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Chapter 5
Some Key Ingredients for Inferential Statistics: The Normal Curve,
Probability, and Population Versus Sample
The Normal Distribution
Normal curve
The Normal Distribution
Normal curve and percentage of scores between the mean and 1 and 2 standard deviations from the mean
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
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)
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
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 starts3. Find the exact Z score using the normal curve table
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
Probability
Probability– Expected relative frequency of a particular
outcome
Outcome– The result of an experiment
outcomes possible All
outcomes successful Possible y Probabilit =
outcomes possible All
outcomes successful Possible y Probabilit =
Probability
Range of probabilities– 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
Sample and Population
Population Sample Methods of sampling
– Random selection– Haphazard selection
Sample and Population
Population parameters and sample statistics
Controversies and Limitations
Is the normal curve really so normal What does probability really mean? Sample and population
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