Randomness of data
Not only do we usually have little interest in the specific individuals from whom data were collected, but we must also acknowledge that our data would have been different if, by chance, we had selected different individuals or even made our measurements at a different time.
We must acknowledge this sample-to-sample variability when interpreting the data. The data are random.
All graphical and numerical summaries would be different if we repeated data collection.
This randomness in the data must be taken into account when we interpret graphical and numerical summaries. Our conclusions should not be dependent on features that are specific to our particular data but would (probably) be different if the data were collected again.
Survival of silkworms
Silkworm larvae must be killed after spinning their cocoons since the silk is damaged when they later emerge. In an experiment to help understand the toxicity of sodium arsenate to silkworm larvae, survival times of 10 fourth-instar silkworm larvae were recorded after being given 0.1 mg of sodium arsenate per gram of body weight.
The results again depend on the specific larvae used. Click Repeat experiment with 80 different larvae to see how the results might change if the data were collected again.
If the experiment was repeated with a different sample of silkworm larvae, different values would be obtained. Click Repeat experiment with 10 different larvae to see how the recorded data might change.
The dot plot, mean and standard deviation all vary considerably.
The results from a single experiment clearly tell us something about survival of larvae when given this amount of poison, but how do we take into consideration the randomness?
Use the pop-up menu to increase the sample size and repeat.
With a bigger data set, the dot plot, mean and standard deviation vary less between the different data sets.