CourseKata Ch. 2.1–2.7

Patterns & Association

Mansour Abdoli, PhD

Today (Ch. 2.1–2.7)

Session goals

By the end of today you can:

explain variation and why we organize data
make and interpret frequency tables (using tally())
identify cases (rows) and variables (columns)
explain variable vs value
tell categorical from quantitative variables
distinguish measurement vs sampling

2.1 Starting with a bunch of numbers

Variation is the point

Two bunches:
- 2, 2, 2, 2, 2, 2, 2, 2, 2
- 2, 1, 3, 3, 2, 3, 1, 2, 1
We reveal patterns by sorting and counting.
We use patterns to find
unusual things
exceptions
outliers

Let’s sort and tally

Pair prompt

x <- c(2, 1, 3, 3, 2, 3, 1, 2, 1)
print(sort(x))

[1] 1 1 1 2 2 2 3 3 3

cat('\n')

tally(x)

X
1 2 3 
3 3 3

What pattern is easier to see after sorting?
What does the frequency table make obvious?

2.2 From numbers to data

Numbers become “data” when they represent the world library(mosaic)

Two core processes:

Measurement: turning attributes into values

Sampling: choosing which cases to measure

Think–Pair–Share (2 minutes)

Pick one:

Stress and school performance
Sleep and mood
Screen time and attention

For your choice:

What is one measurement?
What is your sample?

2.3 A data frame example

Example dataset (MindsetMatters)

Houskeepr Information before and after informing some of them that their job counts as an active-lifestyle.
What do you see?

Cases, variables, values

Rows = cases
Columns = variables
Each cell is a value

  Cond Age  Wt   Wt2  BMI BMI2  Fat Fat2  WHR WHR2 Syst Syst2 Diast Diast2
1    0  43 137 137.4 25.1 25.1 31.9 32.8 0.79 0.79  124   118    70     73
2    0  42 150 147.0 29.3 28.7 35.5   NA 0.81 0.81  119   112    80     68
3    0  41 124 124.8 26.9 27.0 35.1   NA 0.84 0.84  108   107    59     65
4    0  40 173 171.4 32.8 32.4 41.9 42.4 1.00 1.00  116   126    71     79
5    0  33 163 160.2 37.9 37.2 41.7   NA 0.86 0.84  113   114    73     78
6    0  24  90  91.8 16.5 16.8   NA   NA 0.73 0.73   NA    NA    78     76
   Condition
1 Uninformed
2 Uninformed
3 Uninformed
4 Uninformed
5 Uninformed
6 Uninformed

Peek at structure (CourseKata-style: glimpse)

What types of values do you see?

2.7 Values and variables

Variable vs value

Variable: the attribute/column (e.g., Age)
Value: one case’s measurement (e.g., Age = 41)
Variables and Values in a Dataset:

Value Types

Names: character strings, labels
Numbers: A combination of 0 to 9 digits and symbols like . and %

'data.frame':   75 obs. of  15 variables:
 $ Cond     : int  0 0 0 0 0 0 0 0 0 0 ...
 $ Age      : int  43 42 41 40 33 24 46 21 29 19 ...
 $ Wt       : int  137 150 124 173 163 90 150 156 141 123 ...
 $ Wt2      : num  137 147 125 171 160 ...
 $ BMI      : num  25.1 29.3 26.9 32.8 37.9 16.5 27.5 25.9 27.5 19.6 ...
 $ BMI2     : num  25.1 28.7 27 32.4 37.2 16.8 27.4 25.7 27.4 19.7 ...
 $ Fat      : num  31.9 35.5 35.1 41.9 41.7 NA 36.1 36.4 NA 26.6 ...
 $ Fat2     : num  32.8 NA NA 42.4 NA NA 37.3 NA NA NA ...
 $ WHR      : num  0.79 0.81 0.84 1 0.86 0.73 0.9 0.78 0.87 0.69 ...
 $ WHR2     : num  0.79 0.81 0.84 1 0.84 0.73 0.9 0.78 0.85 0.69 ...
 $ Syst     : int  124 119 108 116 113 NA 119 116 110 113 ...
 $ Syst2    : int  118 112 107 126 114 NA 115 135 115 117 ...
 $ Diast    : int  70 80 59 71 73 78 75 67 73 75 ...
 $ Diast2   : int  73 68 65 79 78 76 77 65 74 72 ...
 $ Condition: Factor w/ 2 levels "Informed","Uninformed": 2 2 2 2 2 2 2 2 2 2 ...

