Skill Guide : A
Analysing Evidence and Drawing Conclusions

1. Overview

1.1 Typical Analysis outline

Graphs	A4 size Sensible choice of scales for the axes. Title. Axes labelled with variable name and unit Line of best fit Must be neat and accurate
Calculated values	Equations explained clearly. Calculated values tabulated neatly (as for results).
Scientific model	Prediction may be revised to include additional knowledge. OR Quantitative scientific model created to explain the results.
Test of model	The scientific model is tested by drawing additional graphs OR by numerical analysis of the results.
Conclusions	Trends in graphs and results stated. Scientific explanation for the graphs and results are summarised.
Reliability of conclusions	Discussion of how well the scientific model agrees with the results. Discussion of possible scientific reasons where the two are different.

1.2 Writing up your Analysis

Take care with your graphs. Drawing the graphs should be the easiest part of the analysis to do correctly because graph drawing follows a few standard rules. Make sure that values calculated from the results are tabulated neatly, with correct units. Be thorough with your analysis, whatever you do don't just write "my results prove my prediction is correct".

Conclusions should be straightforward and clear. Make the most of your results, but always be honest, never try to deceive. When you have several graphs make sure that they are clearly titled, or given a number, so that you can refer to an individual graph without there being any confusion.

If your results are very weak it will be impossible to draw reliable conclusions from them. Unless you have good results you can not get a high mark for analysing them.

2. Introduction

2.1 Analysing and Concluding

If this is part of a full investigation then the Analysing skill area should be quite straightforward. The analysis and conclusion should be an in-depth look at the results and a comparison with how well they match the scientific model of the prediction. If a prediction has not previously been made then now is the time to produce a scientific model to explain your investigation. Refer to the Planning skill area for more details of how to do this.

The type of analysis required will depend on the investigation, although most have similar requirements. So, the following lists should be treated as guides rather than prescriptions. Every investigation is different and you must use your own judgement.

• Analysing may require you to...
  • draw graphs/diagrams using the raw data
  • use equations to calculate values from the raw data
  • draw graphs/diagrams using calculated values
  • measure gradients and intercepts from graphs
  • test predicted quantitative relationships

• Concluding will require you to...
  • describe trends and features in the data and graphs
  • create a scientific model to explain trends and features
    OR update the existing scientific model (prediction) to account for new information
  • explain how well the scientific model agrees with the results...
  • ...and give (possible) explanations for any differences

2.2 Processing Results

Quite often the raw data must be processed using mathematical formulae. Explain clearly what you are doing, the formulae used, and make sure you get the units correct. Calculated values must be organised in a logical and neat way, as for the raw results, and to a consistent and sensible accuracy. There is no need to show the workings for repetitive calculations that are made with a calculator.

Remember that if your evidence is insufficient, or unreliable, then no matter how good your analysis is you will not be able to get the highest mark. Similarly, the scientific knowledge used must be at the Higher Level. Check carefully with your syllabus that your are including as much Higher Level knowledge as possible.

3. Graphs and Charts

3.1 Hand drawn or computer generated?

A computer generated graph will not gain any more marks than one that is hand drawn. Quite often a computerised graph loses marks because it has not been done well enough. If you are not already skilled at using a charting package and do not have much time to spare then don't even attempt to produce one - you will most likely waste a lot of time as well as end up rather frustrated. Hand drawing graphs does not take long. Sometimes it is worthwhile to do a rough version first and then copy out a neat version later when you are sure you have got the scales, points and line of best fit correct.

The graphs on this page were all created using Microsoft Excel. For those of you interested in creating similar graphs further details are provided in the IT section.

3.2 Line Graph

Most of the graphs that have to be plotted will be line graphs. A pair of (x,y) values are used to plot points and then a line of best fit is drawn.

size	A4 paper (or bigger)
title	short meaningful title
x axis (across)	independent variable
y axis (up)	dependent variable
axis labels	each axis labelled with variable name and unit
points	accurate, neat, easy to see normally take up at least half of the paper in both directions.
line of best fit	smoothly and neatly drawn
multiple lines	points and lines colour coded, with a key

Example line graph

Full size graph and results table.

NEVER join points dot-to-dot.

