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.