The QEDesigns

# The QEDesigns
## EDP 612 Week 7
### Dr. Abhik Roy

---

section {
    height: 600px;
    width: 60%;
    margin: auto;
    border-radius: 21px;
    background-color: #212121;
}

section p {
    text-align: center;
    font-size: 30px;
    background-color: #212121;
    border-radius: 21px;
    font-family: Roboto Condensed;
    font-style: bold;
    padding: 12px;
    color: #bff4ee;
    margin: auto;
}

#center {
text-align: center;
}

.center p {
  margin: 0;
  position: absolute;
  top: 50%;
  left: 50%;
  -ms-transform: translate(-50%, -50%);
  transform: translate(-50%, -50%);
}

.center2 {
  margin: 0;
  position: absolute;
  top: 50%;
  left: 50%;
  -ms-transform: translate(-50%, -50%);
  transform: translate(-50%, -50%);
}

.tab {
    display: inline-block;
    margin-left: 40px;
}

td, th, tr, table {
    border: 0 !important;
    border-spacing:0 !important;
  }
</style>

---

---

# Modern Descriptions of Experiments

---

## Randomized Experiment

+ Units are assigned to conditions randomly

+ Randomly assigned units are probabilistically equivalent based on expectancy (if certain conditions are met)

+ Under the appropriate conditions, randomized experiments provide unbiased estimates of an effect

---

## Quasi-Experiments

+ Shares all features of randomized experiments except assignment

+ Assignment to conditions occurs by self-selection

+ Greater emphasis on enumerating and ruling out alternative explanations

+ ... through logic and reasoning, design, and measurement

---

#  Basic Design Elements and Notation

---

##  Assignment

--
 
+ Random assignment

+ Cutoff-based assignment

+ Other nonrandom assignment

+ Matching and stratifying

+ Masking

---

##  Measurement

+ Posttest observations

+ Single posttests

+ Nonequivalent dependent variables

+ Multiple substantive posttests

+ Pretest observations

+ Single pretest

+ Retrospective pretest

+ Proxy pretest

+ Repeated pretests over time

+ Pretests on independent samples

+ Moderator variable with predicted interaction

+ Measuring threats to validity

---

##  Comparison Groups

+ Single nonequivalent groups

+ Multiple nonequivalent groups

+ Cohorts

+ Internal versus external controls

+ Constructed contrasts

+ Regression extrapolation contrasts
	
	+ Normed contrasts
	
	+ Secondary data contrasts

---

##  Treatments

+ Switching replications

+ Reversed treatments

+ Removed treatments

+ Repeated treatments

---

##  Notation

$$
  \require{enclose}
$$

<center>
<table class=" lightable-paper" style='font-family: "Arial Narrow", arial, helvetica, sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:center;color: #ffffff !important;vertical-align: middle !important;"> Variable 
   </th>
<th style="text-align:left;color: #ffffff !important;vertical-align: middle !important;"> Description 
  </th>
</tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;width: 20em; color: #ffffff !important;vertical-align: middle !important;"> `X` </td>
   <td style="text-align:left;width: 30em; color: #ffffff !important;vertical-align: middle !important;"> treatment </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 20em; color: #ffffff !important;vertical-align: middle !important;"> `O` </td>
   <td style="text-align:left;width: 30em; color: #ffffff !important;vertical-align: middle !important;"> observation </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 20em; color: #ffffff !important;vertical-align: middle !important;"> `R` </td>
   <td style="text-align:left;width: 30em; color: #ffffff !important;vertical-align: middle !important;"> random assignment </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 20em; color: #ffffff !important;vertical-align: middle !important;"> `NR` </td>
   <td style="text-align:left;width: 30em; color: #ffffff !important;vertical-align: middle !important;"> nonrandom assignment </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 20em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\enclose{horizontalstrike}{X}$` ` </td>
   <td style="text-align:left;width: 30em; color: #ffffff !important;vertical-align: middle !important;"> removed treatment </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 20em; color: #ffffff !important;vertical-align: middle !important;"> `X_+` </td>
   <td style="text-align:left;width: 30em; color: #ffffff !important;vertical-align: middle !important;"> treatment expected to produce an effect in one direction </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 20em; color: #ffffff !important;vertical-align: middle !important;"> `X_-` </td>
   <td style="text-align:left;width: 30em; color: #ffffff !important;vertical-align: middle !important;"> conceptually opposite treatment expected to reverse an effect </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 20em; color: #ffffff !important;vertical-align: middle !important;"> `C` </td>
   <td style="text-align:left;width: 30em; color: #ffffff !important;vertical-align: middle !important;"> cutting score </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 20em; color: #ffffff !important;vertical-align: middle !important;"> --- </td>
   <td style="text-align:left;width: 30em; color: #ffffff !important;vertical-align: middle !important;"> non-randomly formed groups </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 20em; color: #ffffff !important;vertical-align: middle !important;"> ··· </td>
   <td style="text-align:left;width: 30em; color: #ffffff !important;vertical-align: middle !important;"> cohort </td>
  </tr>
</tbody>
</table>
</center>

