Statistical Tool Boxes HSC 445-Statistics in Applied Science and Technology

Statistical Toolboxes There are two major categories of statistical toolboxes: parametric toolboxes (contain P-toolbox1 through P-toolbox4) non-parametric toolboxes (contain NP-toolbox1 and NP-toolbox2)

P-Toolboxes If the variables are: ordinal variable without many ranks or I.R. variable with known normal population distribution or sample size is large enough Open the parametric toolboxes

P-Toolbox 1 Pearson’s r t-test One Var. = Int./Ratio Selection Bias Type of Variables Pearson’s r Measure of Association Selection Bias Confounding Factors Chance: t-test

P-Toolbox 2 Z-test Selection Bias Confounding Factors Chance: One Var. = Ordinal Type of Variables Measure of Association Gamma

P-Toolbox 3 RR or OR Chi-square test Selection Bias Confounding Factors Chance: Chi-square test One Var. = Nominal Type of Variables Measure of Association Lambda RR or OR

P-Toolbox 4 One Var. = Int./Ratio One Var. = Nominal/Ordinal Type of Variables Compare means Measure of Association Selection Bias Confounding Factors If two groups: T test for two samples If more than two groups: ANOVA

Non-parametric Toolboxes If the variables are: ordinal variable with many ranks; or I.R. variable with non-normal population distribution or sample size is not large enough or variance of y is not uniform for each x; Open the non-parametric toolboxes

NP-Toolbox 1 Spearman’s rs t-test One Var. = Int./Ratio (or ordinal variable with many ranks) Type of Variables Spearman’s rs Measure of Association Selection Bias Confounding Factors Chance: t-test

NP-Tool Box 2 One Var. = Int./Ratio or ordinal data with many ranks One Var. = Nominal/Ordinal Type of Variables Compare distribution of different groups Measure of Association Selection Bias Confounding Factors If two groups: Wilcoxon Rank-sum test If more than two groups: Kruskal-Wallis One Way ANOVA