Types of Experiments¶
| Type | Example | ||
|---|---|---|---|
| Natural/Quasi | In non-experimental settings, sometimes implicit randomization occurs, and the treatment occurs “as if” it is random | Uni admission cutoff provides a natural experiment on uni education. Students just above/below are likely to be very similar. For these students, uni education is “as if” random. Comparing these students (ones that went to uni/not) produces an estimate of the causal effect of college education. | |
| Regression Discontinuity Design | Discrete treatment status determined by an underlying continuous variable, which is used for quasi experiments |  | |
| Differences-in-Differences | 2 time-series process \(y_1\) and \(y_2\) have the factors affecting them |  | |
| RCT (Randomized Control Trials) |
Types of RDD¶
| \(x\) | |
|---|---|
| Sharp | \(\begin{cases} 1, & z \ge z_0\\ 0, & \text{o.w}\end{cases}\) |
| Fuzzy | \(\begin{cases} p(z), & z \ge z_0\\ 0, & \text{o.w}\end{cases}\) |
Blocking vs Randomization¶
| Blocking | Randomly assign - half of participants w/ new shoes - half of participants w/ old shoes |
| Randomization | Every participants is given - one new shoe - one old shoe (randomly assigned to left/right foot) |
Block what you can, randomize what you cannot
Random Treatment Assignment¶
Used for removing sources of variation due to nuisance factors
Blocking/Randomized Complete Block Design (RCBD)¶
| \(\alpha_1\) | \(\alpha_2\) | \(\alpha_3\) | \(\alpha_4\) |
|---|---|---|---|
| \(b\) | \(a\) | \(a\) | \(c\) |
| \(a\) | \(c\) | \(b\) | \(b\) |
| \(c\) | \(b\) | \(c\) | \(a\) |
\[ x \in \{ a, b, c \} \\ s \in \{ \alpha_1, \alpha_2, \alpha_3, \alpha_4 \} \]
Note: The term ‘blocking’ originated from agriculture, where a block is typically a set of homogeneous (contiguous) plots of land with similar fertility, moisture, and weather, which are typical nuisance factors in agricultural studies
Latin Square Design (LSD)¶
| \(\alpha_1\) | \(\alpha_2\) | \(\alpha_3\) | |
|---|---|---|---|
| \(\beta_1\) | \(a\) | \(b\) | \(c\) |
| \(\beta_2\) | \(b\) | \(c\) | \(a\) |
| \(\beta_3\) | \(c\) | \(a\) | \(b\) |
\[ \begin{aligned} x &\in \{ a, b, c \} \\ s_1 &\in \{ \alpha_1, \alpha_2, \alpha_3 \} \\ s_2 &\in \{ \beta_1, \beta_2, \beta_3 \} \end{aligned} \]
A Latin square of order \(n\) is an \(n \times n\) array of cells in which \(n\) symbols are placed, one per cell, in such a way that each symbol occurs once in each row and once in each column