Practical Investigation

Variables

A variable in practical work is something that can change.

In a practical there are 3 sorts of variables you need to work out, in terms of what they are and how to tell the difference.

Example

Suppose we wanted to compare different brands of batteries to see which one lasted longest in a torch.

In this case, for the 3 types of variables

• The independent variable. This is the one that you change to try to find something out. In our example, the type of battery would be the independent variable.

• The dependent variable. This is the one that you measure, or otherwise observe, to see how it changes when you change the independent variable. In our example, the time it takes for the torch to go out would be the dependent variable.

• Controlled variables are ones you keep the same to make it a fair test. In our example, this could include the torch and its bulb would have to be the same, the temperature it was at, how dim it got before you decided it was ‘out’. In NCEA you must justify (explain why) you controlled significant variables to improve your outcome. Significant controlled variables are those that will cause noticeable change to the outcome.

Variables can be qualitative or quantitative.

• Qualitative variables are ones you can’t measure. The brand of battery is an example (Eveready, Panasonic and so on).

• Quantitative variables can be measured e.g. the length of time it takes the torch to go out.

For the Physics investigation, both the independent and dependent variables must be quantitative because we would not be otherwise able to construct a meaningful line graph.

Range

If your independent variable is quantitative, you have to decide the range and interval for it. The range means the minimum and maximum amount you are going to test.

For example, suppose you want to know how long it takes an Aspro tablet to dissolve at different temperatures.

The temperature is your independent variable.

• You decide the range, the minimum and maximum temperature. You may decide to do the minimum and maximum possible (zero and 100 degrees). But you may decide to use a smaller range, because you think no-one is going to take an Aspro in icy-cold or boiling water (which could be dangerous). You should give the reasons for your decision about the range in your discussion.

• You decide the interval. For example, if you decided a range from 20 to 50 degrees, you might decide to do a 10 degree interval (20, 30, 40, 50). Someone else might decide on a 5 degree one. Neither one is the “right” answer. Again, you should give your reasons for your decisions in your discussion.

Dependent variable

You also have to decide how you are going to measure or compare your dependent variable, so that it can tell you something about what you are trying to find out. For our example with the Aspro, this could be “with a stopwatch, by timing from when I drop it into the water to when the fizzing stops”. When you do your plan, your statement needs to say exactly what you did. A student who just said they measured “the fizzing” would not have done this. Exact statements are required to gain more than an Achieved grade.

A common mistake is for the statement on the dependen variable to be too vague.

"I will measure the reaction with a stopwatch". This doesn't mean anything: what reaction, how do you tell when it is reacting? When are you starting and stopping i.e. what are your star and end points? Your statement about the dependent variable MUST clearly state what observation you measure and how.

Justifying why you chose the measurement method you used can be evidence towards excellence.

Data

Data is the results of an experiment, usually numbers. Since you do the experiment multiple times to see if your answers are consistent, you can wind up with an lot of numbers to deal with .

For example, the following data is from an experiment melting an ice cube in a cup of water and measuring the temperature of the water: Several students have collected the data for different trials on different bits of paper (this is not a good idea because they could easily get lost).

The students have made a few other mistakes as well.

• They don't have a consistent way of writing their results down,

• they haven't labelled which numbers are the minutes and which is the temperature (mostly). We can guess, in this case - but there are other experiments where guessing would be far too hard.

• One of the trials is labelled "Fifth trial" but there only appear to be four trials; this is confusing.

A better way would be to put the results into a single table prepared in advance. When you plan out your experiments, you should try to draw up such a table in advance if you can. Below is an example

• You must give units everywhere they are needed to get Merit or better. You must give the unit at least somewhere for each quantity to get to Achieved. The units MUST be correct and written correctly.

In the example above we have assumed the results of the 'fifth trial' are really the 4th. There are still a few problems.

We need somehow to show the pattern of results. To do this, the best way is a graph. But which set of results should be graphed?

The answer is all of them, but not as separate points. Instead we average the results. To do this, we add them together and divide but the number of results.

• Be careful you average the correct direction. We want to average all the 1 minute temperatures for four trials, not all the temperatures of Trial 1.

The average of the one minute temperatures is: (17 + 18 + 17 + 17) divided by four = 17.25 degrees.

However, you might not want to graph to this many decimal places and might round this to 17 degrees.

We have a problem with the 5 minute result for Trial 4: should we include it in the average? The answer is usually no, as it appears to be a mistake. However, it should be checked out in case it isn't a mistake. A result like this is called an outlier and outliers are not included when we average results for analysis.

