STAT1008 Lecture 2: 2 Describing Data
2 DESCRIBING DATA
WK 2 TUESDAY- EXPERIMENTS AND OBSERVATIONAL STUDIES SECTION 1.3 DESCRIBING DATA
Outline
- Association versus Causation
- Confounding Variables
- Observational Studies vs Experiments
- Randomized Experiments
ASSOCIATION AND CAUSATION
- Two variables are associated if values of one variable tend to be related to values of the other ariable
- Two variables are causally associated if changing the value of the explanatory variable influences the
value of the response variable
Explanatory, response, causation
- For each of the following headlines:
o Identify the explanatory and response variables (if appropriate)
o Does the headline imply a causal association?
- “Daily Exercise Improves Mental Performance”
- “Want to lose weight! Eat more fiber!”
- “Cat owners tend to be more educated than dog owners”
Association and Causation
- ASSOCIATION IS NOT NECESSARILY CAUSAL!
- Come up with two variables that are associated, but not causally
- Come up with two variables that are causally associated
o Which is the explanatory variable?
o Which is the response variable?
Confounding Variable
- A third variable that is associated with both the explanatory variable and the response variable is called
a confounding variable
- A confounding variable can offer a plausible explanation for an associated between the explanatory
and response variables
- Whenever confounding variables are present (or may be present), a causal association cannot be
determined
Experiment vs Observation Study
- An observation study is a study in which the researcher does not actively control the value of any
variable, but simply observes the values as they naturally exist
- An experiment is a study in which the researcher actively controls one or more of the explanatory
variables
Observational studies
- There are almost always confounding variables in observational studies
- Observational studies can almost never be used to establish causation
- Invalid assumption: correlation (association) implies cause is probably among the two or three most
serious and common errors of human reasoning
Randomisation
- How can we make sure to avoid confounding variables?
- RANDOMLY assign values of the explanatory variable
Randomized Experiment
- In a randomized experiment the explanatory variable for each unit is determined randomly, before the
response variable is measure
- The different levels of the explanatory variable are known as treatments
- Randomly divide the units into groups, and randomly assign a different treatment to each group
- If the treatments are randomly assigned, the treatment groups should all look similar
- Because the explanatory variable is randomly assigned, it is not associated with any other variables.
Confounding variables are eliminated!
- If a randomized experiment yeidls a significant associated between the two variables, we can establish
causation from the explanatory to the response variable. Randomized experiments are very powerful.
They allow you to infer causality
How to Randomize?
- Option 1: As with random sampling, we can put all the names.numebrs into a hat, and randomly pull
out names to go into the different groups
- Option 2: Put names/numbers on cards, shuffle, and deal out cards into are many piles as there are
treatments
- Option 3: Use technology
Control group
- When determining whether a treatment is effective, it is important to have a comparison group, KA the
control group
- It isn’t enough to know that everyone in one group improved, we need to know whether they
improved more than they would have improved without the surgery
CATEGORICAL VARIABLES 2.1
Outline
- One categorical variable
o Summary statistics: frequency table, proportion, relative frequency tab;e
o Visualization: bar chart, pie chart
- Two categorical variables
o Summary statistics: two-way table, difference in proportions
o Visualization: segmented or side-by-side bar chart
ONE CATEGORICAL VARIABLE
Descriptive statistics
- In order to make sense of data, we need ways to summarize and visualize it
- Summarizing and visualizing variables and relationships between two variables is often KA
descriptive statistics (also KA exploratory data anaylsis)
- Types of summary statistics and visualization methods depend on the type of variable(s) being
analysed (categorical or quantitative)
- Frequency tables can describe categorical variables
Document Summary
Wk 2 tuesday- experiments and observational studies section 1. 3 describing data. Two variables are associated if values of one variable tend to be related to values of the other ariable. Two variables are causally associated if changing the value of the explanatory variable influences the value of the response variable. Cat owners tend to be more educated than dog owners . Come up with two variables that are associated, but not causally. A third variable that is associated with both the explanatory variable and the response variable is called a confounding variable. A confounding variable can offer a plausible explanation for an associated between the explanatory and response variables. Whenever confounding variables are present (or may be present), a causal association cannot be determined. An observation study is a study in which the researcher does not actively control the value of any variable, but simply observes the values as they naturally exist.
