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"metadata": {
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"source": [
"plt.figure(figsize=(6,8))\n",
"sns.boxplot(y=\"enem_score\", x=\"Tablet\", data=data).set_title('ENEM score by Tablet in Class')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To get beyond simple intuition, let's first establish some notation. This will be our everyday language to speak about causality. Think of it as the common tongue we will use to identify other brave and true causal warriors, and that will compose our cry in the many battles to come.\n",
"\n",
"Let's call $T_i$ the treatment intake for unit i. \n",
"\n",
"$\n",
"T_i=\\begin{cases}\n",
"1 \\ \\text{if unit i received the treatment}\\\\\n",
"0 \\ \\text{otherwise}\\\\\n",
"\\end{cases}\n",
"$\n",
"\n",
"The treatment here doesn't need to be a medicine or anything from the medical field. Instead, it is just a term we will use to denote some intervention for which we want to know the effect. In our case, the treatment is giving tablets to students. As a side note, you might sometimes see $D$ instead of $T$ to denote the treatment.\n",
"\n",
"Now, let's call $Y_i$ the observed outcome variable for unit i.\n",
"\n",
"The outcome is our variable of interest. We want to know if the treatment has any influence in it. In our tablet example, it would be the academic performance.\n",
"\n",
"Here is where things get interesting. The **fundamental problem of causal inference** is that we can never observe the same unit with and without treatment. It is as if we have two diverging roads and we can only know what lies ahead of the one we take. As in Robert Frost poem:\n",
"\n",
">Two roads diverged in a yellow wood, \n",
"And sorry I could not travel both \n",
"And be one traveler, long I stood \n",
"And looked down one as far as I could \n",
"To where it bent in the undergrowth; \n",
"\n",
"\n",
"To wrap our heads around this, we will talk a lot in term of **potential outcomes**. They are potential because they didn't actually happen. Instead they denote **what would have happened** in the case some treatment was taken. We sometimes call the potential outcome that happened, factual, and the one that didn't happen, counterfactual.\n",
"\n",
"As for the notation, we use an additional subscript:\n",
"\n",
"$Y_{0i}$ is the potential outcome for unit i without the treatment. \n",
"\n",
"$Y_{1i}$ is the potential outcome for **the same** unit i with the treatment.\n",
"\n",
"Sometimes you might see potential outcomes represented as functions $Y_i(t)$, so beware. $Y_{0i}$ could be $Y_i(0)$ and $Y_{1i}$ could be $Y_i(1)$. Here, we will use the subscript notation most of the time.\n",
"\n",
"![img](./data/img/intro/potential_outcomes.png)\n",
"\n",
"Back to our example, $Y_{1i}$ is the academic performance for student i if he or she is in a classroom with tablets. Whether this is or not the case, it doesn't matter for $Y_{1i}$. It is the same regardless. If student i gets the tablet, we can observe $Y_{1i}$. If not, we can observe $Y_{0i}$. Notice how in this last case, $Y_{1i}$ is still defined, we just can't see it. In this case, it is a counterfactual potential outcome.\n",
"\n",
"With potential outcomes, we can define the individual treatment effect:\n",
"\n",
" $Y_{1i} - Y_{0i}$\n",
" \n",
"Of course, due to the fundamental problem of causal inference, we can never know the individual treatment effect because we only observe one of the potential outcomes. For the time being, let's focus on something easier than estimating the individual treatment effect. Instead, lets focus on the **average treatment effect**, which is defined as follows.\n",
"\n",
"$ATE = E[Y_1 - Y_0]$\n",
"\n",
"where, `E[...]` is the expected value. Another easier quantity to estimate is the **average treatment effect on the treated**:\n",
"\n",
"$ATT = E[Y_1 - Y_0 | T=1]$\n",
"\n",
"Now, I know we can't see both potential outcomes, but just for the sake of argument, let's suppose we could. Pretend that the causal inference deity is pleased with the many statistical battles we fought and has rewarded us with godlike powers to see the potential alternative outcomes. With that power, say we collect data on 4 schools. We know if they gave tablets to its students and their score on some annual academic tests. Here, tablets are the treatment, so $T=1$ if the school provides tablets to its kids. $Y$ will be the test score."
]
},
{
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"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2023-03-15T11:20:11.478665Z",
"start_time": "2023-03-15T11:20:11.470021Z"
},
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
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"text/plain": [
" i Y0 Y1 T Y TE\n",
"0 1 500 450 0 500 -50\n",
"1 2 600 600 0 600 0\n",
"2 3 800 600 1 600 -200\n",
"3 4 700 750 1 750 50"
]
},
"execution_count": 3,
"metadata": {},
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],
"source": [
"pd.DataFrame(dict(\n",
" i= [1,2,3,4],\n",
" Y0=[500,600,800,700],\n",
" Y1=[450,600,600,750],\n",
" T= [0,0,1,1],\n",
" Y= [500,600,600,750],\n",
" TE=[-50,0,-200,50],\n",
"))"
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},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The $ATE$ here would be the mean of the last column, that is, of the treatment effect:\n",
"\n",
"$ATE=(-50 + 0 - 200 + 50)/4 = -50$\n",
"\n",
"This would mean that tablets reduced the academic performance of students, on average, by 50 points. The $ATT$ here would be the mean of the last column when $T=1$:\n",
"\n",
"$ATT=(- 200 + 50)/2 = -75$\n",
"\n",
"This is saying that, for the schools that were treated, the tablets reduced the academic performance of students, on average, by 75 points. Of course we can never know this. In reality, the table above would look like this:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2023-03-15T11:20:11.488711Z",
"start_time": "2023-03-15T11:20:11.480950Z"
},
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"text/html": [
"i | Y0 | Y1 | T | Y | TE | |
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0 | 1 | 500 | 450 | 0 | 500 | -50 |

