Multivariate Analysis 多变量分析.ppt

Multivariate Analysis Many statistical techniques focus on just one or two variables Multivariate analysis (MVA) techniques allow more than two variables to be analysed at once Multiple regression is not typically included under this heading, but can be thought of as a multivariate analysis Outline of Lectures We will cover Why MVA is useful and important Simpson’s Paradox Some commonly used techniques Principal components Cluster analysis Correspondence analysis Others if time permits Market segmentation methods An overview of MVA methods and their niches Simpson’s Paradox Example: 44% of male applicants are admitted by a university, but only 33% of female applicants Does this mean there is unfair discrimination? University investigates and breaks down figures for Engineering and English programmes Simpson’s Paradox No relationship between sex and acceptance for either programme So no evidence of discrimination Why? More females apply for the English programme, but it it hard to get into More males applied to Engineering, which has a higher acceptance rate than English Must look deeper than single cross-tab to find this out Another Example A study of graduates’ salaries showed negative association between economists’ starting salary and the level of the degree i.e. PhDs earned less than Masters degree holders, who in turn earned less than those with just a Bachelor’s degree Why? The data was split into three employment sectors Teaching, government and private industry Each sector showed a positive relationship Employer type was confounded with degree level Simpson’s Paradox In each of these examples, the bivariate analysis (cross-tabulation or correlation) gave misleading results Introducing another variable gave a better understanding of the data It even reversed the initial conclusions Many Variables Commonly have many relevant variables in market research surveys E.g. one not atypical survey had ~2000 variables Typically researchers pore over many crosstabs Ho