How NOT to do it

3.3 Scatter Graph

A scatter graph is very similar to a line graph. Instead of plotting a single value (usually the average) all the values are plotted. This gives some idea of the accuracy of the results and may help when drawing the line of best fit. A scatter graph also shows up any value that is completely wrong because it won't be near any of the other points. Although it doesn't tell you anything you couldn't work out from the numbers in the results table, a (good) visual image can often make the job much easier.

In this example the points have been plotted but the line of best fit has not yet been added. It can be seen that all the results appear to follow a consistent pattern. The variation in the measured distance can also be seen to increase as the force is increased. At a force of 2N the variation in distance for the five repeats is 1cm. For 10N the variation has increased to 35cm. This shows that although the results are consistent there are some factors that are difficult to have complete control over.

For this particular experiment these results are perfectly acceptable. In this case, because all the results are consistent, plotting average values would show the same trend as the scatter graph and would be the best thing to do. The scatter graph could be used to comment on the accuracy and reliability of the results. This could also be done equally well by referring directly to the results in the results table.

Full size graph

3.4 Line of Best Fit

In general if you are investigating a simple relationship between two variables you will be able to draw a line of best fit. A line of best fit shows the pattern or trend you (think) you would get if you were to remove all the random measurement errors from your experiment.

A line of best fit may be straight or curved. It may pass through some of the points but won't pass through all of them. The quickest way to lose marks is to join the points dot-to-dot style; you will immediately drop down to 4 marks!

Another common mistake is to make the line of best fit pass through the origin when it shouldn't. Every experiment is different so you need to work out where the graph will go for small and large values of the independent variable if you are unable to measure them.

If you can't draw neat curves by hand then consider getting one of the special flexible rulers that are designed specifically for this. They make the job much easier to complete. It is always a good idea to mark the line in very faintly in pencil, then to go over it again when you are completely happy with it.

3.5 Bar Chart

These are best saved for categoric variables only. These are usually quite easy to produce with a computer because a line of best fit is not appropriate.

Consider an investigation into the electrical resistance of different materials. The five different materials used are an example of a categoric independent variable. There is no obvious relationship between the five different materials apart from the fact they are all metals. Copper and iron are elements while the remainder are alloys (mixtures of different metals). For this selection of metals it would be difficult to think of a simple theory that would predict the resistance values. Any theory would need to be based on atomic physics, and would need a better selection of materials to test it out on.

3.6 Pie Chart

These are useful to show the amount of something compared to the total amount. Individual sectors of the pie may be labelled with the percentage, the number, or the name of the tree, whichever seems the most appropriate.

Here is an example for a tree survey.

Tree type	number	percentage	angle (degrees)
Scots Pine	1	5	19
Silver Birch	2	11	38
Hornbeam	3	16	57
Oak	3	16	57
Beech	10	52	189
Total	19	100%	360°

percentage = 100 × number ÷ total

e.g. Scots Pine = 100 × 1 ÷ 19 = 5.26
This can be rounded down to 5%

angle = 360 × number ÷ total

e.g. Beech = 360 × 10 ÷ 19 = 189.47
This can be rounded down to 189°

4. Trends in Graphs

The most basic part of the conclusion is to describe the trend in the results. Some of the simpler trends are listed below, more complex relationships may be a combination of two or more of these. Remember that it is the analysis of these trends, and explaining them scientifically, that gains high marks.

4.1 Summary of trends

Straight line (linear) graphs
	passes through the origin y increases at a constant rate y is directly proportional to x equation: y = mx
	positive gradient, m y increases at a constant rate y is proportional to x plus a constant equation: y = mx + c
	negative gradient, m y decreases at a constant rate y is proportional to -x plus a constant equation: y = mx + c (m is negative)
	y is not dependent on the value of x i.e. y is constant equation: y = c
Curved (non-linear) graphs
	y increases at an increasing rate possible equations: y = mx², y = mx³,etc e.g. y is proportional to x squared
	y increases at a decreasing rate possible equations: y = m√x or y² = mx, etc e.g. y is proportional to the square root of x.
	y decreases at a decreasing rate possible equations: y = m/x, etc e.g. y is inversely proportional to x
	y decreases at an increasing rate
	y has a maximum value
	y has a minimum value

5. Testing Linear Relationships

5.1 Linear relationship (Straight line graph)

If you predicted a linear relationship and this is what you have got then checking your prediction should be straightforward. Usually the gradient of the graph is required, and sometimes the intercept is useful too. Often the graph is mostly as predicted but may, for example, curve off at the end. Always try and explain why this has happened. It may be because other difficult to control factors are having an effect or that your scientific model is too simple. Showing that you have a clear understanding of the limitations of your experiment is a good way to gain marks.

