Module °Benchmark: Understanding the Tonality effect (Part IV)

Module °Benchmark: Understanding the Tonality effect (Part IV)

The Tonality effect: 

Definition: Impact on the average due to changes of tonality if no change in weights



Considering the assumption that the categories have kept the same weights, what are the impact(s) of the changes in tonality on the global average ?



Ex1: Imagine the following situation in a restaurant: 

(IMPORTANT : To simplify here, 1 comment = 1 category)

2 periods compared: N vs N-1


Category

E-index

N-1

E-index N

Volume

N-1

Volume

 N

Relative Weight N-1

Relative Weight N

Welcome 

30°

30°

1

1

1/4

1/4

Order

10°

10°

1

1

1/4

1/4

Food

40°


1

1

1/4

1/4

Bill



1

1

1/4

1/4

Average

20° 

(80/4)

10° ↘ (40/4)

4

13




Conclusion: Even if each topic weight has not evolved between N-1 and N, the global score has decrease  -10°! And that was due to the LOWER TONALITY of the category Food in the current period (that was the only change in the data). That is a Pure Tonality impact.

For each category:

Tonality effect = Delta E-index (of the 2 periods) x Relative Weight N-1


The same effect can be calculated for the Satisfaction averaged scores, Recommendation averages, etc.

In the graphics, the tonality effect is displayed at the center when the Details button is activated:
Tonality effect (T)







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