2.6 Quantitative & Categorical Variables

Variable Types

Variables:
- Categorical: for qualitative comparison (grouping)
- Numerical: for quantitative comparison (distance, ratio)

'data.frame':   75 obs. of  15 variables:
 $ Cond     : int  0 0 0 0 0 0 0 0 0 0 ...
 $ Age      : int  43 42 41 40 33 24 46 21 29 19 ...
 $ Wt       : int  137 150 124 173 163 90 150 156 141 123 ...
 $ Wt2      : num  137 147 125 171 160 ...
 $ BMI      : num  25.1 29.3 26.9 32.8 37.9 16.5 27.5 25.9 27.5 19.6 ...
 $ BMI2     : num  25.1 28.7 27 32.4 37.2 16.8 27.4 25.7 27.4 19.7 ...
 $ Fat      : num  31.9 35.5 35.1 41.9 41.7 NA 36.1 36.4 NA 26.6 ...
 $ Fat2     : num  32.8 NA NA 42.4 NA NA 37.3 NA NA NA ...
 $ WHR      : num  0.79 0.81 0.84 1 0.86 0.73 0.9 0.78 0.87 0.69 ...
 $ WHR2     : num  0.79 0.81 0.84 1 0.84 0.73 0.9 0.78 0.85 0.69 ...
 $ Syst     : int  124 119 108 116 113 NA 119 116 110 113 ...
 $ Syst2    : int  118 112 107 126 114 NA 115 135 115 117 ...
 $ Diast    : int  70 80 59 71 73 78 75 67 73 75 ...
 $ Diast2   : int  73 68 65 79 78 76 77 65 74 72 ...
 $ Condition: Factor w/ 2 levels "Informed","Uninformed": 2 2 2 2 2 2 2 2 2 2 ...

Quick classification

Age
BMI
Condition
Zip code (in general)

head(MindsetMatters, 3)

  Cond Age  Wt Wt2  BMI BMI2  Fat Fat2  WHR WHR2 Syst Syst2 Diast Diast2
1    0  43 137 137 25.1 25.1 31.9 32.8 0.79 0.79  124   118    70     73
2    0  42 150 147 29.3 28.7 35.5   NA 0.81 0.81  119   112    80     68
3    0  41 124 125 26.9 27.0 35.1   NA 0.84 0.84  108   107    59     65
   Condition
1 Uninformed
2 Uninformed
3 Uninformed

2.7 (again) Values

Switching Value Types: To Factor

Switching Value Types: To Numeric

2.4 Frequency tables and sorting data frames

Frequency table of a categorical variable

Two-way tally (cross-tab)

Sort a data frame

Frequency Table for Numerical Variables

Tally works on numeric but is not alwyas helpful

Grouping works better:

2.5 Measurement

Measurement choices affect meaning

Units and scales (years vs months, miles vs km)
Coding (0/1 vs labels)
Definitions (what counts as “exercise”?)

Example: coding vs labeling

Question: Which one do you prefer: labels or Numerical Codes?

Collaboration activity (15–25 minutes)

“Design a dataset” (teams of 3–4)

Pick ONE scenario:

Sleep & performance
Caffeine & anxiety
Exercise & mood

Your team must produce:

Cases: what counts as one row?
Variables: 4–6 columns
Which are categorical vs quantitative
For Next Class: A dataset with 25-35 rows