Summary Lectures and Readings: Statistics 1 - Introduction (FSWPE1-032)
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Course
Statistics 1 (FSWPE1032)
Institution
Erasmus Universiteit Rotterdam (EUR)
Book
Craig, B: Introduction to the Practice of Statistics
Detailed and cohesive summary covering all the exam relevant topics and mandatory readings. Examples and graphics included for further understanding. Covers all the learning objectives extensively.
Received grade 9 for this course studying with these notes.
Extensive summary Craig, B: Introduction to the Practice of Statistics - Statistics
Detailed Summary: Lectures and Readings STATISTICS 2.2 FSWPE2-022
Summary Tree diagram (ENG!) + Formulas IN DETAIL!
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Erasmus Universiteit Rotterdam (EUR)
Psychologie
Statistics 1 (FSWPE1032)
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L ec + v re 2
least precise
Norminal :
Variable levels group objects into ↑
calegories , differ in kind , not i n degree
no rank
= ⑲
Die Chart Bar ,
Graph
Stemplots :
seperate each observation in to a
system
Order
political party affiliation Gender
Categorical
:
Le . g
,
...
And a leaf that are then plotted to display while main-
Ordinal : Variable group objects in to caregories ,
VCIVES gender
rCNK
) Alves represent caregories
Order
,
differ in Kind , but reflect rank order Impossible to put value in ↓
aining the original values of the Variable .
E
number number doesn't
;
· e
. g
.: SES a s l ow ,
middle , high ,
level of education represent smth ,
meaningful
distance between i n te r va l s O , is abitory difference 212 225
*
23 215 215 219 223
nas SOme ·
G
.
Histogram , stemplats
fa b s e n c e ·
·
Le . 9
:
Temperature grades ,
i
meani RG C 3
14
P
linear transformations allowed
are ladding
Constants or Multiplications) (lascore , grades
Quantit Cil
e
e
Raitio :
Interval scales , but zero point reflects
↳
true
numbers are meaningful
absence of property, scores can be
Related to values , can
be expressed in number
compared as ratios
e . number of questions correct on
sie
:
of the bars
g
re-
ex a m age i absence
Within
B the
corresponding
,
-
. c l a ss
.
add constants multiplications a l l owe d
So
& or are no rank order
↑
·
r
·
an identifier for each case
But NO Linear transformations >
participant number , name or
(Weight l e n g t h reaction t i m e ,
,
most precise ID
Examing Distrubutions
B
Symmetric distrubtion symmetric if the
A C
:
a is left
S
S
M
and right sides of the graph are approximately
longer
mir ror in ages of each Other
Right-sewed right :
side of the graph is much
than the left side
left-skewed :
left side of the graph is much longer
than the right side
X Variable
Describing Distrubutions with numbers
"x-bar" value
Saverage
Measuring ~
Center
·
:
:
differente
↓WO
M
"Center"
·
Median
:
LTv middle valve
·
Mode (Valve that appears most often)
Measuring spread
·
:
of
&Good measure
because
ra
calculation Square
↓
Quartiles C o re s SD
·
!
· Standard Deviation
only for quantative variables
M
Me DICH
5
:
e percentile
Mean cannot resist the influence of
extreme observations :
it's not a resistant
measure of center/presistant measure
-
is sometimes called 'robust measure
Median is more resistant than median
gefa
·
if adistribution is exactly symmetric
the meantmedian are exactly the same
-
· and
Deviation Standard
Deviation
n
Measuring Spread Quartile
:
Percentile percentage of scores lower
flects the
·
re S
Or equal to a par ticular score &
G
s =
n1(x- x) -
scores
=
2
=
:
6 6
25
36 ↳ s
= =
,
4
-
=
-
1
=M
V
V ,41
V
↓ Add all scores
:
number of scores
= 1
Q
5
55 21 ,
Qu median
=
3
Min
=
2
:
=
.
5
11 ,
,LECHU 2: par t
Standard normal distrubutions
Table entry for 2
lable entry
=
0
.7918
is always the area for z
=
. 81
Suppose obtained . of the 3
. The
0
.
a exam mean score
you
7
6 1 .
5
under the cur ve
on this exam is 5. and the SD is 1
.401 . The scores follow a
to the left of 2
distrubution What with
.
Normal the students
is
population of
M ·
,
&
·
a score of 6 .
7
or lower
?
WI
z-Score
·
(6 . 5)
-5 .
=12
:
7
=
0
,8
1, 451
* Table
:
Standard normal probabilities
·
A
(P(Z0 , 81) P(zx0;
, 81) =
,7910 · *
e
0
I I
50 ,7911 of 79 , %1 of the students obtained a .
1
7
, 0
6
3
or l owe r
z
=
0
. 81
Standard normal t a b l e Example
:
·How tall is a man that is taller than exactly 10% of men
aged 18-24 ?
