Common mistake 1 with Summary by group

Reporting an unweighted mean from a weighted survey. This is not imprecision, it is bias: the answer converges to the wrong number as the sample grows.

Common mistake 2 with Summary by group

Grouping by something continuous and getting one group per row. The app refuses past 2,000 groups, but 200 groups of six rows each is legal and useless.

Common mistake 3 with Summary by group

Reading a difference in group means as an effect. Groups differ in everything at once; that is what regression is for.

Common mistake 4 with Summary by group

Forgetting that a mean of a ratio is not the ratio of the means. If you want a rate for the group, aggregate the numerator and the denominator and divide those.

EconStatsCraft › Summary by group

Summary by group

Any statistic you like, for every group in the data - Stata's tabstat and collapse. Supply a survey weight and the means become population means rather than means of whoever was sampled, and the effective sample size is reported so you know what the weighting cost you in precision.

What it needs

Group by - A category, or a continuous column cut into bands first.
Measures - One table per measure.

The intuition

Collapsing rows to group means is the most-used operation in applied work and the least examined. Two things go wrong quietly. An average of averages is not the overall average unless the groups are the same size, and any relationship visible between groups can be the reverse of the relationship within them.

When to use it

Before any model, to see what the data looks like where it matters. And after one, to check that a result holds in each subgroup rather than only on average.

Where the estimator comes from

For groups g with sizes n_g and means \bar{x}_g, the overall mean is the WEIGHTED average \bar{x}=\sum_g n_g\bar{x}_g/\sum_g n_g, not \frac{1}{G}\sum_g\bar{x}_g. The two coincide only when every n_g is equal. The variance decomposes as \underbrace{\textstyle\sum_g\sum_{i\in g}(x_i-\bar{x})^2}_{\text{total}}=\underbrace{\textstyle\sum_g n_g(\bar{x}_g-\bar{x})^2}_{\text{between}}+\underbrace{\textstyle\sum_g\sum_{i\in g}(x_i-\bar{x}_g)^2}_{\text{within}}, and aggregation keeps only the between part. Everything the within part contained - including any within-group relationship - is discarded, which is why a regression on group means answers a different question from a regression on the rows.

The model

\bar{y}_g=\frac{\sum_{i\in g} w_i y_i}{\sum_{i\in g} w_i}\qquad n^{\text{eff}}=\frac{\left(\sum w_i\right)^2}{\sum w_i^2}

What it assumes

The groups are what you think they are. A group with three rows in it will happily report a mean, a median and a standard deviation, and none of them mean anything.
If this is survey data, the weight column is not optional. NSS, NFHS and PLFS all over-sample some groups on purpose, so an unweighted mean estimates the population of whoever was sampled rather than the population of India.
The grouping variable is clean. Two spellings of the same category produce two groups, and the summary will look entirely reasonable while splitting the thing you meant to aggregate.
The statistic is appropriate to the level. A mean of means is not the overall mean unless the groups are the same size, and the difference is Simpson's paradox waiting to happen.

Statistical properties

The mean of group means is not the grand mean unless groups are equal in size. Reporting an unweighted average of country averages as a world figure is the classic instance, and it over-weights small countries enormously.
Aggregating destroys within-group variation, so a regression on group means has fewer observations, higher R-squared and standard errors that are not comparable to the individual-level regression.
Simpson's paradox is the extreme case: an association can reverse sign on aggregation. This is not a rare pathology; it happens whenever group membership is correlated with both variables.
The ecological fallacy is the same error in the other direction - inferring individual behaviour from group-level correlations. Robinson (1950) found a correlation of 0.53 between literacy and being foreign-born across US states, against -0.11 for individuals.
Medians do not aggregate at all. There is no way to compute an overall median from group medians, whatever the weights.
Counts and sums aggregate exactly; means, medians, ratios and percentages need care. A weighted mean of ratios is not the ratio of the sums, which is what most people actually want.

How to read the output

Compare N across groups first. A striking difference in the means of two groups where one has 20 rows is not a finding.
The weighted N is the population each group stands for. It is the number to quote, and it is usually thousands of times the row count.
The effective sample size says what the weighting cost you. If it is 40% of the row count, every standard error in the app that treats n as the row count is optimistic by that much.
Missing counts matter as much as the means. A group where a third of the rows have no value for the measure is telling you about non-response, not about the measure.

A worked reading

Two groups, one with 900 rows averaging 10 and one with 100 rows averaging 20. The unweighted mean of the group means is 15; the actual overall mean is (900 x 10 + 100 x 20)/1000 = 11. A five-point error, from an operation that felt like arithmetic rather than a modelling choice. And if the small group is systematically different in some other way - which is usually why it is a separate group - then any regression run on the two group means has two observations and answers a question about groups rather than about the underlying units.

Symptom → diagnosis → what to do

If you see this	It means	Do this
Group mean of means differing from the overall mean	Unequal group sizes	Weight by size. Correct, not a bug
R-squared jumping after aggregating	Within-group noise removed	Not a better model; a different question
A relationship reversing on aggregation	Simpson's paradox	Show both levels; neither is automatically right
Averaging percentages	The denominators differ	Sum numerators and denominators, then divide
Aggregated medians	Not computable from group medians	Aggregate from the raw rows
One group with a single observation	Its mean has no variance	Report group sizes alongside

Common mistakes

Reporting an unweighted mean from a weighted survey. This is not imprecision, it is bias: the answer converges to the wrong number as the sample grows.
Grouping by something continuous and getting one group per row. The app refuses past 2,000 groups, but 200 groups of six rows each is legal and useless.
Reading a difference in group means as an effect. Groups differ in everything at once; that is what regression is for.
Forgetting that a mean of a ratio is not the ratio of the means. If you want a rate for the group, aggregate the numerator and the denominator and divide those.

Where to read this properly

Robinson (1950), "Ecological Correlations and the Behavior of Individuals", American Sociological Review 15(3).
Simpson (1951), "The Interpretation of Interaction in Contingency Tables", JRSS-B 13(2).
Wooldridge, Econometric Analysis of Cross Section and Panel Data (2010), ch. 10, on group-level regressions.

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Data & variables

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and

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Rules

Base period = 100

Which part

Percent at each tail

Threshold

Survey weight optional

Direction

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Summary by group

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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