Intentional differences
In experiments, different 'individuals' are given different experimental treatments with the intention of comparing these treatments. For example:
The intention of these experiments is to determine whether these differences in experimental treatment cause differences in the measurements.
Signal and noise in experimental data
In experimental data sets, the variability caused by different experimental conditions is the signal in the data since the intention of the experiment is to determine the effect of these differences.
However the signal in the data is usually obscured by the natural variability in the data — the noise in the data set.
A major role of statistics is to estimate the signal from data that also contain noise.
Effect of fertiliser on tomato plants
In the diagram below, 20 tomato plants are grown as described earlier, but 10 of them are given added fertiliser. In practice, this experiment would be conducted to determine the effect of the fertiliser on yield, but in this example it is known that the fertiliser increases yield by 0.5 kg per plant.
Observe that the natural variation in yields obscures the effect of the fertiliser. From these data, you cannot even be certain that the fertiliser has any effect. Click Another 20 plants to repeat the experiment with other tomato plants.
Click the checkbox Vary effect. The slider lets you adjust the true effect of the fertiliser. Observe that when the fertiliser effect is large, it can be fairly clear that the fertiliser does improve yield — the signal is large in relation to the noise. However when the fertiliser effect is small, the signal is so small that the noise masks it.
Note that the data from this experiment would be entered into a data matrix as shown below for analysis.
Yield | Group |
---|---|
6.57 6.53 4.71 5.32 6.15 5.08 6.17 4.93 3.16 4.57 6.13 7.49 6.00 4.84 9.01 6.11 5.55 5.48 6.84 6.18 |
No fertiliser No fertiliser No fertiliser No fertiliser No fertiliser No fertiliser No fertiliser No fertiliser No fertiliser No fertiliser Fertiliser Fertiliser Fertiliser Fertiliser Fertiliser Fertiliser Fertiliser Fertiliser Fertiliser Fertiliser |