5.2 Measuring gradients

For a straight line graph this is simply a matter of taking measurements from appropriate places. For a curved line you must first draw in the tangent at the point where the gradient is to be measured. In both cases make sure that measurements are taken over as big a difference as possible. This improves accuracy.

5.3 Equation for a straight line

The general equation for a straight line is;

y = mx + c

Definitions

y	dependent variable or calculated values
x	independent variable or calculated values
m	gradient (or slope) of the line
c	value of the y intercept (where the line crosses the y axis)

5.4 Calculating a gradient from a straight line

gradient:
m = Y÷X

5.5 Drawing a tangent to calculate a gradient

A tangent has been drawn at x = 0

gradient at x = 0:
m = Y÷X

The gradient decreases as x increases.

5.6 An example

If you are carrying out an investigation into a chemical reaction you may be measuring how fast a gas is given off. You may be measuring the time since the start of the reaction (in seconds) and the volume of gas produced (in cm³). Suppose the graph looks like the one directly above. Measuring the gradient at the start (time=0 seconds) would tell you how fast the gas was being produced at the start of the reaction. This would tell you the initial rate of the reaction. In this case the rate of the reaction would be measured in cm³ per second (cm³/s). The graph curves downwards (away from the tangent), hence the rate of the reaction decreases with time. The rate could be measured at any point on the curve by drawing another tangent and measuring the gradient.

6. Finding and Testing Non-Linear Relationships

6.1 Non-linear relationships (Curved graphs)

It is almost impossible to tell what the equation for a curved line is just by looking at it. To find if there is a relationship you have to study the data and try to make a good guess at what it might be. By plotting another graph you can test if your guess is correct. The easiest way to understand this is by working through an example.

mass (kg)	distance (m)
0.101	1.76
0.151	1.18
0.201	0.87
0.251	0.69
0.302	0.58
0.352	0.49
0.402	0.42

6.2 Finding the relationship

The basic trend of the graph shows that the distance decreases (at a decreasing rate) as the mass increases. Is there a pattern to the results?

• As the mass doubles from approximately 100 to 200g the distance changes from 176 to 87cm. The distance has roughly halved; 176÷2 = 88cm.
• If the mass is trebled from 100 to 300g the distance changes from 176 to 58cm. The distance is now roughly one third; 176÷3 = 59cm.
• Double the mass from 200 to 400g. The distance has again approximately halved from 87cm to 42 cm.

The distance looks like it is inversely proportional to the mass. This is a fairly common relationship. This has the general formula;

y = m/x, or y = m × (1 / x)

Note that 1 / x is another way of writing 1 ÷ x .

So, for the graph above we can write the equation;

distance = constant × (1 / mass)

6.3 Testing the relationship

If this formula is correct plotting a graph of distance against 1/mass should be a straight line. The value of the constant in the equation is the gradient of the graph.

mass (kg)	1/mass 1/kg)	distance (m)
0.101	9.90	1.76
0.151	6.62	1.18
0.201	4.98	0.87
0.251	3.98	0.69
0.302	3.31	0.58
0.352	2.84	0.49
0.402	2.49	0.42

Success! The straight line shows that the distance travelled is inversely proportional to the mass.

6.4 What to test

If you already have a prediction including an equation then just go ahead and test it out. If the resulting graph is an (almost) straight line then you can give yourself a pat on the back. If it is nowhere near straight then either the predicted equation is wrong or the data is not very good. You may be able to produce a better scientific model that explains your results or you may be able to explain why your results do not fit the expected pattern. Simple, well controlled experiments tend to give better results than complex investigations with difficult to control variables.

If you have no idea of what the equation is there are only a few simple relationships you can realistically test. These include squared, cubed, square root and inverse relationships. If it is much more complex it won't be easy to work out. There is no point trying to force an equation to fit the data unless you have a scientific explanation to justify the equation.

A program such as Excel can be used to try out different trend lines and it will also show the equation for the line. Refer to the IT section for more details.

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