F-test: One-way analysis of variance
Quick reference
To request a one-way analysis of variance, type:
stat=anova
on the tab statement.
More information
An F-test or analysis of variance uses a table-level statistic to investigate whether a set of means, calculated from independent samples, differ significantly from one another. It is used in exactly the same way as the two-sample T-test, but instead of independently making pair-wise comparisons between the means, it makes a single overall comparison of them all.
Being a table-level statistic, this test requires a
stat=anova option on the
tab statement. The column axis defines the groups to be compared, which must be mutually exclusive. The row axis must include a base element, a mean (
n12) and a standard deviation (
n17) — these require
fac= options on the axis elements or an
n25 element with the
inc= option. For information on these elements, see
Statistical functions and totals.
Notes
▪The value of F is close to 1 if there is no significant difference to be found between the means, while high values indicate different means.
▪The F-test is invalid if the column axis defines groups which are not mutually exclusive.
▪Elements whose cells are all zeros are included in this test.
▪The calculation uses the sum of totalizable rows and the input to the mean and standard deviation rather than the base and the mean and standard deviation values themselves.
▪If the axis being tested contains fac= and inc=, Quantum scans backwards through the axis from the stat=t1 element and uses whichever of the two it finds first; that is, whichever of fac= or inc= occurs closest to, but still before, the statistical element.
Example
You can use F-test to examine more carefully the results of the example in
F values and T values, used to illustrate the two-sample T-test. The Quantum spec. is the same as that used in the previous example, except that the
tab statement becomes:
tab hours vcr;stat=anova,t2
The table which this produces is:
Q15 Rating for Brand Bought Most Recently
Base: All Respondents
Base Does not own a Owns a video
video recorder recorder
Base 305 181 124
Under 5 hours 45 24 21
5-6 hours 93 50 43
7-10 hours 62 40 22
11-15 hours 51 31 20
16+ hours 54 36 18
Mean 2.921 3.028 2.766
Std. Deviation 1.330 1.335 1.314
ANALYSIS OF VARIANCE F VALUE = 3.365
SIGNIFICANCE LEVEL = 0.068
T TEST - TYPE 2
Owns a video
Does not own a video -1.691
0.091 |
The significance level of the F-statistic (6.8%) enables you to be more confident about the real significance of the differences between the means (9.1% significance level).
See also