Lo o k up the probability closest to 0
. 10 in the table
Mh
We need to "unstandardize" the z- s c o re to find the
·
·
mean
-
·
Observed va l ex :
x = =
x =
x +
2x5x
SD
* 70 + 1 -
1
, 28)x(2 ,B) =
X
&
&
-
&
70 + 1 5 8)
, 66 ,42
=
-
3
12 =
-
1
, 28
~
mecire & ·Manuel
,fet A
Moore Mccabe , , crais
cases :
objects described by a set of data
A Tail
Categorical Variable places of
.
a case in to one of ex t re m e values a distrubution
I
Variables :
characteristic of a case
s eve r a l or
calegories Mode major peak
.
groups .
a
Different cases have different values of the
A quantitative variable takes numerical value for Unimodal distribution with one
major peak
Variables label is special variable used
operations
a
which arithmetic adding
A
such as and distribution with
Biomodal
.
two p e a ks
in some data sets to uniquely identify different averaging make sense .
Trimodal distribution with t h re e p e a ks
cases .
C KartiCS .
and e
C Cnumber
Summary
to calculate the quartiles The five-number of set obser vations consists of
summary of
:
a
Arrange the obser vations in
increasing order and locale the observation the first third
-
smallest , quartile ,
the median, the
the median M in the ordered list of observations .
Quartile ,
and the largest observation ,
written in order from small-
2 The quartile obser- symbols the five-number
.
first Q1
is the median of the est to
largest .
In ,
summary is :
Va t i o n s w h os e positions in the ordered list are to the Minimum Qu M Q2 Maximum
left of the location of the Overall median
3 . The third quartile a,
is the median of the obser-
nterquartile range 2
The interquartile range IQR i s the distance between the first
Vations whose positions in the ordered list are to
and third quar tiles
:
IQR =
Q3-Q 1
& call an o b s e r va t i o n a suspected outlier if it falls more
the
right of the location of the Overall median than 5 X/ Q R
, below the
1
first quartile or a b ove the
third quartile .
This is called the 1 5x1QR
. Rule .
3 VI t also called box and whiskers piots
160-
-
A boxplot graph of the five-number summary 140
-
is a :
·
A
Central box spans the quartiles Q.
and Q3 =
120
.
-
line i n the the
·
A
box marks median .
M
100 -
extend from the to
·
ines box out the smallest
80 >
and
largest o b s e r va t i o n s .
cestacarce at ns
The variance s of a set of observations is the average
of the average of the squares of the deviations of the
obser vations from their mean .
In
symbols ,
the Variance
of n observations X, X ,,
. . . . n
is
sa =
x
-
x)" +
(x+ + x( + . . .
+ (xn + =)
M -
A
o in more compac t notation ,
5
x)
=
/Xe -
n =
1 ,
The Standard deviations is the square root
of the variance s s
nEn
=
R
*
-
:
IX .
, Constycur c
A density curve is a curve that
·
is
always on or above the horizont axis
·
has area exactly A u n d e r n e at h it .
A density curve describes the Overall
pattern of a distribution . The a re a under
TheUnweit
fall in that range
Standarc-igand-score CPS (fee Ge COMEINE OUS YElfiGBIES
# X is an observation from a distribution
that has mean M and Standard deviation ,
0
Discrete Variables :
between any two adjacent values (e .
9 ., 0
, 1
, ,
2
3 Children) ,
the standardized va l u e of x is
X -
M
z inter mediate possible
=
no va l u e s are .
O
A Standardized valve i s often called a
z- s core .
Continuous Variables :
In principle , between any two adjacent scale values ,
intermediate values are possible .
(e
. 9
.,
4 . 11 ,4
. 12 , 14 . 13)
ndependent and dependent Variables
Independent variable is the presumed cause in a cause -effect
EffeCt
:
Mit
cause
relation
;
in experiments ,
it is a factor that researchers man-
Independent
V aricible
·
Influences
*
Dependent
Variable
ipulate or systematically vary in order to assess i ts influence
Type of Technology Number of navigation
e r ro rs
On some behavior or o u tc o m e .
Stimulus intensity Influences Re ac t ion time
Dependent variable i s : the presumed effect in a cause-effect
self-esteem Effort expended at
a c h i eve m e n t tasks
relation in an experiment it is the benavior or outcome that
;
,
the re s e a rch e r measures to d e te r m i n e whether the indep-
endent variable has produced an effect .
Mediator Variable
* a variable that provides acausal Link i n the
sequence between an independent Variable Independent Variable Mediator Variable Dependent Variable
⑱
cell
(while
phone use
Distraction n
⑱ Driving Per for mance
variable
driving) limpairea)
and a dependent . At te n t i o n
* VariCIDIE .
either
impair
don't
it
influence
much less .
driving per for mance or
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