Statistics for anthropology, a starter

Last update: Oct. 14, 2026

Anthropology has a reputation as the least numerical of the social sciences, and the reputation is only half deserved. Fieldworkers have been counting marriages, tallying kin terms and coding societies for well over a century. What they rarely have is a big, tidy random sample. That single fact shapes almost every statistical choice in the field, and it is the thread running through this page.

You do not need calculus for anything here. You need fractions, squares and patience.

What gets counted

Most anthropological numbers fall into a handful of shapes. The table lists the common ones, what a single row of data usually is, and where the analysis tends to go.

Kind of data	One row is	A typical question	Tools you will meet
Marriage tables	one marriage	Do people marry inside their group more often than chance would give?	chi-square, Fisher's exact test, odds ratios
Genealogies	one person, with links to mother and father	How closely related are spouses? How deep do lineages run?	relatedness coefficients, counts of ancestors
Free lists	one person's list of items in a domain	Which items are named most often, and how early?	frequencies, salience indices
Network data	one pair of people or households	Do ties follow kinship, residence or wealth?	density, centrality, permutation tests (QAP)
Answers to set questions	one informant	Is there a shared body of knowledge, and who knows it best?	cultural consensus analysis
Cross-cultural codes	one society	Do two traits go together across societies?	correlation, with corrections for shared history

Two things stand out. First, the "one row" column changes from line to line, and getting it right is half the work. Second, almost none of these rows are independent of each other in the way a textbook assumes. Brothers marry into the same families, neighbors give similar free lists, and neighboring societies share customs because they share ancestors. Keep that in mind through both worked examples.

Three questions before any test

What is one case? A marriage, a person, a household, a pair of households, a society. Many errors come from counting the same thing twice under two names, for instance treating each spouse in a marriage as a separate case.
Are the cases independent? If they are not, a standard test will be overconfident. Sometimes you can fix that by choosing cases differently; sometimes you need a test built for dependent data.
What would "nothing going on" look like? Every test compares what you saw with a null model, a description of the world in which your idea is wrong. Spelling out that null model in plain words is the most useful habit in applied statistics.

Worked example 1: a chi-square test on a marriage table

Imagine a hypothetical region with two sets of villages, one on the coast and one inland. A researcher records 200 marriages, 100 in each set, and notes whether each couple are cross cousins by local reckoning. (Cross cousins are children of a brother and a sister. In kin-type notation, where M is mother, F father, B brother, Z sister and D daughter, a man's cross-cousin wife is his MBD or his FZD.)

	Cross-cousin marriage	Other marriage	Total
Coastal villages	30	70	100
Inland villages	15	85	100
Total	45	155	200

The question: is the difference between 30% on the coast and 15% inland bigger than chance would produce if marriage type had nothing to do with region?

Step 1: expected counts

Under the null model, both regions share the overall rate of 45 in 200. The expected count for each cell is (row total × column total) / grand total.

Coastal, cross-cousin: 100 × 45 / 200 = 22.5
Coastal, other: 100 × 155 / 200 = 77.5
Inland, cross-cousin: 22.5
Inland, other: 77.5

The expected counts add up to the same row and column totals as the observed ones. Check that before going on; it catches most arithmetic slips.

Step 2: the chi-square statistic

For each cell compute (observed - expected)² / expected, then add the four results.

(30 - 22.5)² / 22.5 = 56.25 / 22.5 = 2.500
(70 - 77.5)² / 77.5 = 56.25 / 77.5 = 0.726
(15 - 22.5)² / 22.5 = 56.25 / 22.5 = 2.500
(85 - 77.5)² / 77.5 = 56.25 / 77.5 = 0.726

Total: χ² = 6.45 (to two decimals).

A 2×2 table has a shortcut that makes a good check. With cells a, b, c, d read across the rows, χ² = N × (ad - bc)² / (product of the four margins):

χ² = 200 × (30 × 85 - 70 × 15)² / (100 × 100 × 45 × 155) = 200 × 1500² / 69,750,000 = 6.45

The two routes agree.

Step 3: compare with the chi-square distribution

A table with 2 rows and 2 columns has (2 - 1) × (2 - 1) = 1 degree of freedom. With 1 degree of freedom the 5% cutoff is 3.84. Our 6.45 is above it; the exact p-value is about 0.011. If region and marriage type were unrelated, a gap at least this large would turn up in roughly 1 sample in 90.

Step 4: say how big the difference is

A p-value tells you little about size. Two simple measures:

Odds ratio: (30 × 85) / (70 × 15) = 2550 / 1050 = 2.43. The odds of a cross-cousin marriage are about two and a half times as high on the coast.
Phi coefficient: √(χ² / N) = √(6.45 / 200) = 0.18, a modest association on a scale from 0 to 1.

Two footnotes. Some textbooks apply Yates' continuity correction to 2×2 tables; here it lowers χ² to 5.62 (p about 0.018) and the conclusion stands. And if any expected count falls below about 5, use Fisher's exact test instead, which counts possible tables directly rather than leaning on an approximation.

