Quantitative analysis Alessandra Fermani alessandra fermaniunimc it Variables

Quantitative analysis Alessandra Fermani alessandra. fermani@unimc. it

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 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 (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 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 Educational identity Commitment Exploration in Depth Self Concept Clarity Extraversion Emotional stability Openness to experience . 12** -. 09* . 21** -. 06 -. 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 Openness to stability experience . 11** . 16** . 22** . 16** (. 02) (. 13**) (. 16*) (. 22**) Commitment Exploration in -. 21** -. 08* -. 25** . 14** Depth (-. 18**) (-. 01) (-. 14**) (. 23**) . 11** . 03** . 06** . 08** Total R 2

• Chi square, T- test • 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 • http: //www. ateneonline. it/chiorri/studenti/isbn 6 556 -1_guida. SPSS. pdf • ftp: //public. dhe. ibm. com/software/analytics/sps s/documentation/statistics/20. 0/en/client/Manu als/IBM_SPSS_Statistics_Core_System_Users_Gui de. pdf • Video (it): https: //www. youtube. com/watch? v=ft. U 4 Tau. Csh g

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