Statistics: The Art & Science of Learning from Data

An exploration of statistics as the art and science of learning from data, covering data science, biostatistics, and bioinformatics principles.

knitr::read_chunk("2022-05-20_TUF.R")

Introduction

Statistics

• Statistics is the science of uncertainty & variability
• Statistics turns data into information
• Data -> Information -> Knowledge -> Wisdom
• Data Driven Decisions (3Ds)
• Statistics is the interpretation of Science
• Statistics is the Art & Science of learning from data

 

Variable

• Characteristic that may vary from individual to individual
• Height, Weight, CGPA etc

 

Measurement

• Process of assigning numbers or labels to objects or states in accordance with logically accepted rules

Figure 1: Measurement

 

Measurement Scales

• Nominal Scale: Obersvations may be classified into mutually exclusive & exhaustive classes or categories
• Ordinal Scale: Obersvations may be ranked
• Interval Scale: Difference between obersvations is meaningful
• Ratio Scale: Ratio between obersvations is meaningful & true zero point

Figure 2: Measurement Scales

 

Exploring Data with Graphs & Numerical Summaries

Graphs

Numerical Summaries

Example

The following data shows the ID, Gender (Male, Female), Age, Race (Mexican American, Non-Hispanic Black, Non-Hispanic White, Other Hispanic, Other/Mixed), BMI, and BMI.Cat (Under Weight, Normal Weight, Over Weight, Obese) from the National Health and Nutrition Examination Survey (NHANES). The survey is conducted by the National Center for Health Statistics (NCHS), and data are publicly available at: https://www.cdc.gov/nchs/nhanes.htm . NHANES data are reported in well over one thousand peer-reviewed journal publications every year.

Descriptive Statistics

• Number of Observations
• Measures of Central Tendency
• Measures of Central Dispersion
• Measures of Skewness
• Measures of Kurtosis

 

Example

The following data shows the ID, Gender (Male, Female), Age, Race (Mexican American, Non-Hispanic Black, Non-Hispanic White, Other Hispanic, Other/Mixed), BMI, and BMI.Cat (Under Weight, Normal Weight, Over Weight, Obese) from the National Health and Nutrition Examination Survey (NHANES). The survey is conducted by the National Center for Health Statistics (NCHS), and data are publicly available at: https://www.cdc.gov/nchs/nhanes.htm . NHANES data are reported in well over one thousand peer-reviewed journal publications every year.

Correlation Analysis

Example

The following data shows the ID, Gender (Male, Female), Age, Race (Mexican American, Non-Hispanic Black, Non-Hispanic White, Other Hispanic, Other/Mixed), BMI, and BMI.Cat (Under Weight, Normal Weight, Over Weight, Obese) from the National Health and Nutrition Examination Survey (NHANES). The survey is conducted by the National Center for Health Statistics (NCHS), and data are publicly available at: https://www.cdc.gov/nchs/nhanes.htm . NHANES data are reported in well over one thousand peer-reviewed journal publications every year.

 

An Introduction to Linear Models

Regression Analysis

• Quantifying dependency of a normal response on quantitative explanatory variable(s)

 

Figure 3: Population Regression Function

 

Example

The following data shows the ID, Gender (Male, Female), Age, Race (Mexican American, Non-Hispanic Black, Non-Hispanic White, Other Hispanic, Other/Mixed), BMI, and BMI.Cat (Under Weight, Normal Weight, Over Weight, Obese) from the National Health and Nutrition Examination Survey (NHANES). The survey is conducted by the National Center for Health Statistics (NCHS), and data are publicly available at: https://www.cdc.gov/nchs/nhanes.htm . NHANES data are reported in well over one thousand peer-reviewed journal publications every year.

Analysis of Variance (ANOVA)

• Comparing means of Normal dependent variable for levels of different factor(s)

 

Figure 4: Analysis of Variance

 

Example

The following data shows the ID, Gender (Male, Female), Age, Race (Mexican American, Non-Hispanic Black, Non-Hispanic White, Other Hispanic, Other/Mixed), BMI, and BMI.Cat (Under Weight, Normal Weight, Over Weight, Obese) from the National Health and Nutrition Examination Survey (NHANES). The survey is conducted by the National Center for Health Statistics (NCHS), and data are publicly available at: https://www.cdc.gov/nchs/nhanes.htm . NHANES data are reported in well over one thousand peer-reviewed journal publications every year.

Analysis of Covariance (ANCOVA)

• Quantifying dependency of a normal response on quantitative explanatory variable(s)
• Comparing means of Normal dependent variable for levels of different factor(s)

 

Figure 5: Analysis of Covariance

 

Example

The following data shows the ID, Gender (Male, Female), Age, Race (Mexican American, Non-Hispanic Black, Non-Hispanic White, Other Hispanic, Other/Mixed), BMI, and BMI.Cat (Under Weight, Normal Weight, Over Weight, Obese) from the National Health and Nutrition Examination Survey (NHANES). The survey is conducted by the National Center for Health Statistics (NCHS), and data are publicly available at: https://www.cdc.gov/nchs/nhanes.htm . NHANES data are reported in well over one thousand peer-reviewed journal publications every year.

R Software

NoteR Software

R is a free, open-source programming language and software environment for statistical computing, bioinformatics, visualization and general computing. R provides a wide variety of statistical and graphical techniques, and is highly extensible. The latest version of R can be obtained from https://cran.r-project.org/bin/.

RStudio

NoteRStudio

RStudio is a powerful integrated development environment (IDE) for R, and it can be downloaded from https://www.rstudio.com/products/rstudio/download/.

Figure 6: An Introduction to R

R Short Reference Card

Figure 7: R Short Reference Card

2009 New York Times Article on R

Figure 8: 2009 New York Times Article on R

2015 Nature Article on R

Figure 9: 2015 Nature Article on R