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LIS 570

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

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LIS 570

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

  2. Selecting analysis and statistical techniques De Vaus p133

  3. Methods of analysis (De Vaus, 134)

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

  5. 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 (Sm) Sm = s N Standard deviation Total number in the sample

  6. 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

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

  8. Bivariate Analysis

  9. 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?

  10. 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) Correlation Coefficient Cross Tabulation

  11. 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

  12. 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

  13. Cross tabulation tables Occupation Calculate percent Vote Read Table (De Vaus pp 158-160)

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

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

  16. 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)

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

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

  19. Description of scatterplots Y Y X X Strength and direction Y Y X X

  20. Description of scatterplots Y Y Nature X X Strength and direction Y Y X X

  21. 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 -1.00 Perfect Negative Correlation 1.00 Perfect Positive Correlation 0.00 No relationship

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

  23. 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

  24. 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

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