Transcript Many Possible Explanations Exist

Quick Review
Central tendency: Mean, Median, Mode
Shape: Normal, Skewed, Modality
Variability: Standard Deviation, Variance
Quick Review
SAM PLE  PO PULATIO N
X  X
X 
X

X
S 
2
X
SX 
2
n
X
2
N
SX   X
2
X
 (X  X )
2
n 1
(X  


N
X)
SX 
2
X 
 (X  X )
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n 1
 (X  
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2
Evaluating scores
Raw score of X:
-Measure of absolute standing
-Difficult to interpret
Z-SCORE
- Measure of relative standing
Z-Transformation
-Transforming all raw scores
in a distribution does not
change the shape of a
distribution, it does change
the mean and the standard
deviation
Z Transformation
-Z transformation
provides a common
metric to compare scores
on different variables
Given X , find Z
Given Z , find X
Find Z
Find X
-THEORETICAL PROBABILITY
DISTRIBUTIONS (Z, F, T)
-Used for testing hypothesis
-Provide a way of determining probability
of an obtained sample result (experimental
outcome)
-Usually, the probably that experimental
result occurred by chance given null distribution
A THEORETICAL PROBABILITY
DISTRIBUTION
The standard normal curve:
- Bell-Shaped, symmetrical, asymptotic
- Mean, Median and Mode all equal
- Mean = 0; SD (δ) = 1; Variance (δ2) = 1
THE NORMAL CURVE
Area under curve  probability
-Z is continuous so one can only compute
probability for a range of values
THE (STANDARD) NORMAL CURVE
BASIC RULES TO REMEMBER:
THE (STANDARD) NORMAL CURVE
BASIC RULES TO REMEMBER:
50% above Z=0, 50% below Z = 0
34% between Z=0 & Z= 1 / between Z=0 & Z = -1
68% between Z = -1 and Z = +1
96% between Z = -2 and Z = +2
99% between Z = -3 and Z = +3
THE (STANDARD) NORMAL CURVE
TWO-TAILED CRITICAL VALUES
5% + and -1.96
1% + and – 2.58
THE NORMAL CURVE
ONE-TAILED CRITICAL VALUES
5% + OR - 1.645
1% + OR – 2.33