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

2. 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)

3. 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

4. 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

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

6. 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

7. 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

8. 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

9. 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

10. 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