Intensity scales
9. Mean comparisons - non balance factors
Two data groups with unknown and unequal variances are considered.
On the two unknown means m1 and m2 will be carried out appropriate hypothesis test: ASPIN WELCH test.
This test is referenced in NF X 06-065 norm, and can also be consulted in:
Aide-mémoire statistique - CISIA/CERESTA Editor, 1995.
In case of not balanced factors in analysis of variance in TASTEL, this test is automatically calculated and
printed.
The main steps of this calculation are the following ones:
- Identification of pair comparisons according to the related factors:
PRODUCT, ASSESSOR, DATE, for example.
- Then, for each comparison:
- Counting of the two sample number, n1, n2
- Computation of each pair mean, for the two samples m1, m2
- Computation of each pair variance, for the two samples s²1, s²2
- Computation of a mu value:
1/mu = 1/(n1-1) [s²1/n1/s²d]² + 1/(n2-1) [s²2/n2/s²d]² , with s²d = s²1/n1+s²2/n2
Test is then the following: H0 (m1 = m2) against H1 (m1<>m2) with a threshold for a Student distribution
m1-m2 < -t1-a/2 (mu) * sd -> hypothesis H0 rejected
Remark: Real risks are given by interpolation line/column of the t table values.
- Result printing for all comparisons
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