Descriptive Analysis

Summary statistics, balance tables, and visualization

Summary Statistics

Before running any regressions, you need to understand your data. Summary statistics tell you about the distribution of each variable: What's the average? How much variation is there? Are there outliers or missing values? This is essential for catching data errors and understanding what your results will mean.

Basic Summary Statistics

Start with the basics: mean, standard deviation, min, and max. The mean tells you the central tendency. The standard deviation tells you how spread out the data is—if it's small relative to the mean, values cluster tightly; if it's large, there's wide variation. Check min and max for implausible values (negative ages, incomes in the billions) that signal data errors.

* Basic summary
summarize income age education

* Detailed summary with percentiles
summarize income, detail

* Summary by group
bysort treatment: summarize outcome

pacman::p_load(dplyr)

# Basic summary
summary(data[, c("income", "age", "education")])

# Detailed summary
data %>%
  summarize(
    mean = mean(income, na.rm = TRUE),
    sd = sd(income, na.rm = TRUE),
    min = min(income, na.rm = TRUE),
    p25 = quantile(income, 0.25, na.rm = TRUE),
    median = median(income, na.rm = TRUE),
    p75 = quantile(income, 0.75, na.rm = TRUE),
    max = max(income, na.rm = TRUE)
  )

# Summary by group
data %>%
  group_by(treatment) %>%
  summarize(
    mean_outcome = mean(outcome, na.rm = TRUE),
    sd_outcome = sd(outcome, na.rm = TRUE),
    n = n()
  )

import pandas as pd

# Basic summary
data[["income", "age", "education"]].describe()

# Detailed summary with percentiles
data["income"].describe(percentiles=[.25, .5, .75])

# Summary by group
data.groupby("treatment")["outcome"].agg(["mean", "std", "count"])

Tabulations and Cross-tabs

Tabulations count how many observations fall into each category. Use one-way tabs for categorical variables (education level, state, treatment status) to see the distribution. Use two-way tabs (cross-tabs) to see how two categorical variables relate—for example, what percentage of treated individuals have each education level? This is your first look at whether groups differ systematically.

* One-way tabulation
tab education

* Two-way tabulation
tab education treatment

* With row/column percentages
tab education treatment, row col

* Tabulate continuous variable
tabstat income, by(education) stat(mean sd n)

# One-way tabulation
table(data$education)

# Two-way tabulation
table(data$education, data$treatment)

# With proportions
prop.table(table(data$education, data$treatment), margin = 1)  # row %
prop.table(table(data$education, data$treatment), margin = 2)  # col %

# Summarize continuous by group
data %>%
  group_by(education) %>%
  summarize(
    mean_income = mean(income, na.rm = TRUE),
    sd_income = sd(income, na.rm = TRUE),
    n = n()
  )

# One-way tabulation
data["education"].value_counts()

# Two-way tabulation (cross-tab)
pd.crosstab(data["education"], data["treatment"])

# With row/column percentages
pd.crosstab(data["education"], data["treatment"], normalize="index")  # row %
pd.crosstab(data["education"], data["treatment"], normalize="columns")  # col %

# Summarize continuous by group
data.groupby("education")["income"].agg(["mean", "std", "count"])

Balance Tables

A balance table compares characteristics across treatment and control groups. This is essential for any study with a treatment/control design because it reveals whether groups are comparable on observable characteristics.

In our framework, we typically control for observable characteristics in our regressions. So differences in observables between treatment and control groups aren't necessarily fatal—we're adjusting for them. However, if there are big differences in observables, that raises concern about big differences in unobservables, which we're not controlling for. On the flip side, if observables look similar across groups, that gives us some assurance that unobserved confounders are less likely to be biasing our results.

A balance table typically shows: (1) the mean of each variable in the control group, (2) the mean in the treatment group, (3) the difference, and (4) a p-value testing whether the difference is statistically significant. You hope to see small differences—if treatment and control groups look similar on observables, it's more plausible they're also similar on unobservables. Large, significant differences don't doom your analysis (you can control for them), but they should make you more cautious about potential unobserved confounding.

