At least I might understand the piss taking.
Below an answer to a question I asked about some figures from work this morning....
Shaun,
The most important thing is to have a prediction and calculate the variation from that prediction. If you also know the random variation in the sample that you are measuring (as per Malcolm’s email), assuming that is normally distributed (ie. bell shaped) you can see if the actual value is more than 1.96 times (basically twice) the standard deviation. If it is, you can be pretty sure you’ve had an effect.
For something like web visits, you will also want to make sure you look at the business performance of that channel only, otherwise it will be drowned out by the other channels.
I’ve got a little example below for you re: the calculations of standard deviations. The example I’ve chosen is a random Premier League football team’s results.
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Goals Scored Goals Scored Home / Away
QPR 0 Fulham 6 A
QPR 1 Aston Villa 1 H
QPR 3 Wolves 0 A
QPR 0 Newcastle 0 H
QPR 0 Wigan 2 A
QPR 0 Rochdale 2 H
QPR 1 Everton 0 A
QPR 0 Bolton 4 H
QPR 0 Cesena 1 A
Average 0.6 1.8
Standard Deviation 1.0 2.0
Average (exc. Last game) 1.3
Standard Deviation (exc. Last game) 1.3
Low End 0 0
Top End 2.5 5.8
Low End (exc. LG) 0
Top End (exc. LG) 3.7
________________________________________
The table basically shows, that you can be confident that 95% of the time, QPR will score between NONE and 2.5 goals in a game. Up until Saturday, you could also be confident that the opposition would score somewhere between NONE and 3.7 goals. However, given the debacle on Sunday which has led to a significantly increased variation, you can be confident that the opposition will score between NONE and 5.8 goals in a game.
I have made a couple of assumptions here. Firstly, that the distribution of scoring goals is normal. This is almost certainly not the case, and it is more likely to be a Poisson distribution. Secondly, the assumption has been made that the teams that QPR has yet to play are as difficult as the teams that have currently been played. Given that the “biggest” name teams they have currently played are Aston Villa and Newcastle, I would suggest that you can be confident that the lower end of the goals conceded will move above NONE as more data points are obtained.
I hope this email (and specifically the example) helps
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