Data

Material based on Chapter 1 Introduction to Modern Statistics and A/B Testing in R

Learning objectives

• Types of data collection

  • experimental vs observational

• Types of variables

  • numeric vs categorical

• Tidy data

• Summary statistics

Medical case

Question: does the use of stents reduce the risk of strokes?

Data to address the question?

451 patients at risk for strokes randomly assigned to 2 groups

• treatment receive stent (224)

• control no stent (227)

Data

Outcome of stent experiment

group	no event	stroke	Total
control	199	28	227
treatment	179	45	224

Does the use of stents reduce the risk of stroke?

Compare 2 summary statistics:

• Proportion who had a stroke in the treatment (stent) group: \(45/(179 +45) = 0.20 = 20\%.\)

• Proportion who had a stroke in the control group: \(28/(199 +28) = 0.12 = 12\%.\)

• summary statistic is a single number summarizing data from a sample

group	no event	stroke
control	88%	12%
treatment	80%	20%

Your turn

How would you calculate 88% and 80% in the table?

group	no event	stroke
control	88%	12%
treatment	80%	20%

Types of variables

Tidy Data

A data frame where

• each row is a unique case (observational unit),
• each column is a variable
• each cell is a single value

Explanatory and response variables

explanatory variable → might affect → response variable

Relationship between variables

• associated variables: two variables that show some connection with one another

• independent variables: not associated

Types of studies: observational vs experiment

• observational observe associations
  • collect information via surveys or company records, or follow a cohort
• experimental can infer causation when effectively randomize

Your turn

12 Smoking habits of UK residents. A survey was conducted to study the smoking habits of 1,691 UK residents.

• Observational or experimental data collection

• What does each row of the data frame represent?

• How many participants were included in the survey?

• Indicate whether each variable in the study is numerical or categorical. If numerical, identify as continuous or discrete. If categorical, indicate if the variable is ordinal.

gender	age	marital_status	highest_qualification	nationality	ethnicity	gross_income	region	smoke	amt_weekends	amt_weekdays	type
Male	38	Divorced	No Qualification	British	White	2,600 to 5,200	The North	No	NA	NA
Female	42	Single	No Qualification	British	White	Under 2,600	The North	Yes	12	12	Packets
Male	40	Married	Degree	English	White	28,600 to 36,400	The North	No	NA	NA
Female	40	Married	Degree	English	White	10,400 to 15,600	The North	No	NA	NA
Female	39	Married	GCSE/O Level	British	White	2,600 to 5,200	The North	No	NA	NA
Female	37	Married	GCSE/O Level	British	White	15,600 to 20,800	The North	No	NA	NA

Experiment: online wine retailer

Wine retailer email test data

Data

user_id	cpgn_id	group	email	open	click	purch
1000001	1901Email	ctrl	FALSE	0	0	0.00
1000002	1901Email	email_B	TRUE	1	0	0.00
1000003	1901Email	email_A	TRUE	1	1	200.51

chard	sav_blanc	syrah	cab	past_purch	days_since	visits
0.00	0	33.94	0.00	33.94	119	11
0.00	0	16.23	76.31	92.54	60	3
516.39	0	16.63	0.00	533.02	9	9

Your turn

names	var type
user_id
cpgn_id
group
email
open
click
purch
chard
sav_blanc
syrah
cab
past_purch
days_since
visits

Summary

• tidy data

• variables

  • explanatory vs response variables
  • associated vs independent
  • type of variable
    • numeric: discrete vs continuous
    • categorical: nominal vs ordinal

• summary statistic

Quiz

• two questions
• may be multiple answers
• use sample presented in question (not entire sample)