How can we tell if frogs jump further?

• Samples are often compared by first proposing that they could have come from the same population • Two random samples from the same population are unlikely to be the same • Although not exactly the same, is it probable that two samples have been drawn from the same population? • If the probability they came from the same population is small, then the original proposal is not supported • If it is improbable that the difference between the mean values of the two samples could be zero, this is poor support for the proposal that the samples have come from the same source • A ‘confidence interval’ is the range of values that could contain the true value • Small samples are often imprecise, so a difference between samples may be concealed • Precision is also affected by the variability in a population: this could swamp the ‘signal’ difference • Significant does not mean important, only unlikely to have happened by chance