Download Quantitative analysis

Quantitative analysis
Alessandra Fermani
[email protected]
SPSS
• 1 version 1968 IBM
• Last: 22.0 (13 agosto 2013)
• Language: java
• Java System: Microsoft Windows, Mac OS,
Linux ect…
Manual and video
• http://www.ateneonline.it/chiorri/studenti/isbn6
556-1_guidaSPSS.pdf
• ftp://public.dhe.ibm.com/software/analytics/spss
/documentation/statistics/20.0/en/client/Manual
s/IBM_SPSS_Statistics_Core_System_Users_Guid
e.pdf
• Video (it):
https://www.youtube.com/watch?v=ftU4TauCshg
2 windows
• Data view
• variable view (name, Type, with, decimals,
label, values, missing, columns, align,
measure)
• Application
Variables
variable type: numeric or string
Dependent: satisfation
Independent: age, gender
Ordinal: children, adolescents, adult etc…
Likert scale eg. 1= never (disagree) 2 3 4 5 6 7 =
always (agree) (odd - better)
Dummy: dicotomic variables eg. Yes/no or gender
Unidirectional / bidirectional
relationship between variables
• bidirectional (correlation, regression)
• unidirectional (cause and effect)
Formula: Trust index
reliability significance
• p<.05
good level p<.01, p<.001
• Rule of transcription:
eg: (F (1,361) = 6.90, p < .01)
Descriptive statistics
• To take statistics: Frequencies, mean, median,
mode
to operate dispersion, use standard
deviation (SD)
Mean or average
• In statistics, mean and expected value are
used synonymously to refer to one measure of
the central tendency either of a probability
distribution or of the random variable
characterized by that distribution.
Eg. 10 students, grades in a test:
5,7,4,8,5,6,5,7,6,4
mean equal 5,7 because
(5+7+4+8+5+6+5+7+6+4/10 = 5,7)
Standard deviation
Deviazione standard o varianza = dispersione dei dati attorno alla
media
In statistics and probability theory, the standard deviation (SD)
(represented by the Greek letter sigma, σ) measures the amount of
variation or dispersion from the average
• Classroom A – student’s grades:
2,7,4,4,3,4,5,4,4,1,6,4,4,5,4,3
• Classroom B - student’s grades: 6,4,3,4,5,5,2,3,4,2,1,3,5,7,4,6
mean is 4 (GPA), the same in both, but classes are different. the
classroom B is more different compare to classrom A and the SD is
the index that measures.
Median =
In statistics, the median is the numerical value
separating the higher half of a data sample, a population, or
a probability
distribution, from the lower half
Legenda: 1 very good, 2 good, 3 not bad, 4 sufficient, 5 not
sufficient
9 students
scores: 1,4,1,2,3,2,5,2,4
Put in order 1,1,2,2,2,3,4,4,5
Median= (9+1)/2 = 5; 5th position therefore is 2 (good)
N. divided by2
Formula
i= n+1/2
Mode
• The mode is the value that appears most often in a
set of data.
• Eg. 100 subjects are divided into three categories: 33
prefer action movies; 54 romantic ; 13 horror
• The mode is «category of romantic movies» because
this category is most represented
Ex. 1) Find the mean, median and mode
19, 18, 21, 16, 15, 17, 20, 18
Ex. 2) Find the mean, median and mode
Set A: 2, 2, 3, 5, 5, 7, 8
Set B: 2, 3, 3, 4, 6, 7
Measure
The Mean
To find the mean, you
need to add up all the
data, and then divide
this total by the number
of values in the data.
The Median
To find the median, you
need to put the values
in order, then find the
middle value. If there are
two values in the middle
then you find the mean
of these two values.
Set A
2, 2, 3, 5, 5, 7, 8
Set B
2, 3, 3, 4, 6, 7
Adding the numbers up gives:
2 + 2 + 3 + 5 + 5 + 7 + 8 = 32
Adding the numbers up gives:
2 + 3 + 3 + 4 + 6 + 7 = 25
There are 7 values, so you divide
the total by 7:32 ÷ 7 = 4.57...
There are 6 values, so you divide
the total by 6:25 ÷ 6 = 4.166...
So the mean is 4.57 (2 d.p.)
So the mean is 4.17 (2 d.p.)
The numbers in order:
2 , 2 , 3 , (5) , 5 , 7 , 8
The numbers in order:
2 , 3 , (3 , 4) , 6 , 7
The middle value is marked in
brackets, and it is 5.
This time there are two values in
the middle. They have been put
in brackets. The median is found
by calculating the mean of these
two values:(3 + 4) ÷ 2 = 3.5
So the median is 5
RESULTS
So the median is 3.5
The Mode
The mode is the value
which appears the most
often in the data. It is
possible to have more
than one mode if there
is more than one value
which appears the most.
The Range
To find the range, you
first need to find the
lowest and highest values
in the data. The range is
found by subtracting the
lowest value from the
highest value.
The data values:
2 , 2, 3 ,5 , 5, 7 , 8
The data values:
2 ,3 , 3, 4 , 6 , 7
The values which appear most
often are 2 and 5. They both
appear more time than any
of the other data values.
This time there is only one value
which appears most often - the
number 3. It appears more times
than any of the other data values.
