Quantitative analysis Alessandra Fermani

Variables variable type: numeric or string Dependent: satisfation Independent: age, gender Ordinal: children, adolescents, adult etc… Likert scale eg. 1= never (disagree) = 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.statistical inferencescientific experiment In statistical significance, the null hypothesis is often denoted H 0 (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.statistical significancesignificance testingRonald Fisher 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 retainedhypothesis testingJerzy NeymanEgon Pearsonalternative hypothesisstatistical hypothesis testing

Formula: Trust index significance p<.05 good level p<.01, p<.001 Rule of transcription: eg: (F (1, 2114) = 7.11, 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 ( /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 position therefore is 2 (good) 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

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

Eg. Correlation more/more; more/less *** = P<.001 **= minor.01 *= minor.05 Variable Self Concept Clarity Extraversion Emotional stability Openness to experience Educational identity Commitment.12** -.09*.21** -.06 Exploration in Depth -.09*.11*** -.11**.16**

Integration with linear regression Table: Standardized Betas and Proportion Explained Variance for the Regression Analyses of SCC, emot. stab. and personality on Identity (italian 1976) Variable Self Concept Clarity Extraversion Emotional stability Openness to experience Commitment.11** (.02).16** (.13**).22** (.16*).16** (.22**) Exploration in Depth -.21** (-.18**) -.08* (-.01) -.25** (-.14**).14** (.23**) Total R 2.11**.03**.06**.08**

Chi square, T- test v ANOVA and MANOVA compare means (variables independent or fix factor as age or e.g. Motivation with variables dependent as satisfation). More 3 groups «v» on post hoc test-Takey 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). 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

Statistical software: Why ? To predict To understand

SPSS 1 version 1968 IBM Last: 22.0 (13 agosto 2013) Language: java Java System: Microsoft Windows, Mac OS, Linux ect…

Manual and video _guidaSPSS.pdf _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 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):

2 windows Data view variable view (name, Type, with, decimals, label, values, missing, columns, align, measure) Application