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Chapter 7 - Analysing the Data Part IV - Analysis of Variance Chapter 1 - Behavioural Science and research Chapter 2 - Research Design Chapter 3 - Collecting the Data Chapter 4 - Analysing the Data Part I - Descriptive Statistics Chapter 5 - Analysing the Data Part II - Inferential Statistics Chapter 6 - Analysing the Data Part III - Common Statistical Tests Probability Sampling distributions Steps in hypothesis testing Type I and Type II decision errors Power Bonferroni Confidence Intervals Readings and links


Chapter 5: Analysing the Data
Part II : Inferential Statistics


Probability and "proof" in statistics

Statistics 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 low, a better decision might be to conclude that maybe these aren't random fluctuations that are being observed. Maybe there is a systematic, predictable, or understandable, relationship going on? In this case, we reject the initial randomness hypothesis in favour of one that says, "Yes we do have a real relationship here" and then go on to discuss or speculate about this relationship. How has this discovery of a real relationship, or this piece of new knowledge, going to help us understand behaviour? How have we solved some particular theoretical or practical problem out there in the general mass of humanity!

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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