EHS 655 Lecture 7 Exposure modeling categorical analysis

EHS 655 Lecture 7: Exposure modeling – categorical analysis

Review: uses of ANOVA and linear regression o ANOVA n n n o Ordinal or nominal independent variables effects on continuous dependent variable Comparison of group means Example: exposure level by job title Linear regression accomplishes the same n n But can use nominal, ordinal, or continuous independent variables Example: exposure level by date 2

What we’ll cover today o Categorical analyses 3

ANALYZING CATEGORICAL VARIABLES o What about categorical variables? o Use nonparametric tests that do not assume normality (but still assume independence) n n o Lose some statistical power as assumptions relaxed Nonparametric tests typically more robust to presence of outliers Rank tests (which assume variables are ordinal) are more powerful than categorical 4

Chi-square test: goodness of fit o Test whether observed proportions for categorical variable differ from hypothesized proportions n n o Example: suppose we believe construction workforce is 30% carpenters, 10% electricians, 10% ironworkers, 30% laborers, 20% operating engineers Significant results indicates observed proportions differ from hypothesized proportions Stata: download csgof program that performs test n Stata: csgof depvar, expperc (30 10 10 30 20) http: //www. stat. yale. edu/Courses/1997 -98/101/chigf. htm 5

Chi-square test: independent groups o Use to evaluate relationship between ≥ 2 categorical variables (i. e. , n x n table) n n Evaluates difference between observed frequencies and those expected if variables independent (i. e. relative risk of 1) Assumes cell counts (frequencies) >5 o Significant result indicates categories associated (not independent) o Example: perceived exposure type by job title n Stata: tab varname 1 varname 2, chi 2 6

Fisher’s exact test o Similar to chi-square, but n n Assumes 2 x 2 table Robust with small sample sizes (i. e. , 5 or less in at least one cell) o Significant result indicates categories associated (not independent) o Example: perceived exposure type by gender n Stata: tabulate varname 1 varname 2, exact 7

Wilcoxon Mann-Whitney (U) rank test o Non-parametric analog to independent samples t-test n n Used to test differences between two groups (i. e. , independent variables is categorical) Dependent variable either ordinal or continuous (but normally distributed) o Significant result indicates difference in distributions o Example: perceived exposure level by gender n Stata: ranksum varname, by(groupname) 8

Kruskal-Wallis rank (H) test o Use to evaluate ordinal dependent and nominal independent variables with 2 or more levels n o Significant result means at least one level different than others n o Non-parametric version of oneway ANOVA Doesn’t say where/how many differences occur Example: perceived noise by job n Stata: kwallis varname, by(groupname) 9

Wilcoxon signed rank test o Non-parametric analog of paired sample t-test (i. e. , for matched groups) n n n o Does not assume difference between variables or paired samples is interval and normally distributed But does assume variables at least ordinal Significant result indicates difference between variables or samples Example: categorized version of measured exposure vs perceived exposure level n Stata: signrank varname 1 = varname 2 10

Non-parametric (Spearman) rank correlation o Use when one or both variables not assumed to be normally distributed n Values converted to ranks, then correlated o Significant results indicate monotonic relationship between variables o Example: perceived vs measured noise level n Stata: spearman varname 1 varname 2 11