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