The Rule of Three

Prof. Stephen Senn

11 days ago
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The importance of deciding whether it is necessary to use nitrogen in manures needs no further comment. It was to settle definitely questions like this that John Bennet Lawes began his experiments at Rothamsted in Hertfordshire on the manuring of crops.

T B Wood (1913), The Story of a Loaf of Bread, p4.

The towering trio

Three great heads of statistics at Rothamsted made important contributions to the design and analysis of experiments. Ronald Aylmer Fisher (1890-1962) was at Rothamsted Experimental Station from 1919 to 1933, initially as the sole statistician and then as the head of statistics. When he left to become Galton Professor of Eugenics at University College London he was succeeded as head of statistics by Frank Yates (1902-1994), who had only arrived to work at Rothamsted two years earlier. Yates was to remain the head of statistics for 35 years. When he retired in 1968, his successor was John Nelder (1924-2010), who had previously worked briefly at Rothamsted but who was, at the time of his appointment, head of statistics at The National Vegetable Research Station in Wellesbourne. John Nelder remained head until his retirement in 1984.

All three made considerable contributions to many fields of statistics and Fisher also to genetics and evolutionary biology. Yates worked on sampling theory and computing, Nelder on computing and modelling and Fisher on just about everything. A common interest of all three, however, was the design and analysis of experiments. Together they created what I like to think of as The Rothamsted School of design and analysis of experiments. Of course, they were not the only statisticians who did this. Many others who worked at Rothamsted made important contributions, as did others elsewhere. Nevertheless, the work of these three was crucial and the theory they created has been extremely influential, although not, as I shall explain in due course, as influential as it deserves to be.

Field work

An important context for the development of this theory was that agriculture was the field (a word that always causes one to pause, given the subject) of application. Agricultural scientists were ingenious and ambitious in constructing complex experiments. Typically a field would be subdivided into plots, to which treatments would be applied, but it could be that other treatments were applied at a lower subplot level. Due to spatial autocorrelation in fertility, variation between plots would generally be higher than variation between subplots. Thus, care had to be taken in judging whether the effects of the treatments applied differed from each other by more than could be expected by chance. Discovering exactly how this should be done is something that took half a century, and all the three heads made important contributions.

In 1910 Thomas Barlow Wood (1869-1929), an agricultural scientist, and Frederick John Marrian Stratton (1881-1960), an astronomer, collaborated to write a paper that described how the accuracy of results from an agricultural experiment could be estimated [1]. They showed how a technique that astronomers had long been using to assess the reliability of a mean of a number of differing observations could be applied to agricultural yields also. (They took an example of the percentage of dry matter in 160 roots of a variety of Golden Globe mangold.) They also showed how two treatments could be compared.

The theory of errors was well established amongst astronomers. George Bidell Airy (1801-1892) had written a monograph on the subject [2] in 1862 that had become a standard work of reference. From a modern perspective, it is slightly surprising that Wood and Stratton felt it necessary to explain a common technique amongst astronomers to agronomists but as they put it:

It might seem at first that no two branches of study could be more widely separated than Agriculture and Astronomy. A moment's consideration, however, will show that they have one point in common: both are at the mercy of the weather. (p425)

Furthermore, only two years earlier, Student (William Sealy Gosset, 1976-1937), whose work involved regular contact with problems of agricultural experiments, had published his later-to-become-famous paper  The Probable Error of A Mean [3]. This was in many ways in advance of that of Wood and Stratton. Presumably, they were unaware of Student’s work but we now know that Student himself had been anticipated in 1876 by Jakob Luroth(1844-1910) [4], a German mathematician who was originally an astronomer, so the story of astronomers and agronomists advancing the theory of errors by stumbling past each other has some history.

An interesting connection (it has perhaps a causal explanation and cannot be marked down definitively as a coincidence) is that both Wood and Stratton had connections to Caius College Cambridge, as did Fisher.

Starting in the middle

I am going to pick up the story with the second of these statisticians. Frank Yates studied mathematics at Cambridge, graduating in 1924 and after a brief period teaching at Malvern college worked from 1927-1931 as a surveyor in what is now Ghana [5]. This either honed or provided an outlet for a talent for efficient computation and developing effective algorithms. Surveying required a lot of calculation using least squares and as David Finney put it [6]:

Gaussian least squares was not a topic then taught to undergraduate mathematicians; the need for regularly using this technique undoubtedly developed in him the concern for efficient, well-organised, and accurate computation that characterised his later career. (p2)

Interestingly, Yates never saw the need for matrix algebra and generations of statisticians working at Rothamsted subsequently had to hide their interest in matrices from the head of statistics!

