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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


How unlikely is "unlikely"?

Let us consider what a probability of 5% means. How unlikely is it? Well, imagine someone coming up to you and saying that they could select an Ace on one draw from a standard pack of cards. The chance of doing this would be = 0.067 (= about 7%). Now suppose this actually happened! At one selection from the pack, this person picked out an Ace! This seems pretty unlikely! Would you think that this was a trick (e.g., cut corners, slightly thicker cards, more than 4 Aces in the deck!) or was it just a fluke? In other words, was this likely to be a systematic event with a logical explanation or 'cause', or, "just one of those things", a random coincidence?

Well in this case, we could describe our null hypothesis as being, Ho: the selection process used was random. Assuming this to be true, we then calculate the probability of drawing an Ace from 52 cards as 7%. Using statistics here as the basis for making a decision we would therefore have to conclude that this is not a "significant" event. We would retain the null hypothesis of a fair selection and conclude that the event was just a fluke (i.e., nothing can explain it other than "It was just one of those things!", or a coincidence). Even though this is a pretty unlikely event, there is not enough evidence to say that a systematic trick is going on (or that a rule has been applied).

But what if this person did the same thing again!! The chance of this (assuming our null hypothesis to be true) is about 0.07 x 0.07 = 0.0049 (or about 0.5%). In this case, the probability of this event happening twice in a row (just by chance, or by ‘fair selection’) is pretty remote (about one chance in 200!). We might be better advised to reject the null hypothesis and conclude that a trick of some sort is going on! That is, there is some selection rule being used here, some association or relationship is going on that will allow us to understand how such an unlikely event could have occurred. In effect, we have decided that this is such an unlikely event that it could not have occurred randomly!! One should be on the alert for sleights of hand, aces up sleeves, or a rigged deck!




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