Orange or Yellow:
Interpretation, Reliability and Credibility of Testimonies
We want to demonstrate in this article how easy it is to misinterpret testimonies, even if they are truthfull. There are two football teams - it doesn't matter if it's American football or soccer- let's call them Money Wanderers FC and Yellowback Rangers FC.
After a difficult and important game for both teams, the official fan-clubs and the unofficial ones of both teams have a hard night of riots. The yellowrangers' goal which would have been decisive wasn't acknowledged by the referee. Therefore the Yellowback Rangers think that the victory of the Money Wanderers was not fair, because they have won in the end by a penalty shoot-out.
Mr. Dog-Walker, who is walking his dog in a dark alley, is witnessing how somebody is thrown to the floor and nearly killed. The only thing he remembers when questioned by the police is that the guy was wearing a yellow jacket. The Yellowback Rangers use the colour yellow as their club colour of course, while orange is the choice of the Money Wanderers.
It's easy enough for the yellow press, who is specialized in condemnations in advance of trial: A fan of the Money Wanderers was knocked down by a hooligan of the Yelloback Rangers. The Yelloback Rangers haven't come to terms with their defeat.
But a amateur mathematician sends a letter to the editor. He argues that it is very hard if not impossible to distinguish in the twilight between the colours yellow and orange. So it might as well has been an orange jacket. Furthermore, he stated that there have been about 1,000 hooligans of the Money Rangers in town, while the there have been just 200 Yellowback hooligans around. So, 1,000 of 1,200 hooligans have been Money Rangers. So according to probability the victim was beaten down by one of his kind with a likelyhood of 1,000/1,200 = 0.8333333
Mr. Fermat a mathematics teacher is sending another letter to the publishers, writing that he thinks that it is necessary to include the error likelyhood of Mr Dog-Walker. If the witness is mistaken in 20 percent of all cases, which would be impressive taking into account the bad light quality in the alley, the case would look different.
If the witness saw all the hooligans, one after the other, he would classify 200 of the 1,000 hooligans of the Money Wanderes as Yellowback Rangers, and 40 of the 200 Yelloback Ranges as belonging to the other team.
||Number of Hooligans
||Witness believes having seen a
||Witness believes having seen a orange jacket|
|man wore a yellow jacket
||20 % of 200: 40 times
||80 % of 200: 160 times
|man wore an orange jacket
||20 % of 1,000: 800 times
||80 % of 1000: 200 times
The witness believes in 360 cases (160 + 200) that he has seen an orange jacket, but he is wrong in 200 cases. The error rate, if the witness believes to see orange is therefore 56% (200/350*100)
The witness is wrong in more than half of the cases!