Unit 3 assignment psych stats

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Statistics for Psychology

CHAPTER

SIXTH EDITION

Some Key Ingredients for Inferential Statistics

Describing a Score

Knowing one score tells little about how it relates to the whole distribution of scores
Comparing a score to the mean of a distribution does indicate whether a score is above or below average

Relating a Score to the Mean

Knowing the standard deviation of a distribution indicates how much above or below average a score is in relation to the spread of scores in the distribution

Z Scores -1

Number of standard deviations a score is above or below the mean
Formula to change a raw score to a Z score:

Z Scores -2

Formula to change a Z score to a raw score:

Distribution of Z scores
Mean = 0
Standard deviation = 1

Two Properties of Z Scores

The sum of a set of z-scores is always zero because the mean has been subtracted from each score, and following the definition of the mean as a balancing point, the sum and average of deviation scores must be zero

Two Properties of Z Scores

The SD of a set of standardized scores is always 1 because the deviation scores have been divided by the standard deviation

The Normal Distribution -1

Normal curve

Normal Distribution Characteristics

Symmetrical
Unimodal
Most scores fall near center, fewer at extremes

Percentage of Areas under the Normal Distribution

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

The Normal Distribution and Z Scores

The normal curve table and Z scores
Shows the precise percentage of scores between the mean (Z score of 0) and any other Z score
Table also includes the precise percentage of scores in the tail of the distribution for any Z score
Table lists positive Z scores

Figuring Areas under the Normal Distribution -1

Steps for figuring percentage area above or below particular raw or Z score:

Convert raw score to Z score (if necessary)

Draw normal curve, locate where Z score falls on it, and shade in area for which finding percentage

Figuring Areas under the Normal Distribution -1

Steps for figuring percentage area above or below particular raw or Z score:

Make rough estimate of shaded area’s percentage (using 50%-34%-14% rule)

Figuring Areas under the Normal Distribution -2

Steps for figuring percentage area above or below particular raw or Z score:

Find exact percentage using normal curve table

If needed, add or subtract 50% from this percentage

Check that exact percentage is within range of estimate from Step 3

Figuring Z Scores and Raw Scores from Percentages -1

Steps for figuring Z scores and raw scores from percentages:

Draw normal curve, shade in approximate area for the percentage (using the 50%-34%-14% rule)

Make rough estimate of Z score where shaded area stops

Find exact Z score using normal curve table

Figuring Z Scores and Raw Scores from Percentages -2

Steps for figuring Z scores and raw scores from percentages:

Check that Z score similar to rough estimate from Step 2

To find a raw score, change it from Z score

Samples and Populations

Population
Sample
Methods of sampling
Random selection
Haphazard selection

Table 3-2 Population Parameters and Sample Statistics

Probability

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

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

Controversies and Limitations

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

End of Chapter 3