1 | 2 | 600 | 600 | 0 | 600 | 0 |

2 | 3 | 800 | 600 | 1 | 600 | -200 |

3 | 4 | 700 | 750 | 1 | 750 | 50 |

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"text/plain": [
" i Y0 Y1 T Y TE\n",
"0 1 500.0 NaN 0 500 NaN\n",
"1 2 600.0 NaN 0 600 NaN\n",
"2 3 NaN 600.0 1 600 NaN\n",
"3 4 NaN 750.0 1 750 NaN"
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},
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"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pd.DataFrame(dict(\n",
" i= [1,2,3,4],\n",
" Y0=[500,600,np.nan,np.nan],\n",
" Y1=[np.nan,np.nan,600,750],\n",
" T= [0,0,1,1],\n",
" Y= [500,600,600,750],\n",
" TE=[np.nan,np.nan,np.nan,np.nan],\n",
"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is surely not ideal, you might say, but can't I still take the mean of the treated and compare it to the mean of the untreated? In other words, can't I just do $ATE=(600+750)/2 - (500 + 600)/2 = 125$? Well, no! Notice how different the results are. You've just committed the gravest sin of mistaking association for causation. To understand why let's look into the main enemy of causal inference.\n",
"\n",
"## Bias\n",
"\n",
"Bias is what makes association different from causation. Fortunately, it can be easily understood with our intuition. Let's recap our tablets in the classroom example. When confronted with the claim that schools that give tablets to their kids achieve higher test scores, we can refute it by saying those schools will probably achieve higher test scores anyway, even without the tablets. That is because they probably have more money than the other schools; hence they can pay better teachers, afford better classrooms, etc. In other words, it is the case that treated schools (with tablets) are not comparable with untreated schools. \n",
"\n",
"Using potential outcome notation is to say that $Y_0$ of the treated is different from the $Y_0$ of the untreated. Remember that the $Y_0$ of the treated **is counterfactual**. We can't observe it, but we can reason about it. In this particular case, we can even leverage our understanding of how the world works to go even further. We can say that, probably, $Y_0$ of the treated is bigger than $Y_0$ of the untreated schools. That is because schools that can afford to give tablets to their kids can also afford other factors that contribute to better test scores. Let this sink in for a moment. It takes some time to get used to talking about potential outcomes. Reread this paragraph and make sure you understand it.\n",
"\n",
"With this in mind, we can show with elementary math why it is the case that association is not causation. Association is measured by $E[Y|T=1] - E[Y|T=0]$. In our example, this is the average test score for the schools with tablets minus the average test score for those without them. On the other hand, causation is measured by $E[Y_1 - Y_0]$.\n",
"\n",
"Let's take the association measurement and replace the observed outcomes with the potential outcomes to see how they relate. For the treated, the observed outcome is $Y_1$. For the untreated, the observed outcome is $Y_0$.\n",
"\n",
"$\n",
"E[Y|T=1] - E[Y|T=0] = E[Y_1|T=1] - E[Y_0|T=0]\n",
"$\n",
"\n",
"Now, let's add and subtract $E[Y_0|T=1]$. This is a counterfactual outcome. It tells what would have been the outcome of the treated, had they not received the treatment.\n",
"\n",
"$\n",
"E[Y|T=1] - E[Y|T=0] = E[Y_1|T=1] - E[Y_0|T=0] + E[Y_0|T=1] - E[Y_0|T=1]\n",
"$\n",
"\n",
"Finally, we reorder the terms, merge some expectations, and lo and behold:\n",
"\n",
"$\n",
"E[Y|T=1] - E[Y|T=0] = \\underbrace{E[Y_1 - Y_0|T=1]}_{ATT} + \\underbrace{\\{ E[Y_0|T=1] - E[Y_0|T=0] \\}}_{BIAS}\n",
"$\n",
"\n",
"This simple piece of math encompasses all the problems we will encounter in causal questions. I cannot stress how important it is that you understand every aspect of it. If you're ever forced to tattoo something on your arm, this equation should be a good candidate for it. It's something to hold onto dearly and understand what is telling us, like some sacred text that can be interpreted 100 different ways. In fact, let's take a deeper look. Let's break it down into some of its implications. First, this equation tells why the association is not causation. As we can see, the association is equal to the treatment effect on the treated plus a bias term. **The bias is given by how the treated and control group differ before the treatment, in case neither of them has received the treatment**. We can now say precisely why we are suspicious when someone tells us that tablets in the classroom boost academic performance. We think that, in this example, $E[Y_0|T=0] < E[Y_0|T=1]$, that is, schools that can afford to give tablets to their kids are better than those that can't, **regardless of the tablets treatment**.\n",
"\n",
"Why does this happen? We will talk more about that once we enter confounding, but for now, you can think of bias arising because many things we can't control are changing together with the treatment. As a result, the treated and untreated schools don't differ only on the tablets. They also differ on the tuition cost, location, teachers...\n",
"For us to say that tablets in the classroom increase academic performance, we would need for schools with and without them to be, on average, similar to each other."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2023-03-15T11:20:11.602399Z",
"start_time": "2023-03-15T11:20:11.490391Z"
},
"tags": [
"hide-input"
]
},
"outputs": [
{
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\n",
"text/plain": [
"i | Y0 | Y1 | T | Y | TE | |
---|---|---|---|---|---|---|

0 | 1 | 500.0 | NaN | 0 | 500 | NaN |

1 | 2 | 600.0 | NaN | 0 | 600 | NaN |

2 | 3 | NaN | 600.0 | 1 | 600 | NaN |

3 | 4 | NaN | 750.0 | 1 | 750 | NaN |