m