So the modes are 2 and 5
So the mode is 3
The data values:
2, 2 , 3 , 5 , 5 , 7 ,8
The data values:
2, 3 , 3 , 4 , 6 ,7
The lowest value is 2 and the
highest value is 8. Subtracting
the lowest from the highest
gives:8 - 2 = 6
The lowest value is 2 and the
highest value is 7. Subtracting
the lowest from the highest
gives:7 - 2 = 5
So the range is 6
So the range is 5
Ex 1) all three averages equal 18
File eg proloco
1. Find the AGE mean and SD
2. Recod variables (and control if you have mistake in the words eg
have you write always macerata? Or have write Macerata and
macerata) : prov (provincia) with this values below
•
•
•
•
3.
4.
5.
6.
1 ancona
2 macerata
3 ascoli piceno
4 pesaro urbino
Cross tabs gender and prov
Split variable “gender”
Selected females
Save the sintax in a new file sintax
• Chi square, T- test
• ANOVA (univariate analysis) and MANOVA
(multivariate analysis) compare means
(variables independent or fix factor
(age/gender or e.g. Motivation with variables
dependent e.g. « satisfation» «pay more»).
More 3 groups «v» on post hoc test-Takey
• Save as excell or word – copy
• Graph
• Sintax
Ex: file ProLoco
Specify level of sign.:
0.014 .983 .000
.523
.054
.007 .002
____ _____ _____ _____ _____ _____ _____
Execute an ANOVA (agerec and efficacia collettiva) a
MANOVA (gender, agerec and motivation). Explain
the meaning in word
Execute a graphs in excell (ANOVA)
Inferential Statistics
• Correlation = In statistics, dependence is any
statistical relationship between two random
variables or two sets
of data. Correlation refers to any of a broad
class of statistical relationships involving
bidirectional dependence. (2 variables are
associated: perfect positive +1, perfect
negative -1);
• Regression = measure as independent
variables (predictors) associated with the
dependent variable are better
Urban Bird Diversity as an Indicator of Human
Social Diversity and Economic Inequality in
Vancouver, British Columbia
Figure 4
Figure 4: Variance decomposition based on partial redundancy analyses of the bird community in Greater Vancouver, BC. Pink
represents variance explained by social and neighborhood-age variables, after removing the effects of covariates area and
space (XY coordinates). Yellow represents variance explained by census tract area alone, after removing the effects of the
space covariate and social + neighborhood-age variables. Green represents variance explained by space alone, after removing
the effects of the area covariate and social + neighborhood-age variables. Amounts of shared variance were calculated by
running a further series of partial redundancy analyses and calculating the joint or shared effects of 1) social + neighborhoodage variables, constrained by area, 2) social + neighborhood-age variables constrained by space, and 3) area, constrained by
space.
Eg. Correlation
more/more; more/less
*** = P<.001 **=.01 *=.05
you have to look minus /plus -/+ and stars/asterisk
Variable
Self Concept
Clarity
Extraversion
Emotional
stability
Openness to
experience
.12**
-.09*
.21**
-.06
-.09*
.11***
-.11**
.16**
Educational identity
Commitment
Exploration in
Depth
Integration with linear regression
Table: Standardized Betas and Proportion Explained Variance for the Regression
Analyses of SCC, emot. stab. and personality on Identity (Correlation)
cons/pros variance
Variable
Self Concept
Clarity
Extraversion
Emotional
Openness to
stability
experience
.11**
.16**
.22**
.16**
(.02)
(.13**)
(.16*)
(.22**)
-.21**
-.08*
-.25**
.14**
(-.18**)
(-.01)
(-.14**)
(.23**)
.11**
.03**
.06**
.08**
Commitment
Exploration in
Depth
Total R2
LOGISTIC REGRESSION
• In statistics, logistic regression, or logit
regression, or logit model is
a regression model where the dependent
variable (DV) is categorical/dummy.
• logistic regression predicts the probability of
particular outcomes
e.g. LOG REG
Note: *p<.05. **p<.01. ***p<.001.
Would you be willing to spend more to be in a eco-friendly accommodation?
Coeff B
Sig.
Exp(B)
Gender
(ref females)
Males
.619
.019*
1.857
-.776
.003**
.460
1.175
.000***
3.239
Class age
(ref adults)
Young people
Constant
Case numbers
374
Ex: file ProLoco
Specify level of sign.:
.016 .083 .001
.453
.056
.008 .032
____ _____ _____ _____ _____ _____ _____
Execute a correlation and a linear regression
(motivation and efficacia collettiva). Explain the
meaning in word
• Factor analysis = (data reduction) is
a statistical method used to
describe variability among observed,
correlated variables in terms of a potentially
lower number of unobserved variables
called factors. (PCA and EFA are 2 type of
exploratory factor analysis; CFA confirmatory
factor analysis). Cronbach’s alpha >.60
Cluster analysis = (data reduction) or clustering is the
task of grouping a set of objects in such a way that
objects in the same group (called a cluster) are more
similar (in some sense or another) to each other than to
those in other groups (clusters).
GORE (2000) 2 steps (only Likert scale no dummy and
standard. ):
1) Hierarchic for number of cluster
2) No Hierarchic (K mean) for the best classification
,5
0,0
Zscore: trust F
Zscore: comm F
-,5
Zscore: clos F
-1,0
Zscore: trust M
-1,5
Zscore: clos M
e
M
r
fo
te
P
Cluster Number of Case
l
bo
de
/M
P
rte
fo
/M
P
le le P
bo bo
de de
M
-2,0
Zscore: comm M
rte
fo
Mean
1,0
Statistical software:
Why ?
• To predict
• To understand