MODULE 02

Crosstabs

A crosstab only answers your question if the percentages are computed in the right direction. The rule: percentage within the categories of the independent variable, then compare across them.

Research question
Variables
Variable roles
Measurement levels
Method choice (trained here)
Statistical logic (trained here)
SPSS workflow (trained here)
Output interpretation (trained here)
Defensible conclusion

Understand

Which total is the percentage computed from?

Xage group and Yspeaks a foreign language, N = 1,600. Switch between counts and percentages and watch which cells are shaded together: shaded cells share a denominator and add up to 100%.

	YSpeaks a foreign language
XAge group	Yes	No	Total
18–34	62.4%	37.6%	100%
35–54	45.0%	55.0%	100%
55+	24.0%	76.0%	100%
Total	43.9%	56.1%	100%

: each row total (every row sums to 100%), i.e. each category of age group (X).

Compares Y within X ✓

Reading: 62.4% of 18–34-year-olds speak a foreign language, compared with 24.0% of those aged 55+. Younger age groups are more likely to speak a foreign language (an association, not a causal claim).

Row or column is not the point

The question is never “row % or column %?” in the abstract. It is “where is X?”. Use the Transpose button: the right percentages switch from row to column, but the numbers you compare stay the same.

Try

Which percentages should we compare?

Choose percentage direction

X = age group is in the rows, Y = speaks a foreign language (yes / no) is in the columns. Which percentages should we compare?

Choose percentage direction

Now education (X) is placed in the columns and voted in the last election (Y) in the rows. Which percentages?

Before interpreting a crosstab

0/9

1Valid categories · Only substantive answer categories belong in the table.
2Missing / nonresponse codes removed · Don't know, refused, not applicable: define them as missing in SPSS.
3Correct X and Y · Decide from the research question which variable is independent and which is dependent.
4Relevant percentage direction · Percentages within categories of X: row % if X is in the rows, column % if X is in the columns.
5Expected counts · Check the footnote: at most 20% of cells with expected count < 5, none below 1.
6Chi-square significance · Is there evidence of an association in the population? Read Pearson Chi-Square, Asymptotic Sig.
7Cramer's V · How strong is the association?
8Substantive interpretation · Describe the pattern in words with the key percentages.
9Association ≠ causation · Say ‘is associated with’, ‘differs between’, not ‘causes’ or ‘affects’.

Understand

χ², Cramer's V and p answer different questions

Keep the three apart and most interpretation errors disappear.

Chi-square (χ²)

“Is there evidence of an association?”

Compares observed with expected counts. Grows with N.

Cramer's V

“How strong is the association?”

0 = none, 1 = perfect. Does not grow with N.

p-value

“Is the observed pattern statistically compatible with the null hypothesis of no association?”

Not an effect size.

Same percentages, different sample size

The slider multiplies every cell of the age × language table by the same factor. The row percentages, and therefore the strength of the association, never change.

Sample size NN = 80

χ²(2): 7.5
p: .023
Cramer's V: .31

SPSS

Crosstabs in SPSS

Before you open SPSS

1What is the research question?Do age groups differ in whether people speak a foreign language?
2What are X and Y?Xage group Yspeaks a foreign language
3Measurement levels?Ordinal (age group) and nominal (yes/no): categorical, so a crosstab.
4Compare or associate?Compare the distribution of Y across categories of X.
5Which method?Crosstab with percentages within X, χ² test, Cramer's V.

Analyze›Descriptive Statistics›Crosstabs

Crosstabs

gender

educ

settlement

polint

1Row(s):

agegroup (X)

2Column(s):

forlang (Y)

Cells › ObservedCells › ExpectedCells › RowStatistics › Chi-squareStatistics › Phi and Cramer's V

PasteResetCancelOK

1
Row(s):
X in the rows…
2
Column(s):
…and Y in the columns, so row percentages are percentages within X.
Cells › Expected
Lets you see where observed and expected counts differ most.
Cells › Row
Percentages within each row, i.e. within X.

Chi-Square Tests
	Value	df	Asymptotic Sig. (2-sided)
Pearson Chi-Square	150.196	2	.000
Likelihood Ratio	—	2	.000
N of Valid Cases	1600

1Read the Pearson Chi-Square row.
2.000 means p < .001: evidence of an association.

a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 219.38.

Symmetric Measures
		Value	Approximate Sig.
Nominal by Nominal	Phi	.306	.000
	Cramer's V	.306	.000
N of Valid Cases		1600

3Strength of the association: moderate. (For a 2-column table, Phi and V coincide in size.)

Reporting

Speaking a foreign language differs by age group: 62.4% of 18–34-year-olds, 45.0% of 35–54-year-olds and 24.0% of those aged 55+ speak one (χ²(2) = 150.2, p < .001, Cramer's V = .31). The association is moderate; the data do not show why it exists.

Test yourself

Mastery check

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Choose percentage direction

X = age group is in the rows, Y = speaks a foreign language (yes / no) is in the columns. Which percentages should we compare?

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