Miscellaneous: Statistical Testing

Hypothesis Testing

Basics

Testing Used to Determine the Significance of a Result
Tests Obtain a p-Value (Probability of Obtaining a Test Result by Random if the Null Hypothesis is Correct)
Types of Variables:
- Quantitative – Numerical/Numbers
  - Continuous: Range (e.g. Age)
- Qualitative – Categorical/Descriptive
  - Binary: Two Options (e.g. Sex)
  - Ordinal: More Than Two Options That Are Ranked (e.g. Pain Scale)
  - Nominal: Naming (e.g. Blood Type)
Types of Tests:
- Parametric – Assume Statistical Distributions
- Nonparametric – Do Not Rely on Any Statistical Distributions

Quantitative-Parametric Variables:

Quantitative-Nonparametric Variables

Wilcoxon Signed-Rank Test: Matched Samples or Paired Values from a Single Group
- First Assign Pairs a “Sign” (+1 if Difference is Positive, -1 if Difference is Negative)
- Calculate the Absolute Difference of Each Pair & Rank by Ascending Order (1,2,3…)
- Then Calculate the Test Statistic “W” by Adding All of the (Sign x Rank) Values for Each Pair
- Use “W” in a Reference Table to Calculate the p-Value
Mann-Whitney U Test/Wilcoxon Rank-Sum Test: Compares 2 Independent Groups
- First Rank All Values of Both Groups by Ascending Order (1,2,3…)
- Calculate the Rank-Sum “R” by Adding All of the Ranks in Each Separate Group
- Then Calculate the Test Statistic “U” for Each Separate Group
- Use the Smallest “U” in a Reference Table to Calculate the p-Value
Kruskal-Wallis Test: Compares > 2 Groups

Qualitative Variables

Chi-Squared Test: Compares Qualitative Variables
- Variations:
  - Pearson’s Chi-Squared Test
  - Fisher’s Exact Test
  - McNemar’s Test

Comparison Mn

Groups	Parametric	Nonparametric	Qualitative
1 (Paired)	Paired T-Test	Wilcoxon Signed-Rank	Chi-Squared
2	Independent T-Test	Mann-Whitney U (Wilcoxon Rank-Sum)
> 2	ANOVA	Kruskal-Wallis

Error

Hypothesis:
- Hypothesis: States that There is a Difference Between the Groups
- Null Hypothesis: States that There is No Difference Between the Groups
Types: Mn
- Type I Error: Incorrectly Rejects the Null Hypothesis
- Type II Error: Incorrectly Accepts the Null Hypothesis
Avoid Error by Increasing Sample Size

Regression

Regression: Used to Predict the Value of a Dependent Variable from One or More Independent Variables
Types of Regression:
- Linear Regression: Compare Independent Variables to a Single Continuous Dependent Variable
  - Simple Linear Regression: Uses a Single Independent Variables
  - Multiple Linear Regression: Uses Multiple Independent Variables
- Logistic Regression: Compare Independent Variables to a Single Categorical Dependent Variable
  - Simple Logistic Regression: Uses a Single Independent Variables
  - Multiple Logistic Regression: Uses Multiple Independent Variables

Survival Analysis

Survival Analysis: Statistical Approaches to Determine the Time-to-Event (Survival/Death)
Functions:
- Survival Function S(t): Probability of Survival to a Given Time
- Hazard Function h(t): Event (Death) Rate Over a Specific Time Period Given Survival to the Beginning of the Time Period
Types of Survival Analysis:
- Kaplan-Meier Curve/Plot: Estimates a Survival Curve Over Time
- Log-Rank Test: Compares the Survival Curves of at Least Two Groups
- Cox Proportional Hazards Model (Cox Regression): Compares the Effect of Multiple Variables from Time-to-Event

Basic Statistical Tests

Parametric Tests:
- Student’s T-Test are Easy for Students – The Basic Parametric Tests (Paired & Independent
- ANOVA – NOVA PBS Series from School was Scientific & Complex – Used for Multiple Groups
Nonparametric Tests:
- Nonparametric Tests Are All Named After People
- Differentiating the Wilcoxon Tests: “Signed-Rank” Requires the “Sign” from Comparing Two Paired Values
- Mann-Whitney U (Two “n”s in Mann) is Another Name of Wilcoxon Rank-Sum for “2” Groups
- Kruskal-Wallis is the Only Other Nonparametric Test – Rule Out Others
Qualitative Tests:
- Chi-Squared: “Chi” Tea is Drank by Hippies Who Would Rather Look at “Qualities” than Hard Numbers

Types of Error