Roger J Barlow - Collected Quotes

"Averaging results, whether weighted or not, needs to be done with due caution and commonsense. Even though a measurement has a small quoted error it can still be, not to put too fine a point on it, wrong. If two results are in blatant and obvious disagreement, any average is meaningless and there is no point in performing it. Other cases may be less outrageous, and it may not be clear whether the difference is due to incompatibility or just unlucky chance." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"In everyday life, 'estimation' means a rough and imprecise procedure leading to a rough and imprecise result. You 'estimate' when you cannot measure exactly. In statistics, on the other hand, 'estimation' is a technical term. It means a precise and accurate procedure, leading to a result which may be imprecise, but where at least the extent of the imprecision is known. It has nothing to do with approximation. You have some data, from which you want to draw conclusions and produce a 'best' value for some particular numerical quantity (or perhaps for several quantities), and you probably also want to know how reliable this value is, i.e. what the error is on your estimate." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"Least squares' means just what it says: you minimise the (suitably weighted) squared difference between a set of measurements and their predicted values. This is done by varying the parameters you want to estimate: the predicted values are adjusted so as to be close to the measurements; squaring the differences means that greater importance is placed on removing the large deviations." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"Probabilities are pure numbers. Probability densities, on the other hand, have dimensions, the inverse of those of the variable x to which they apply." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"Science is supposed to explain to us what is actually happening, and indeed what will happen, in the world. Unfortunately as soon as you try and do something useful with it, sordid arithmetical numbers start getting in the way and messing up the basic scientific laws." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"Statistics is a tool. In experimental science you plan and carry out experiments, and then analyse and interpret the results. To do this you use statistical arguments and calculations. Like any other tool - an oscilloscope, for example, or a spectrometer, or even a humble spanner - you can use it delicately or clumsily, skillfully or ineptly. The more you know about it and understand how it works, the better you will be able to use it and the more useful it will be." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"Subjective probability, also known as Bayesian statistics, pushes Bayes' theorem further by applying it to statements of the type described as 'unscientific' in the frequency definition. The probability of a theory (e.g. that it will rain tomorrow or that parity is not violated) is considered to be a subjective 'degree of belief - it can perhaps be measured by seeing what odds the person concerned will offer as a bet. Subsequent experimental evidence then modifies the initial degree of belief, making it stronger or weaker according to whether the results agree or disagree with the predictions of the theory in question." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"The principle of maximum likelihood is not a rule that requires justification - it does not need to be proved. It is merely a sensible way of producing an estimator. But although the name 'maximum likelihood' has a nice ring to it - it suggest that your estimate is the 'most likely' value - this is an unfair interpretation; it is the estimate that makes your data most likely - another thing altogether." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"There is a technical difference between a bar chart and a histogram in that the number represented is proportional to the length of bar in the former and the area in the latter. This matters if non-uniform binning is used. Bar charts can be used for qualitative or quantitative data, whereas histograms can only be used for quantitative data, as no meaning can be attached to the width of the bins if the data are qualitative." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989) 

"There is an obvious parallel between an expectation value and the mean of a data sample. The former is a sum over a theoretical probability distribution and the latter is a (similar) sum over a real data sample. The law of large numbers ensures that if a data sample is described by a theoretical distribution, then as N, the size of the data sample, goes to infinity […]." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"When you want to use some data to give the answer to a question, the first step is to formulate the question precisely by expressing it as a hypothesis. Then you consider the consequences of that hypothesis, and choose a suitable test to apply to the data. From the result of the test you accept or reject the hypothesis according to prearranged criteria. This cannot be infallible, and there is always a chance of getting the wrong answer, so you try and reduce the chance of such a mistake to a level which you consider reasonable." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)