Z-test on sub-sample proportions
Quick reference
To request a Z-test on subsample proportions, type:
stat=z3
on the tab statement.
More information
The Z-test on sub-sample proportions is a table-level statistic. It is used to test differences between all row percentages in a single row of a table. For example, you might want to test whether you have the same proportion of respondents in each age group.
This test requires a stat=z3 option on the tab statement. The table must consist of a base row only, and the first element of the column axis must be a base element. The test calculates a Z-value comparing each row percentage with each of the other row percentages, and produces a triangular table showing all the Z-values and their associated significance levels. The table is labeled with the text ‘Z TEST – TYPE 3’.
Notes
▪The percentages (proportions) which are compared are always calculated by dividing the count in the base column into the count in each other element of the row. It is not necessary for the row percentages to be printed using the option op=0.
▪The columns of the table should define groups of respondents in such a way that the groups are mutually exclusive — for example, age groups or sex. If the column axis defines more than one set of mutually exclusive elements the test will still be printed, but the comparisons between elements which are not mutually exclusive are meaningless and should be ignored. For example, if the column axis contains both sex and age breakdowns, the comparison between, say, ‘Female’ and ‘Age 18–25’ must be ignored since some respondents may be women and aged 18–25.
▪The Z-tests may give misleading results when the base from which proportions are calculated is small. In this test the base should be at least 20.
▪The calculation for Z subtracts the first proportion from the second, rather than the more usual method of subtracting the second proportion from the first.
Example
The Quantum program below compares the proportions of respondents in different age-groups:
tab justbase age2;stat=z3
ttlAge group distribution
ttlBase: All respondents
l justbase
n10Base
l age2
col 120;Base;18–24;25–34;35–44;45+
The table produced is:
Age group distribution
Base: All respondents
Base 18-24 25-34 35-44 45+
Base 400 96 104 104 96
Z TEST - TYPE 3
18-24 25-34 35-44
25-34 0.556
0.571
35-44 0.556 0.000
0.571 1.000
45+ 0.000 -0.556 -0.566
1.000 0.571 0.571 |
These results show that there is no evidence to suggest that there is a difference in the proportion of respondents who fall into each of the four age groups.
See also