Topic 5_Normal Curve.pdf - Probability and Normal Curve...

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Probability and Normal Curve Chapter 5
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In This Topic …. l The material we will deal with is fairly abstract and conceptual. l There is likely to be a ‘so what?’ factor to this material. l However, what we are learning today is the foundation for many of the statistical procedures we will utilize in the future.
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In This Topic…. (contd.) l Previously, we have looked at ways to describe data – relative frequencies, measures of central tendency, measures of dispersion. l We will now switch our focus, to decision making or what is called inferential statistics. l Rather than just examining the data itself, we will learn how to use the data to make inferences about the population.
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In This Topic…. (contd.) l Probability l Probability Distribution l Normal Probability Distribution/Normal Curve l Computing z-scores and Area Under the Normal Curve
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Probability l Probability is the cornerstone of inference and decision- making (pages 133-136). l By combining data analyses with probability, we can make statements like, ‘if the prediction were true in the sample, it is likely we would find the same given set of results in the population.’ l Formal definition: ‘the probability associated with an event is the number of times the event of interest (success) can occur relative to the total number of times any event can occur.’
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Probability (contd.) l Symbolized by P l Ranges from 0.0 to 1.0 = 0 means completely impossible, while 1 means certain to happen. l In the social sciences the convention is to express in proportions (decimals). Sometimes they are presented in percentages. l Simplest and most commonly used example is tossing of coin – what is the probability of a head when a coin is tossed once? Probability of an outcome of event = Number of times the outcome or event of interest can occur Total number of times any outcome or event can occur
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Probability (contd.) l Standard examples; what is the probability of getting a head when a coin is tossing once; getting a number 2 when a dice is rolled once; getting a heart from a full deck of 52 cards ? l As likelihood of an event increases (meaning there is a greater chance of it occurring than not occurring), the probability increases towards 1 and as the likelihood decreases (meaning there is a greater chance of it not occurring), the probability approaches zero. l What does a probability of 0.25 versus a probability of 0.75 imply?
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Probability Distribution l Defined as: a listing of possible outcomes for a variable, together with their probabilities. l eg. probability distribution of rolling a single dice; two dice? l As the number of possible values for the variable increases, the graph of the probability distribution looks more like a continuous line function. l coin flip, roll of dice, roll of two dice, roll of three dice l Probability distributions are theoretical, that is what should happen as samples approach infinity and all possible outcomes in every sample being equally likely.
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Probability Distribution (contd.) l What if we were flipping two coins? If we flip each coin once, what is the probability distribution for getting heads?
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