* Install if needed: ssc install balancetable

* Create balance table
balancetable treatment age female income education ///
    using "balance_table.tex", ///
    ctitles("Control" "Treatment" "Difference") ///
    varlabels replace

* Manual approach with estout
estpost ttest age female income education, by(treatment)
esttab using "balance.tex", ///
    cells("mu_1 mu_2 b se") ///
    label replace

pacman::p_load(modelsummary)

# Create balance table
datasummary_balance(
  ~ treatment,
  data = data,
  fmt = 2
)

# Export to file
datasummary_balance(
  ~ treatment,
  data = data,
  output = "balance_table.tex"
)

from scipy import stats

# Create balance table manually
vars = ["age", "female", "income", "education"]
balance = []
for var in vars:
    control = data.loc[data["treatment"] == 0, var]
    treated = data.loc[data["treatment"] == 1, var]
    tstat, pval = stats.ttest_ind(control, treated, nan_policy="omit")
    balance.append({
        "Variable": var,
        "Control": control.mean(),
        "Treatment": treated.mean(),
        "Difference": treated.mean() - control.mean(),
        "p-value": pval
    })
balance_df = pd.DataFrame(balance)
print(balance_df.to_string(index=False))

Data Visualization

Good visualizations reveal patterns that tables obscure. A scatter plot can show you nonlinearity that summary statistics miss. A time series plot can reveal trends and structural breaks. Economists use visualization both for exploratory analysis (understanding your data) and for communication (convincing readers of your findings).

Graphs Should Stand Alone

Every figure should be understandable without reading the paper. Include clear axis labels, legends, and titles. Use notes to explain any non-obvious details.

Histograms and Density Plots

Use histograms and density plots to visualize the distribution of a single variable. They answer: Is the distribution symmetric or skewed? Are there multiple modes (peaks)? Are there outliers? Comparing distributions across groups (overlapping densities) is a powerful way to see if treatment and control groups differ—before running any regressions.

* Histogram
histogram income, frequency ///
    title("Distribution of Income") ///
    xtitle("Annual Income ($)") ytitle("Frequency")
graph export "hist_income.png", replace

* Kernel density
kdensity income, ///
    title("Income Distribution") ///
    xtitle("Annual Income ($)")

* Overlapping densities by group
twoway (kdensity income if treatment == 0, lcolor(blue)) ///
       (kdensity income if treatment == 1, lcolor(red)), ///
    legend(label(1 "Control") label(2 "Treatment")) ///
    title("Income by Treatment Status")

pacman::p_load(ggplot2)

# Histogram
p <- ggplot(data, aes(x = income)) +
  geom_histogram(bins = 30, fill = "steelblue", color = "white") +
  labs(title = "Distribution of Income",
       x = "Annual Income ($)", y = "Frequency") +
  theme_minimal()
ggsave("hist_income.png", p, width = 8, height = 6)

# Kernel density
p <- ggplot(data, aes(x = income)) +
  geom_density(fill = "steelblue", alpha = 0.5) +
  labs(title = "Income Distribution", x = "Annual Income ($)")

# Overlapping densities by group
p <- ggplot(data, aes(x = income, fill = factor(treatment))) +
  geom_density(alpha = 0.5) +
  scale_fill_manual(values = c("blue", "red"),
                    labels = c("Control", "Treatment")) +
  labs(title = "Income by Treatment Status", fill = "Group")

import matplotlib.pyplot as plt
import seaborn as sns

# Histogram
plt.figure(figsize=(8, 6))
plt.hist(data["income"].dropna(), bins=30, color="steelblue", edgecolor="white")
plt.title("Distribution of Income")
plt.xlabel("Annual Income ($)")
plt.ylabel("Frequency")
plt.savefig("hist_income.png")

# Kernel density
data["income"].plot(kind="kde", title="Income Distribution")

# Overlapping densities by group
fig, ax = plt.subplots()
for treat, color, label in [(0, "blue", "Control"), (1, "red", "Treatment")]:
    data.loc[data["treatment"] == treat, "income"].plot(
        kind="kde", ax=ax, color=color, label=label
    )
ax.legend()
ax.set_title("Income by Treatment Status")

Scatter Plots

Scatter plots show the relationship between two continuous variables. Look for: Is the relationship positive or negative? Is it linear or curved? How much scatter is there around the trend? A fitted line helps readers see the overall relationship, but be careful—it can hide important nonlinearity. Binned scatter plots (binscatter) are particularly useful: they divide the x-axis into bins, calculate the mean y-value in each bin, and plot those means. This smooths out noise while revealing the true relationship.

