The math behind statistical significance
Z-test for Vert% statistics
The following formula is used to compare percentages
Where:
n1 and n2: unweighted counts for compared groups
P1: share in group 1
P2: share in group 2
P1 = 87/100 = 0.87
P2 = 89/100 = 0,89
Statistically significant differences are all of the Z values that are bigger than 1.96 (values indicate a positive relationship between the items) and smaller than -1.96 (the values say about the negative relationship between the items).
-3,480 < -1.96, respectively, we can conclude that the consumption of the TOURER brand is NOT typical for males, with a probability of 95% (Z-value = 1.96).
T-test for Mean (Average) statistics
The formula for the T-test is as follows:
Where:
M1 and M2 - Average metric
m1 and m2 - Average error of the arithmetic mean
The formula for the average error of the arithmetic mean is:
Where:
n - unweighted count,
σ - standard deviation
The formula for standard deviation:
Example:
M1 = 787,1
M2 = 948,1
m1 = 47,12
m2 = 62,18
t - Criterion is -2,06
-2,06 < -1.96, respectively, we can conclude that the average costs have become significantly lower compared to Wave 10.