One-sample Z-test on proportions
Quick reference
To request a one-sample Z-test, type:
stat=z1[, element_text] ;fac=factor [;options]
as an element in the axis. factor is a value between 1 and 100 and is the proportion against which values are to be compared.
More information
This is an axis-level statistic which is used to test whether the percentage of respondents in a particular element differs from a given value. For example, if you wanted to see whether more than 40% of yogurt buyers buy low-fat brands only, you would compare each sample percentage with the number 40.
To request a one-sample Z-test, place a stat=z1;fac=n element in the axis. The fac= option on the stat statement specifies the value, expressed as a percentage, with which the percentages in the preceding element are to be compared. n may be a whole number or a decimal number with up to six decimal places. Each stat= element must be preceded by a base element and a single element of basic counts.
The Z-tests may give misleading results when the bases from which proportions are calculated are small. In this case, the base element should contain at least 10 respondents for the test to be valid.
The Z-value is zero if the difference is zero, otherwise it is negative if the calculated percentage is smaller than the specified value, and positive if it is greater.
Example
This example defines an axis for a survey investigating purchases of dairy products. It checks whether 50% of respondents buy low-fat brands of yogurt, and then testing this hypothesis among different age-related sub-samples.
The Quantum specification is:
tab brand age
ttlQ9: Type of Yogurt Purchased
ttlBase: All Yogurt Buyers
l tried
col 121;Base;Buys Low-Fat
stat=z1,Z Value for 50%;fac=50
l age
col 108;Base;18–24;25–34;35–44;45–54;55+
The table it produces is:
Q9: Type of Yogurt Purchased
Base: All Yogurt buyers
Base 18-24 25-34 35-44 45-54 55+
Base 605 96 194 91 126 98
Buys Low-Fat 334 50 108 51 73 52
Z value for 50% 2.56 0.41 1.58 1.15 1.78 0.61
0.010 0.683 0.114 0.249 0.075 0.544
The results in the Base column show a significant result at the 99% confidence level. This suggests that you should reject the null hypothesis that 50% of yogurt buyers buy low fat yogurt. However, none of the age groups differ significantly from the 50% figure at the 95% confidence level.
See also