What the test cannot see

It assumes the 200 marriages are independent. Suppose a dozen of the coastal cross-cousin marriages come from four large families who arrange marriages with each other generation after generation. The 30 then holds fewer independent decisions than it appears to, and the true uncertainty is wider than the test reports. Genealogical data almost always has this structure, which is why network methods and permutation tests keep appearing in kinship studies.

Correlation and its traps

Correlation coefficients (Pearson's r for measurements, Spearman's rho for ranks) are the workhorse of cross-cultural comparison. They also hide four common traps:

Tiny samples. With six or eight societies, one unusual case can create or erase a strong correlation, so plot the points before trusting the number.
Mixed levels. A correlation across villages does not describe individuals. Villages with more cattle may have more polygynous marriages without the cattle owners being the polygynous husbands. This is the ecological fallacy.
Restricted range. If your sample only includes societies of similar size, a real relation with size can vanish.
Shared history. Two traits can travel together because neighboring or related societies inherited both from a common source, not because one causes the other.

The last trap has a name. When Edward Tylor presented one of the first statistical comparisons of societies (published in the Journal of the Anthropological Institute in 1889), Francis Galton, chairing the meeting, asked how many of the cases were really independent copies of one another. "Galton's problem" has shaped comparative work ever since. One response was the Standard Cross-Cultural Sample of 186 societies (Murdock and White 1969), chosen one per cultural region to reduce dependence. Later responses model the dependence directly, using language trees or geographic distance. Our explainer on Galton's problem works through a toy example.

Agreement as data: consensus analysis

Some anthropological questions are about knowledge rather than behavior: which plants count as remedies, what the right answer to a question about local custom is. Cultural consensus analysis (Romney, Weller and Batchelder 1986, American Anthropologist 88) starts from the pattern of agreement among informants. If people share a cultural answer key, those who agree most with others are probably the most knowledgeable, and their competence can be estimated from the agreement matrix alone, without the researcher knowing the answers in advance. The explainer on cultural consensus analysis runs the calculation on five hypothetical informants.

Worked example 2: a permutation test on a tiny network

Permutation tests answer the independence problem with brute honesty: instead of assuming a textbook distribution, they build the null distribution from your own data by shuffling labels.

Imagine six hypothetical households. Households 1, 2 and 3 belong to lineage A; households 4, 5 and 6 belong to lineage B. A researcher records which households regularly share food, giving seven ties:

Tie	Same lineage?
1 and 2	yes
1 and 3	yes
2 and 3	yes
4 and 5	yes
4 and 6	yes
5 and 6	yes
3 and 4	no

Six of the seven ties stay inside a lineage. Is that more than chance?

The null model

If lineage had nothing to do with food sharing, the network would look the same but the labels A and B could have landed on any three households. So keep the ties exactly as they are and reassign the labels in every possible way. There are 20 ways to choose which three of six households get the label A (6 × 5 × 4 / (3 × 2 × 1) = 20).

Counting

For each of the 20 labelings, count the within-lineage ties:

Within-lineage ties	Number of labelings
6	2
3	8
2	10
Total	20

The two labelings that give 6 are the observed one and its mirror image (households 4, 5 and 6 called A). Every other split cuts through at least one of the two triangles and loses ties. You can check a row by hand: put households 1, 2 and 4 together, and only the ties 1 and 2, and 5 and 6, stay inside a group, so that labeling scores 2.

The p-value

The share of labelings that score at least as high as the observed 6 is 2 / 20 = 0.10.

That result is not "significant" at the usual 5% level, and there is a lesson in why. With six households split three and three, even a perfect split cannot reach a p-value below 0.10, because the mirror image always ties it. The data could not have convinced a skeptic, however clean the pattern. With eight households split four and four there are 70 labelings; if only the observed split and its mirror image reached the observed count, the p-value would be 2 / 70, about 0.029. Small networks need either more cases or more modest claims.

From labels to matrices

The quadratic assignment procedure, or QAP, uses the same idea for a harder question: does one network predict another? Put the food-sharing ties in one matrix and, say, kinship distances in another, then shuffle the rows and columns of one matrix together, so the network's shape survives while the identities move. Recompute the correlation after each shuffle, thousands of times, and see where the observed value falls. The network measures behind such tests are introduced in our explainer on density and centrality, and you can compute density for your own small network with the network density calculator.

Habits that make results easier to trust

Report the counts, not just percentages. "30 of 100" says more than "30%".
Pair every test with a size measure, such as an odds ratio, a difference in proportions or a correlation.
Write the null model in one sentence before running anything.
With small samples, prefer exact and permutation tests to approximations.
Treat "statistically significant" as "unlikely under this null model", nothing more.
Keep the field notes that explain odd cases. A statistic can show that a coastal marriage pattern differs; only the notes can say why the four large families keep marrying each other.