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CHAPTER 1: THE MEAN, THE NUMBER OF OBSERVATIONS, THE VARIANCE, AND
THE STANDARD DEVIATION
•
Data – observations that involve measurements – “scores”
o
Data set – distribution
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Statistics – consists of series of rules and methods used to organize and interpret data
o
Descriptive statistics – describe and summarize data
summary
o
Inferential statistics – make inferences about large populations from samples
draw conclusions
•
Population – comprises all individuals (and scores) that are of interest in study
o
Population parameters – numbers we use to describe population characteristics
Use Greek alphabet
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Sample – comprises part of population selected for study – representation of population
o
Sample statistics – summary numbers describing samples; used to estimate
population parameters
Use English alphabet
•
Sampling error – difference between sample statistic and its population parameter caused
by random error in measuring sample
o
Difference between mean of sample and mean of population
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Sampling fluctuation – difference among samples caused by random factors
o
Individual differences and measurement problems
o
Difference between means of two+ samples
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Each score is symbolized by letter X
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Average (or mean) of all scores in population is call mu – predict everyone score at mean
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Distance (or deviation) of score from mean is (X – μ)
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Variance – average amount wrong if predict everyone score at mean
o
“mean square for error”
o
•
N – 1
st
population parameter that tells us how many scores or observations there are
denoted
•
μ – 2
nd
population parameter tells us mean
•
σ
2
– 3
rd
population parameter tells us variance
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“A measure of central tendency” – most typical scores
o
Mean, median, mode
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Population mean 
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Most used measures of variability
o
range, interquartile range, variance, standard deviation
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Deviation – distance between score and mean
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SS – “sum of squared deviations around the mean”
o
Σ(Xμ)
2
•
Variance – “mean squared deviation”
o
•
Standard deviation – “average unsquared distance, standard distance from mean”
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•
Steps for computing variance and standard deviation
1.
Add up all scores
ΣX
2.
Divide by N to find μ
3.
Subtract μ from each score to compute deviations around mean
(X
4.
Add up deviations and make sure they sum to 0
Σ(X=0
5.
Square each deviation
6.
Add up squared deviations to find Sum of Squares
7.
Divide Sum of Squares by N to obtain Variance, sigma
2
8.
Take square root of Variance to obtain Standard Deviation, sigma
•
Mean – unbiased predictor or unbiased estimate; deviations around it sum to zero
o
Least squares, unbiased predictor – number that is minimum average squared
distance from number it estimates
o
Unbiased estimate – one around which deviations sum to zero
o
Mean squared error – sigma
2
=σ
2
=(ID
2
+MP
2
)
CHAPTER 2: FREQUENCY DISTRIBUTIONS AND HISTOGRAMS
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 Spring '11
 Ackroff

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