Quantitative analysis Alessandra Fermani alessandra.fermani@unimc.it

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/isbn6556-1_guidaSPSS.pdf ftp://public.dhe.ibm.com/software/analytics/spss/documentation/statistics/20.0/en/client/Manuals/IBM_SPSS_Statistics_Core_System_Users_Guide.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)

hypothesis In statistical inference of observed data of a scientific experiment, the null hypothesis refers to a general statement or default position that there is no relationship between two measured phenomena. In statistical significance, the null hypothesis is often denoted H0 (read “H-nought”) and is generally assumed true until evidence indicates otherwise. The concept of a null hypothesis is used differently in two approaches to statistical inference. In the significance testing approach of Ronald Fisher, a null hypothesis is potentially rejected or disproved on the basis of data that is significant under its assumption, but never accepted or proved. In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis H1, and these are distinguished on the basis of data, with certain error rates. Proponents of these two approaches criticize each other, though today a hybrid approach is widely practiced and presented in textbooks. This hybrid is in turn criticized as incorrect and incoherent—see statistical hypothesis testing. Statistical significance plays a pivotal role in statistical hypothesis testing where it is used to determine if a null hypothesis can be rejected or retained H1 (hypothesis of research)

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

Ex 1) all three averages equal 18 RESULTS Ex 1) all three averages equal 18

File eg proloco Find the AGE mean and SD 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 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

Openness to experience 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 Educational identity   Commitment .12** -.09* .21** -.06 Exploration in Depth .11*** -.11** .16**

Openness to experience 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 stability Openness to experience Commitment   .11** (.02) .16** (.13**) .22** (.16*) (.22**) Exploration in Depth -.21** (-.18**) -.08* (-.01) -.25** (-.14**) .14** (.23**) Total R2 .03** .06** .08**

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 Class age (ref adults) Young people -.776 .003** .460 Constant 1.175 .000*** 3.239 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. ): Hierarchic for number of cluster No Hierarchic (K mean) for the best classification

Statistical software: Why ? To predict To understand