IE Notes (week 3)

Variables must be identified.
Expected causal relationships between variables are known (hypotheses, models).
Variables can be isolated from each other (in order to avoid confounding of effects).
The (main) treatment variable must vary (by definition).
Experiment must be replicable.
Precision and accuracy are essential.
Causal effects (variables) can be dichotomous or continuous.

Laboratory experiments: Researcher creates conditions with full control over independent variables, reducing bias and external influences and has full control over assignment of experimental units.
Field experiments: Experiment in an authentic, more realistic setting with limited control. Only some of the independent variables can be controlled by the researchers.
Quasi experiments: Setting cannot be controlled fully, e.g., only one measurement, no randomization, etc. (often "ex-post-facto").

The example explains whether Internet Voting had an effect on turnout on the municipal level.
Number of trials: Includes categories such as 0, 1-5, 6-10, 11-15, 16-22.
Geneva (a) Not all municipalities affected by treatment.
Geneva (b) Treatment varies over time per municipality.

Randomization: Assignment of treatments to experimental units in order to reduce bias. Ensure that each treatment is equally likely to be applied to any given unit.
Replication: Allows for the isolation of treatment effects by controlling for variation caused by chance. It also allows us to study the precision of estimates of the variables being studied.
- External replication
- Internal replication
- Subsampling
- Repeated measures

(a) External replication: Multiple samples, e.g., water probes from a lake.
(b) Internal replication: Multiple samples, e.g., water probes from a lake.
(a) Subsampling: Different ways to obtain multiple samples.
(b) Repeated measures: Best to capture cumulative effects such as learning.
Combinations of these procedures are applied, depending on the research question and feasibility.

Pre-Experimental:
- $M1$ $X$ $M2$
- The effects of one independent treatment variable ( $X$ ) is measured ( $M$ ) in two points in time ( $t1$ , $t2$ ).
- Changes in the dependent variable could also originate from other causes, other changes over time, false measurement at point $t1$ , etc.
Randomized Pre-Test Post-Test Experimental Design
- $E: M1$ $X$ $M2$
- $C: M3$ $N$ $M4$
- We randomly assign objects into the experimental ( $E$ ) or control group ( $C$ ), measure in two points in time ( $t1$ , $t2$ ), whereas only E receives the treatment X, and C receives no treatment ( $N$ ).
SOLOMON four-group experimental test design
- $E1: M1$ $X$ $M2$
- $C1: M3$ $N$ $M4$
- $E2: NM$ $X$ $M5$
- $C2: NM$ $N$ $M6$
- We randomly assign objects into two experimental ( $E1$ , $E2$ ) and two control groups ( $C1$ , $C2$ ), measure in two points in time ( $t1$ , $t2$ ), whereas only $E1$ receives the treatment $X$ , and $C1$ receives no treatment ( $N$ ).
- In addition, $E2$ and $C2$ are not measured at $t1$ , whereas $E2$ receives a treatment ( $X$ ) and $C2$ not ( $N$ ).
- Mainly to exclude interaction effects between the measurement and the treatment.

Variables ( $V$ ) denote features of the units ( $N$ ) in an experiment or study.
Variables must have more than one possible value. Otherwise, we are dealing with a constant.
We want to measure the variables at one or several points in time ( $T$ ).
The measurement of the variable is not defined yet.

Variables can be discrete or continuous
- Discrete: Units dispose of a finite number of categories (classes) within a certain range (e.g., level of education).
- Continuous: Units can take on any measurable value within a certain interval (e.g., height of a human body).
- A variable with exactly two features is called dichotomous (presence or absence of a trait, event, etc.). Sometimes also called "dummy" variable.
The type of variable you (can) define largely determines what kind of statistical analysis you can use later on in the process.
In addition, variables should not have overlapping categories (classes) and they must be complete (cover all possible values).

A hypothesis is a statement about logically connected features of the units under study.
In a hypothesis, we, therefore, postulate the relation between a minimum of two variables.

Independent variable: The part providing the explanation (explanans), the cause, denoted as $X$ .
Dependent variable: The part in which we can (potentially) observe the effect (explanandum), usually denoted as $Y$ .
Example: Seniority in a company is related to the wages: The more senior an employee ( $X$ ) the higher the wage ( $Y$ ).

A hypothesis is not a question, not an order.
It is a statement relating two meaningful terms.
The terms are connected by "if-then" or "the more, the more" or "because" (or can be transformed into this form) statements.
Statements are not tautological, without contradiction, can be related to the empirical world, can be operationalized, and can be falsified.

Individual features: information, data about a single unit in our experiment or study (e.g., the age of a person).
Collective features: information about aggregates of units (e.g., average age of people living in a municipality).

"If-Then" formulation of a hypothesis - only works with dichotomous variables.
"The more $X$ , the more (or the less) $Y$ formulations - we need more than two categories and be able to at least rank them.
The relations between variables can be:
- linear
- exponential
- logarithmic
- logistic (S-shaped)
- quadratic (U-shaped)