LIS 570 Summarising and presenting data - Univariate analysis continued Bivariate analysis

Selecting analysis and statistical techniques De Vaus p133

Methods of analysis (De Vaus, 134)

Summary  Inferential statistics for univariate analysis  Bivariate analysis crosstabulation the character of relationships - strength, direction, nature correlation

Inferential statistics - univariate analysis  Interval estimates - interval variables estimating how accurate the sample mean is based on random sampling and probability theory Standard error of the mean (S m ) Sm = s  N Standard deviation Total number in the sample

Standard Error  Probability theory for 95% of samples, the population mean will be within + or - two standard error units of the sample mean this range is called the confidence interval standard error is a function of sample size to reduce the confidence interval, increase the sample size

Inference for non-interval variables  For nominal and ordinal data  Variable must have only two categories may have to combine categories to achieve this S B = PQ N Standard error for binominal distribution P = the % in one category of the variable Q = the % in the other category of the variable Total number in the sample

Association  Example: gender and voting Are gender and party supported associated (related)? Are gender and party supported independent (unrelated)? Are women more likely to vote Republican? Are men more likely to vote Democrat?

Association Association in bivariate data means that certain values of one variable tend to occur more often with some values of the second variable than with other variables of that variable ( Moore p.242)

Cross Tabulation Tables  Designate the X variable and the Y variable  Place the values of X across the table  Draw a column for each X value  Place the values of Y down the table  Draw a row for each Y value  Insert frequencies into each CELL  Compute totals (MARGINALS) for each column and row

Determining if a Relationship Exists  Compute percentages for each value of X (down each column) Base = marginal for each column  Read the table by comparing values of X for each value of Y Read table across each row  Terminology strong/ weak; positive/ negative; linear/ curvilinear

Cross tabulation tables Calculate percent Read Table (De Vaus pp ) Occupation Vote

Cross tabulation  Use column percentages and compare these across the table  Where there is a difference this indicates some association

Describing association Direction Strength Nature Positive - Negative Strong - Weak Linear - Curvilinear

Describing association Two variables are positively associated when larger values of one tend to be accompanied by larger values of the other The variables are negatively associated when larger values of one tend to be accompanied by smaller values of the other (Moore, p. 254)

Describing association  Scattergram a graph that can be used to show how two interval level variables are related to one another Shoe size Age Variable N Variable M

Description of Scattergrams Strength of Relationship Strong Moderate Low Linearity of Relationship Linear Curvilinear Direction Positive Negative

Description of scatterplots Strength and direction Y XX XX Y Y Y

Description of scatterplots Strength and direction Nature X X X X Y YY Y

Correlation  Correlation coefficient number used to describe the strength and direction of association between variables Very strong =.80 through 1 Moderately strong =.60 through.79 Moderate =.50 through.59 Moderately weak =.30 through.49 Very weak to no relationship 0 to.29 Perfect Negative Correlation 0.00 No relationship 1.00 Perfect Positive Correlation

Correlation Coefficients Nominal Phi (Spss Crosstabs) Cramer’s V (Spss Crosstabs) Ordinal (linear) Gamma (Spss Crosstabs) Nominal and Interval Eta (Spss Crosstabs)

Correlation: Pearson’s r (SPSS correlate, bivariate) Interval and/or ratio variables Pearson product moment coefficient (r) two interval normally distributed variables assumes a linear relationship Can be any number from  0 to -1 : 0 to 1 (+1) Sign (+ or -) shows direction Number shows strength Linearity cannot be determined from the coefficient r =.8913

Summary  Bivariate analysis  crosstabulation X - columns Y - rows calculate percentages for columns read percentages across the rows to observe association  Correlation and scattergram describe strength and direction of association