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# Randomisation

 Is the observed difference by random chance? (Excellence) How can we estabilsh if a 'test group' is mathematically different from a 'control group' 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.

 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