---

# The Logic of Quasi-Experimentation

---

##  Rationale

+ Quasi-experiments are often a necessity given practical and logistical constraints

+ Greater emphasis on construct or external validity rather than cause-effect associations - ***least common***

+ Funding, ethics, administration - ***somewhat common***

+ The intervention has already occurred - ***most common***

+ Sometimes they are the best alternative, even if causal inferences are weaker than is possible with other designs

---

## Central Principles 
  
--
  
  + Identification and study of plausible threats to internal validity

--
  
  + Careful scrutiny of plausible alternative explanations for treatment-outcome covariation

--
  
  + Primacy of control by design

--
  
  + Use carefully planned and implemented design elements rather than statistical controls for anticipated confounds

--
  
  + Coherent pattern matching
  
--

+ Complex (a priori) causal hypotheses that reduce the plausibility of alternative explanations

+ Even so, great care must be taken when planning such studies as numerous threats that cannot be controlled are often operating
  
---

# Designs without Control Groups

---
  
## One-Group Posttest Only Design

<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
> Absence of pretest makes it difficult to know if change has occurred and absence of a control group makes it difficult to know what would have happened without treatment

<br>
> Known as a one-shot study

---

## One-Group Pretest-Posttest Design

<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
> Adding a pretest provides weak information concerning what might have happened to participants had the treatment not occurred

<br>
> Known as a one-shot study

---

## One-Group Pretest-Posttest Design with Double Pretest

<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
> Adding multiple pretests reduces the plausibility of maturation and regression effects

<br>
> Additional pretests can confirm maturational trends

---

## One-Group Pretest-Posttest Design Using a Nonequivalent Variable

<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
> Measure `$A$` is expected to change because of treatment, `$B$` is not

<br>
> Both `$A$` and `$B$` are expected to respond to the same validity threats in the same way

---

### Example

*Lottery ticket sales in convenience stores after introduction of signs in store windows reading “did you buy your ticket?”*

---

## Removed-Treatment Design

$$
  \require{enclose}
$$

.center2[
<table>
 <thead>
  <tr>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_1` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `X` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_2` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_3` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\enclose{horizontalstrike}{X}$` ` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_4` </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Pretest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Treatment </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Pretest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Removal </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
  </tr>
</tbody>
</table>
]

<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
> Demonstrates that outcomes rise and fall with the presence or absence of treatment

---

### Example

*Generally interpretable outcome pattern*

---

## Repeated-Treatment Design

$$
  \require{enclose}
$$

.center2[
<table>
 <thead>
  <tr>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_1` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `X` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_2` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\enclose{horizontalstrike}{X}$` ` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_3` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `X` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_4` </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Pretest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Treatment </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Removal </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Treatment </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
  </tr>
</tbody>
</table>
]

<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
> Few threats could explain a close relationship between treatment introductions and removals and parallel outcome changes

---

### Example

*Mean narcotics use over multiple Methadone maintenance on/off conditions*

---

# `$A - B$` Designs

--
  
+ Multiple-baseline design (a class of single-subject designs), or collection of `$A - B$` designs, to assess the effects of an intervention across separate baselines

+ Variables

>- `$A$` = baseline

>- `$B$` = treatment

+ The intervention is introduced in a staggered manner and the baseline provides a predicted level of the dependent variable in absence of the treatment

+ `$A - B - A$` designs are sometimes called removal designs (i.e., the treatment is removed)

---

### Example

---

# Designs that use a Control Group but no Pretest

---

##  Posttest-Only Design with Nonequivalent Control Group

.center2[
<table class="table" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `NR` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `X` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_1` </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `NR` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_1` </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Non Random Assignment </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Treatment </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
  </tr>
</tbody>
</table>
]

<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
> Unknown pretest group differences make it extremely difficult to separate treatment effects from selection effects

