Download Diseño y análisis de datos en Psicología

School of Psychology
Dpt. Experimental Psychology
Design and Data Analysis in
Psychology I
English group (A)
Salvador Chacón Moscoso
Susana Sanduvete Chaves
Milagrosa Sánchez Martín
Lesson 4
Normal distribution
1. Normal distribution

The normal distribution is represented as the
limit of a bar chart (increasing indefinitely the
number of bars).
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5
4
20
18
16
14
12
3
2
10
8
6
1
4
2
0
0
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1. Normal distribution: characteristics
1
  0
- 
  
+ 
This distribution depends on 2 parameters :  and 
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1. Normal distribution: characteristics
2
Mo = Mdn = 
The normal curve has a single maximum.
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1. Normal distribution: characteristics
3
 
  1
  1
The normal curve has 2 inflection points
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1. Normal distribution: characteristics
4
The normal curve is asymptotic to the abscissa.
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1. Normal distribution: characteristics
5
As = 0
It is a symmetric distribution (As = 0)
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1. Normal distribution: characteristics
6
Kr = 0
It is a mesokurtic distribution (Kr = 0).
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1. Normal distribution


The parameter  gives the center of the distribution and the parameter
the variability , verifying the following relations:
,
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1. Normal distribution
-3
-2
-
68 %

2
3
95,5 %
99,7 %
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1. Normal distribution
 A   B  C
A

B

C
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2. Standard normal distribution
It exists infinite normal distributions, each
one with their means and standard
deviations.
 Solution: to convert raw scores into
standard scores.
 It implies to convert the normal
distribution into a standardized normal
distribution (with mean 0 and standard
deviation 1).

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2. Standard normal distribution: use
of table, example 1
What standard distance does represent the
33.4% of data immediately over the
mean?
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2. Standard normal distribution: use
of table, example 1
Z=0.97
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2. Standard normal distribution: use
of table, example 2
In a normal distribution with mean 100 and
standard deviation 15, which proportion
do the values between 70 and 130 have?
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2. Standard normal distribution: use
of table, example 2
Xi  X
Z
S
70  100  30
Z1 

 2
15
15
130  100 30
Z1 

2
15
15
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2. Standard normal distribution: use
of table, example 2
p=0.4772x2=0.9544
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2. Standard normal distribution: use
of table, example 3

In a normal distribution with mean 100
and standard deviation 15, what raw score
does define the highest 10% of data?
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2. Standard normal distribution: use
of table, example 3
40%
Z=1.28
10%
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2. Standard normal distribution: use
of table, example 3
Xi  X
Z
S
X  100
1.28 
15
1.28 x15  X  100
19.2  X  100
19.2  100  X
X  119.2
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