Firstly the small numbers effect:  The Bill and Melinda gates foundation commissioned a study to examine schools in search of the most effective schools.    It found, unsurprisingly that small size, in terms of student numbers, schools achieved the best results, over larger schools.   Contradictory it also found that small schools also achieved the worst results.   The reason for this as explained by Kahneman is that where a data set contains only a small number of items the potential for variability is high.   As such, due to a variety of random variables and possibly a little helping of luck, some small schools do particularly well, out achieving big schools.    Other small schools are not so lucky and the variables don’t fall so well, resulting in the worst results.

To clarify this consider throwing three darts at a dart board aiming for the centre.   This represents the results of a school with a small number of students with higher scores being nearer centre and a lower score being those darts ending further from the centre.   In the case of student results an average result would then be calculated for the school and the same can be done looking at the position of the darts.   Assuming you are not a professional darts player you may do well or you may not do so well due to a variety of random variables.     Given the limited number of darts the potential for variability is high hence a high average or low average is very possible.   Next consider if you were to continue and throw sixty darts at the dart board, taking the average across all the dart throws.    Given the number of darts the average will regress towards your mean darts throwing ability.    The increased number of data items means that variability is reduced as each significant good or poor throw is averaged out among the other throws.

Within schools a great deal of value is being attached to statistical analysis of school data including standardised testing however care must be taken.   As I have suggested above a statistical analysis showing school A is better than school B could easily be the result of random factors such as school size, school resourcing and funding, etc as much as it may be related to better quality teaching and learning, and improved student outcomes.

Another issue if how we respond to the results.  Kahneman suggests that commonly we look for causal factors.   As such we seek to associate the data with a cause which in schools could be a number of different things however our tendency is to focus on that which comes easily to mind.   As such poorer (and better, although not as often,) results are associated most often attributed to teachers and the quality of their teaching as this is what is most frequently on the mind of school leaders.    We arrive at this conclusion often without considering other possible conclusions such as the variable difficulty of the assessments, assessment implementation, the specific cohort concerned, the sample size as discussed earlier and a multitude of other potential factors.   We also, due to arriving so quickly at a causal factor which clearly must be to blame and therefore needs to be rectified, fail to consider the statistical validity of our data.   We fail to consider the margins for error which may exist in our data including what we may consider acceptable margins for error.   We also fail to consider a number of other factors which influence our interpretation of the data including the tendency to focus more on addressing the results which are perceived to be negative.   This constant focus on the negative can result in a blame culture developing which can result in increasing negative results and increasing levels of blame.   Maybe an alternative approach which may work would be to focus more on the marginally positive results and how they were achieved and how they could be built upon.

The key issue in my belief is that we need to take care with data and the conclusions we infer from it.   We cannot abandon the use of data as how else would we measure how we are doing, however equally we cannot take it as fully factual.   The world is a complex place filled with variables, randomness and luck, and we need to examine school data bearing this fact in mind.   We also need to bear in mind that data is a tool to help us deliver the best learning opportunities for students;  data is not an end in itself!