---

##  Posttest-Only Design using an Independent Sample Pretest

.center2[
<table class="table" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `NR` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_1` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ¦ </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `X` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_2` </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `NR` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_1` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ¦ </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_2` </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Non Random Assignment </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Pretest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Treatment </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
  </tr>
</tbody>
</table>
]

<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
> Assumes overlapping group membership

> Useful when

>> Pretest measurements may be reactive

>> Cannot follow same groups over time

>> When interested in studying intact communities whose members change over time

---

#  Case Control Studies

--
  
+ Predominant method for many forms of epidemiological research

+ Used to identify factors that may contribute to a condition by comparing subjects who have that condition (i.e., 'cases ') with those who do not have the condition but are otherwise similar (i.e., 'controls' )

+ Example: Famously used to determine the association between smoking and lung cancer

---

##  Untreated Control Group Design with Dependent Pretest and Posttest Samples

.center2[
<table class="table" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `NR` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_1` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `X` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_2` </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> ------ </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `NR` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_1` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_2` </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Non Random Assignment </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Pretest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Treatment </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
  </tr>
</tbody>
</table>
]

<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
> A selection bias is always present, but the pretest observation allows for determining the magnitude and direction of bias

---

### Outcome Pattern 1

> *Both groups grow apart at different average rates in the same direction*

> This pattern is consistent with treatment effects and can sometimes be causally interpreted, but it is subject to numerous threats, especially selection-maturation

---

### Outcome Pattern 2

> *Spontaneous growth only occurs in the treatment group*

> Not a lot of reliance can be placed on this pattern as the reasons why spontaneous growth only occurred in the treatment group must be explained (e.g., selection-maturation)

---

### Outcome Pattern 3

> *Initial pretest differences favoring the treatment group diminish over time*

> Same internal validity threats as outcome patterns #1 and #2 except that selection-maturation threats are less plausible

---

### Outcome Pattern 4

> *Initial pretest differences favoring the control group diminish over time*

> Subject to numerous validity threats (e.g., selection-instrumentation, selection-history), but generally can be causally interpreted

---

### Outcome Pattern 5

> *Outcomes that crossover in the direction of relationships*

> Most amenable to causal interpretation and most threats cannot plausibly explain this pattern

---

# Modeling Selection Bias

- *Simple matching and stratifying*

- Overt biases with respect to measured variables/characteristics

- *Instrumental variable analysis*

- Statistical modeling of covariates believed to explain selection biases

- *Hidden bias analysis*

- Difference with respect to unmeasured variables/characteristics
  
  - Sensitivity analysis (how much hidden bias would need to be present to explain observed differences)
  
--

- *Propensity score analysis* 
  
  - Predicted probabilities of group membership
  
  - Propensities then used for matching or as covariate

---

# Interrupted Time-Series

A large series of observations made on the same variable consecutively over time

- Observations can be made on the same units (e.g., people) or on constantly changing units (e.g., populations)

- Must know the exact point at which a treatment or intervention occurred (i.e., the interruption)

- Interrupted time-series designs are powerful cause-probing designs when experimental designs cannot be used and when a time series is feasible

---

## Types of Effects

- Form of the effect (slope or intercept)

- Permanence of the effect (continuous or discontinuous)

- Immediacy of the effect (immediate or delayed)

- Independence of observations

- (Most) statistical analyses assume observations are independent (one observation is independent of another)
  
--

- In interrupted time-series, observations are autocorrelated (related to prior observations or lags)
  
--

- Requires a large number of observations to estimate autocorrelation
  
--

- Seasonality

- Observations that coincide with seasonal patterns
  
--

- Seasonality effects must be modeled and removed from a time-series before assessing treatment impact

---

---

.center2[
<table class=" lightable-paper" style='font-family: "Arial Narrow", arial, helvetica, sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'>
 <thead>
  <tr>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
   <th style="text-align:center;">  </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_1` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_2` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_3` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_4` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_5` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `X` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_6` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_7` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_8` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_9` </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> `O_{10}` </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Prettest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Pretest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Pretest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Pretest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Pretest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Treatment </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
   <td style="text-align:center;width: 3em; color: #ffffff !important;vertical-align: middle !important;"> ` `$\rightarrow$` ` </td>
   <td style="text-align:center;width: 10em; color: #ffffff !important;vertical-align: middle !important;"> Posttest </td>
  </tr>
</tbody>
</table>
]

<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
> The basic interrupted time-series design requires one treatment group with many observations before and after a treatment

---

---

---

---

---

---

---

#  That's It!

Any questions?