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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

3.10 Inference HOME | Achievement Objectives | Overview | Statistical Cycle | Introduction & Research Question | Discussing Samples | Sample Variability | Sampling Methods | Informal Confidence Interval | Bootstrapping Confidence Interval | Comparing two populations | Using iNZight | Writing a report | Assessment Practice

Randomisation

10

Is the observed difference by random chance?

(Excellence)
How can we estabilsh if a 'test group' is mathematically different from a 'control group'

Video Chris Wilds overview of sample variation etc, (view from 20:10 for randomisation)

Treat the data as completly randomly allocated. Re-sample from the randomly grouped sample data and find the probability that the observed group difference would happen by random chance.

If the chance of the observed difference occurring is low then this indicates that the two group population medians (or means) would be different.

If the chance of the observed difference occurring is NOT low then this indicates that the two group population medians (or means) cannot be seen to be different.

Class notes, Class notes
Class site

 

 

 

We want to compare a control group to a test group

Does the experiment cause the difference seen between the groups (or could it be by random?)

 

 

Does exercising a baby lower the age of first walking?

The Randomisation test is a way to find out if the observed difference is by chance or not.

Re-samples are taken from the sample and the groups are randomly allocated to the re-sample data

The difference between the two (randomly allocated) groups is found.

This is repeated (1000 times) and a distribution of the differences is formed. The distribution is used to calculate the probability that the actual observed difference would happen.

 

 

If this is a low probability then this would indicate that the ‘test’ group population median (or mean) is statistically different from the control group.

If this is not a low probability then this would indicate that the ‘test’ group population median would not statistically different from the control group median (or mean).

Using the Mean instead of Median


What is the chance that the observed difference (of 2.50) between the Exercise and Control group?     0.006

So it is very unlikely that the observed difference is by random chance alone

So therefore there is evidence that the ‘test’ group population mean is different from the ‘control’ group population mean

   
 

 

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