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Chapter 5 Some Key Ingredients for Inferential Statistics: The Normal Curve, Probability, and Population Versus Sample

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**The Normal Distribution**

Normal curve

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**The Normal Distribution**

Normal curve and percentage of scores between the mean and 1 and 2 standard deviations from the mean

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**The Normal Distribution**

The normal curve table and Z scores Gives the precise percentage of scores between the mean (Z score of 0) and any other Z score Table lists positive Z scores

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**The Normal Distribution**

Steps for figuring the percentage above of below a particular raw or Z score: 1. Convert raw score to Z score (if necessary) 2. Draw normal curve, where the Z score falls on it, shade in the area for which you are finding the percentage 3. Make rough estimate of shaded area’s percentage (using 50%-34%-14% rule)

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**The Normal Distribution**

Steps for figuring the percentage above of below a particular raw or Z score: 4. Find exact percentage using normal curve table 5. If needed, add or subtract 50% from this percentage 6. Check the exact percentage is within the range of the estimate from Step 3

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**The Normal Distribution**

Steps for figuring Z scores and raw scores from percentages: 1. Draw normal curve, shade in approximate area for the percentage (using the 50%-34%-14% rule) 2. Make rough estimate of the Z score where the shaded area starts 3. Find the exact Z score using the normal curve table

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**The Normal Distribution**

Steps for figuring Z scores and raw scores from percentages: 4. Check that your Z score is similar to the rough estimate from Step 2 5. If you want to find a raw score, change it from the Z score

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**Probability Probability Outcome**

Expected relative frequency of a particular outcome Outcome The result of an experiment

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**Probability Range of probabilities Probabilities as symbols**

Proportion: from 0 to 1 Percentages: from 0% to 100% Probabilities as symbols p p < .05 Probability and the normal distribution Normal distribution as a probability distribution

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**Sample and Population Population Sample Methods of sampling**

Random selection Haphazard selection

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Sample and Population Population parameters and sample statistics

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**Controversies and Limitations**

Is the normal curve really so normal What does probability really mean? Sample and population

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Chapter 4 The Normal Distribution EPS 625 Statistical Methods Applied to Education I.

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