Below is the table of averaged data. We call this the processed data.

Now we can graph the results. Some graph rules for Science:

• Science graphs are mostly line graphs - one quantitative variable against another.

• A bar graph or pie graph could be used if one of the data sets is not quantitative. The Physics practical will never involve this as it would be impossible to draw a meaningful line. A biology or chemistry graph will usually not involve an equation so there are cases when a bar or pie graph may be appropriate.

• Science graphs should have a title explaining what the graph is about

• Usually, the independent variable goes along the horizontal axis, which is called the x-axis. However, there are times when it is mathematically preferable to have the independent variable on the y-axis. An example would be a graph of current against voltage, because having the voltage on the y-axis means that the gradient of your graph is mathematically directly related to the resistance

• Both axes must be labelled and with units. Units must be written with their name (e.g. seconds) or the correct SI abbreviation (s). A unit written with a non-standard abbreviation such as "secs" for seconds will be marked wrong. Note that wrong units anywhere in your write up will prevent you getting a M or E grade.

• not all graphs have to start at zero, but graphs should NEVER have a 'break' in them. Graphs MUST start at zero if the zero point is important from a maths or science point of view. The x-axis MUST start from zero if a y-intercept is required for the equation. This will be the case in most practicals you might do. Numbers must be consistent along the axes (e.g. a graph with an x-axis labelled 0 below the y-axis then , 20, 30, 40... would fail; but if the y-axis was unlabelled or had 10 below it that would be OK)

• the numbers on the axes have to go up in even amounts

• the data points are best plotted as a small cross (x)

• a smooth line or curve should show the trend of your results. All graphs for the Physics practical should be a STRAIGHT line of best fit. More on best fit lines later. Biology and Chemistry graphs may be a curve.

A graph of results for the experiment above might look something like what is shown below. Note that if this was a graph for the Physics standard, the flattening of the line at the end would be ignored and only the straight sloping part would be drawn (you will not be given a procedure that would produce this sort of result)

Below is an annotated version of this graph showing some of the features. Note that your graph should not flatten at the end like this one (here, the cup stopped cooling once it reached room temperature).

Equations of lines

One of the things you will have to do to get a M or higher grade is to get an equation for your line. The example below should help show you how to do this.

A student does an experiment where he drops marbles one by one into a measuring cylinder containing an initial 40 mL of water. After each marble is dropped in, the water level is measured. The results are shown below. In this case I have not averaged because there is no significant variation in results between trials due to the nature of this experiment, but you can be absolutely sure the experiment chosen for your assessment WILL have plenty of variation between trials. Therefore you would graph the processed result table.

To get the equation you need two things: the gradient and the y-intercept.

The calculation for the gradient is shown on the graph. Gradient is rise over run. The points where I have calculated the gradient are shown with the green lines; notice that this goes to the red best-fit line NOT the data point. Your triangle for calculating gradient must NOT use points that are too close together (they should take more than half the best fit line).

For the green triangle I have used, the rise is 11.8 mL and the run is 5 marbles (notice I have given the units for both). The calculations are:

rise = 51.8 mL - 42 mL = 9.8 mL

run = 6 marbles - 1 marble = 5 marbles

(note; the best fit line on this graph could theoretically have had a fractional number of marbles, even though that is not possible in reality; in practice, I chose the points for my triangle so that this did not happen). I rounded to two significant figures because that was the level of precision of my data).

Therefore the gradient is 9.8 ml/5 marbles = 2.0 mL/marble

(note that the units of the answer here are mL per marble; I can't easily use negative index notation on the web page)

The equation of the line is given by y = (gradient)x + (y-intercept)

so here the equation is y = 2x + 40 where y is the level to which the water rose, in mL, and x was the number of marbles. You MUST state the meanings of x and y from the equation. An alternative way to write this equation would be

water level (mL) = 2(number of marbles) + 40

Either answer would be marked correct in NCEA. Failure to interpret the equation is a significant cause of not reaching a M grade so this is important.

Note that although you could state this equation as a sentence:

"the water level in mL is given by two times the number of marbles plus 40"

Feedback from the moderator says that the equation MUST be in mathematical form and that a sentence by itself is not acceptable (I'm guessing the moderator is a maths teacher). Writing a sentence as well may help you to understand what the equation means.

In the frames below are an example Physics Investigation (for an electricity context) with data only so you could have a go at writing it up yourself, and an annotated model answer from me to show what a high excellence write-up might look like.

Open the blank one in a tab instead of the frame

Open the model answer in a tab instead of a frame