Chapter 5: Analysing the Data |

## Probability and "proof" in statisticsStatistics can never "prove" anything. All a statistical test can do is assign a probability to the data you have, indicating the likelihood (or probability) that these numbers come from random fluctuations in sampling. If this likelihood is Uncertainty is present whenever we deal with samples rather than populations in that we can never claim anything about populations with 100% certainty. The goal of the game of statistical inference, is to keep the level of uncertainty in our results within acceptable limits. Notice how the word "acceptable" implies an element of human judgement (i.e., subjectivity). This is a correct perception; what counts as an acceptably low level of uncertainty (even though it may be an objective or analytically established probability) depends upon who you ask and how strong your arguments are in defence of your claims. There is no absolute standard against which the errors associated with statistical claims may be judged. We say this to provide you with a realistic perspective on statistical analysis of behavioural data - all statistical procedures do is "crunch the numbers" (this is the "objective" aspect); however, humans must ultimately decide what is to be made of those numbers (this is the "subjective" part). |

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