* Basic scatter plot
scatter income education, ///
    title("Income vs. Education") ///
    xtitle("Years of Education") ytitle("Income")

* With fitted line
twoway (scatter income education) ///
       (lfit income education), ///
    legend(off) ///
    title("Income vs. Education")

* Binned scatter plot (binscatter)
* Install: ssc install binscatter
binscatter income education, ///
    title("Income vs. Education") ///
    xtitle("Years of Education") ytitle("Mean Income")

# Basic scatter plot
p <- ggplot(data, aes(x = education, y = income)) +
  geom_point(alpha = 0.5) +
  labs(title = "Income vs. Education",
       x = "Years of Education", y = "Income")

# With fitted line
p <- ggplot(data, aes(x = education, y = income)) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", se = TRUE) +
  labs(title = "Income vs. Education")

# Binned scatter plot
pacman::p_load(binsreg)
binsreg(y = data$income, x = data$education)

# Basic scatter plot
plt.figure(figsize=(8, 6))
plt.scatter(data["education"], data["income"], alpha=0.5)
plt.title("Income vs. Education")
plt.xlabel("Years of Education")
plt.ylabel("Income")

# With fitted line
import numpy as np
z = np.polyfit(data["education"], data["income"], 1)
p = np.poly1d(z)
plt.scatter(data["education"], data["income"], alpha=0.5)
plt.plot(data["education"].sort_values(), p(data["education"].sort_values()), "r-")

# Seaborn regression plot (easier)
sns.regplot(x="education", y="income", data=data)

Time Series and Line Plots

Time series plots show how a variable changes over time. They're essential for any analysis with a temporal component—especially difference-in-differences designs, where you want to show parallel pre-trends. When comparing groups over time, use separate lines for each group. Look for: Do the lines move together before treatment? Does one line diverge after treatment? Any sudden jumps or level shifts? It's reassuring when raw trends look parallel before treatment, though keep in mind that unit and time fixed effects can make trends parallel even when the raw data isn't—so non-parallel raw trends aren't necessarily fatal.

* Collapse to year-level means
preserve
collapse (mean) income, by(year)

* Line plot
twoway line income year, ///
    title("Average Income Over Time") ///
    xtitle("Year") ytitle("Mean Income")
restore

* Multiple lines by group
preserve
collapse (mean) income, by(year treatment)
twoway (line income year if treatment == 0) ///
       (line income year if treatment == 1), ///
    legend(label(1 "Control") label(2 "Treatment"))
restore

# Aggregate to year level
yearly <- data %>%
  group_by(year) %>%
  summarize(mean_income = mean(income, na.rm = TRUE))

# Line plot
p <- ggplot(yearly, aes(x = year, y = mean_income)) +
  geom_line(linewidth = 1) +
  geom_point(size = 2) +
  labs(title = "Average Income Over Time",
       x = "Year", y = "Mean Income")

# Multiple lines by group
yearly_by_group <- data %>%
  group_by(year, treatment) %>%
  summarize(mean_income = mean(income, na.rm = TRUE))

p <- ggplot(yearly_by_group, aes(x = year, y = mean_income,
                            color = factor(treatment))) +
  geom_line(linewidth = 1) +
  geom_point(size = 2) +
  scale_color_manual(values = c("blue", "red"),
                     labels = c("Control", "Treatment")) +
  labs(color = "Group")

# Aggregate to year level
yearly = data.groupby("year")["income"].mean()

# Line plot
plt.figure(figsize=(8, 6))
plt.plot(yearly.index, yearly.values, marker="o")
plt.title("Average Income Over Time")
plt.xlabel("Year")
plt.ylabel("Mean Income")

# Multiple lines by group
yearly_by_group = data.groupby(["year", "treatment"])["income"].mean().unstack()
yearly_by_group.plot(marker="o")
plt.legend(["Control", "Treatment"])

Box Plots

Box plots summarize a distribution's key features: the median (center line), interquartile range (the box, showing where the middle 50% of data falls), and outliers (individual points beyond the "whiskers"). They're especially useful for comparing distributions across many groups—you can see at a glance which groups have higher medians, more spread, or more outliers. Unlike histograms, box plots work well even when you have many categories to compare.

* Box plot by group
graph box income, over(education) ///
    title("Income Distribution by Education Level")

# Box plot by group
p <- ggplot(data, aes(x = factor(education), y = income)) +
  geom_boxplot(fill = "steelblue", alpha = 0.7) +
  labs(title = "Income Distribution by Education Level",
       x = "Education Level", y = "Income")

# Box plot by group
data.boxplot(column="income", by="education")
plt.title("Income Distribution by Education Level")
plt.suptitle("")  # Remove automatic title
plt.xlabel("Education Level")
plt.ylabel("Income")

# Or with seaborn
sns.boxplot(x="education", y="income", data=data)

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