Common mistake 1 with Descriptive statistics

Reading correlation as causation. It is not, ever.

Common mistake 2 with Descriptive statistics

A correlation of zero rules out a linear relationship, not a relationship. Look at the plot.

Common mistake 3 with Descriptive statistics

Deleting outliers because they are inconvenient. Investigate first - they are often the most informative observations, or a data-entry error worth fixing.

Common mistake 4 with Descriptive statistics

Reading the mean of a heavily skewed variable as typical. With skewness above about one the median is the more honest summary, and quoting both costs nothing.

EconStatsCraft › Descriptive statistics

Descriptive statistics

Means, dispersion, skewness, Jarque–Bera normality, a starred correlation matrix and distribution plots. Always run this first.

What it needs

Variables to describe - Drop as many as you like.

The intuition

Every statistic here is a different question about the same cloud of numbers. The mean asks where the cloud sits, the standard deviation how wide it is, skewness whether it leans, kurtosis whether the tails are heavy. Correlation asks whether two clouds move together. None of them asks why, which is the whole reason the rest of econometrics exists.

When to use it

Always, before anything else. Every regression you run rests on what these numbers show, and half the mistakes in student projects are visible here - a variable that is 90% zeros, an impossible negative age, a wage of 10 million.

Where the estimator comes from

The sample mean is the value that minimises the sum of squared deviations: \bar{x}=\arg\min_c \sum_i (x_i-c)^2. The median minimises absolute deviations, \arg\min_c \sum_i |x_i-c|, instead. That single difference - squares versus absolutes - is why the mean is dragged by outliers and the median is not, and it reappears later as the difference between OLS and quantile regression.

The model

\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i \qquad s^{2}=\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^{2} \qquad r_{xy}=\frac{\operatorname{cov}(x,y)}{s_x s_y}

What it assumes

Nothing - these are descriptions, not inferences.
The Jarque–Bera p-value does assume the observations are independent.
The rows are the population you mean to describe. A summary of the observations that survived cleaning is a summary of the survivors, and the mean of a filtered sample is not the mean of the original.
The variables are of a type where these statistics mean something. A mean of a coded category is arithmetic on labels, and the software will compute it without complaint.

Statistical properties

x̄ is unbiased for μ and consistent: it converges in probability to μ as n grows.
Var(x̄) = σ²/n, so precision improves with the SQUARE ROOT of sample size - quadrupling the data halves the standard error.
The n−1 divisor in s² (Bessel's correction) makes it unbiased for σ²; dividing by n understates the variance systematically.
By the CLT, x̄ is approximately Normal in large samples whatever the shape of x itself.

How to read the output

Mean far from median → the distribution is skewed; consider using logs.
Skewness ≈ 0 and excess kurtosis ≈ 0 is what a Normal distribution looks like.
A correlation above 0.8 between two regressors is a multicollinearity warning.
Compare the N column across variables: a much lower N means missing values.

A worked reading

Mean log wage 2.3565 with a standard deviation of 0.4532 and skewness 0.0912 - close enough to symmetric that Jarque-Bera does not reject (p = 0.4337). Because the variable is already in logs, exp(2.3565) is the GEOMETRIC mean wage - a little over ten currency units, not the arithmetic one, and the distinction matters the moment you report levels: the arithmetic mean of the wages themselves is higher, because exponentiating is convex. Two other columns repay attention. Experience is visibly skewed (0.8882) with Jarque-Bera at 185.8, so its mean of 15.86 sits above its median of 14.6. And the female indicator has a "kurtosis" of 1.0070 and a JB of 200 purely because it is binary - normality statistics on a 0/1 column describe the fact that it is binary, not a problem with the data, and reading them as a diagnostic is a common and harmless-looking mistake.

Symptom → diagnosis → what to do

If you see this	It means	Do this
Mean far above median	Right-skewed, a long upper tail	Take logs; report the median alongside
Excess kurtosis above 3	Fat tails - extreme values more common than Normal	Robust standard errors; consider Student-t
One variable has far fewer observations	Missing data concentrated in that column	Check whether it is missing at random before dropping rows
\|r\| > 0.9 between two regressors	Near-collinearity	Drop one, combine into an index, or accept wide intervals
Zero correlation but obvious pattern in the scatter	The relationship is non-linear	Add a squared term, or use logs

Common mistakes

Reading correlation as causation. It is not, ever.
A correlation of zero rules out a linear relationship, not a relationship. Look at the plot.
Deleting outliers because they are inconvenient. Investigate first - they are often the most informative observations, or a data-entry error worth fixing.
Reading the mean of a heavily skewed variable as typical. With skewness above about one the median is the more honest summary, and quoting both costs nothing.

Where to read this properly

Wooldridge (2019), Introductory Econometrics: A Modern Approach, 7th ed., Cengage - Math Refresher C (Appendix C in earlier editions)
Tukey (1977), Exploratory Data Analysis, Addison-Wesley - on looking at the data before testing anything about it.
Anscombe (1973), "Graphs in Statistical Analysis" - four datasets, identical statistics, completely different shapes

All analyses

Data & variables

Each example is simulated from a known model, so you can check whether the estimator recovers the truth - and nothing here is anyone's private data.

Filter variables

Drag a variable into a slot on the right - or just click it.

Choose an example dataset above to begin.

Choose a transformation - it opens in the data editor, with a live preview.

Apply to

Multiply by

Columns ctrl-click for several

Group by ctrl-click for several

Within groups

Statistic

Bands

How many

Cut points

Keep rows where

Value

and

Fill with

Value

Also mark which rows were filled

Rules

Base period = 100

Which part

Percent at each tail

Threshold

Survey weight optional

Direction

Names column

Values column

Largest first

Delete them, not just count them

Read this column as

Tidy the text

New name optional

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Descriptive statistics

What it needs

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

See also

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