On his arrival at Rothamsted, Yates started collaborating with Fisher, developing, in particular, the work on the design and analysis of experiments; he achieved much rapidly. A good example is given by his Royal Statistical Society(RSS) read paper of 1935, ‘_Complex Experiments_[7]. This presents a dazzling array of ideas with much of what has become standard theory to support them, but is also grounded in application. Many of the ideas come directly from Fisher, some indirectly, but there are also many felicitous and ingenious touches that are clearly due to Yates. In it he covers complex treatment structures, in particular for factorial designs, but also how to deal with different sources of variation in the experimental material, including their influence on efficient estimation and appropriate error estimation, for example for incomplete block designs, a topic he was to develop more fully the following year. [8]

As was usual for a read paper, a number of commentaries were also published. Neyman pointed out that interactive effects in factorial experiments would be estimated with low precision. Yates changed his definition in the published version of the paper from the version read to the RSS and in reply to Neyman added the remark:

Since the meeting, I have altered my definition of an interaction by the inclusion of a factor 1/2, for reasons stated in the text. (p247)

This had the effect of reducing the standard error. However, this response was not quite fair. I once discussed this with Michael Healy, a statistician who also worked at Rothamsted, and he agreed with me that however useful this modification might be algorithmically, it was not an answer to Neyman’s criticism.

Back to the beginning

In his published comment on Yates’s read paper, Fisher drew attention to two aspects of any experiment (in Genstat we now call these the block structure and the treatment structure). He gave an example of a field with plots arranged in five rows and five columns, with each of the 25 plots subdivided into two, giving 50 units and thus 49 degrees of freedom in total. As an example of the second kind, he considered studying two factors: one with five levels and one with two with each combination studied with five replications, making 5 x 2 x 5 = 50 applications and again 49 degrees of freedom. He then stated:

The choice of the experimental design might be regarded as the choice of which items in the first analysis were to correspond to any chosen items in the second, and this could be represented by a two-way analysis of the 49 elements.

In other words, it was the way that the treatment structure mapped onto the block structure that guided the way that the experiment was to be analysed and, of course, the anticipated analysis would guide the way the experiment should be designed.

An example of a modern application of Fisher’s insight is shown in the following image, which gives the Genstat code I used to carry out analysis of variances for three possible treatment models, defined by TREATMENTSTRUCTURE commands, on a cross-over design for which the basic experimental units were defined by the BLOCKSTRUCTURE command.alt text

Use of the ANOVA command without mentioning an outcome variable gives me a so-called dummy analysis, showing how the degrees of freedom should be apportioned but not, of course, giving me a full analysis since no outcome data are used. The example is described in a blog of mine: https://www.linkedin.com/pulse/designed-inferences-stephen-senn/.

Well before Yates’s arrival at Rothamsted, Fisher had realised that these distinctions between block and treatment structure were crucial and that in particular careful attention had to be paid to the former when calculating errors. He had, however, learned by making mistakes. Two years after Fisher’s death, in reviewing his contributions to experimental design, in commenting on an early example dating from 1923 of Fisher analysing a complex experiment, Yates, having first criticised the design, wrote:

To obtain a reasonable estimate of error for these interactions, however, the fact that the varietal plots were split for the potash treatments should have been taken into account. This was not done in the original analysis, a single pooled estimate being used...

But adding:

The need for the partition of error into whole-plot and sub-plot components was recognised by 1925. Part of the data of the above experiment was re-analysed in Statistical Methods for Research Workers in the now conventional form. (P311-312)

Fisher had taught himself fast. [9]

In fact, by the appearance of his classic text Statistical Methods for Research Workers [10], Fisher had developed analysis of variance (indeed, the term variance is due to him), the principles of blocking and replication, and his most controversial innovation, randomisation. An important point about this is still regularly misunderstood. As Fisher put it:

In a well-planned experiment, certain restrictions may be imposed upon the random arrangement of the plots in such a way that the experimental error may still be accurately estimated, while the greater part of the influence of heterogeneity may be eliminated. [11] (p232)

Thus, randomisation was not an alternative to balancing known influences but an adjunct to it.

As Yates put it in summing up what Fisher had achieved:

Apart from factorial design, therefore, all the principles of sound experimental design and analysis were established by 1925. [9] (p312)

On to the end

One day John Nelder was analysing a complex experiment. He was doing so in the tradition of Fisher and Yates. This is what he subsequently had to say about it:

During my first employment at Rothamsted, I was given the job of analyzing some relatively complex structured experiments on trace elements. There were crossed and nested classifications with confounding and all the rest of it, and I could produce analyses of variance for these designs. I then began to wonder how I knew what the proper analyses were and I thought that there must be some general principles that would allow one to deduce the form of the analysis from the structure of the design. The idea went underground for about 10 years. I finally resurrected it and constructed the theory of generally balanced designs, which took in virtually all the work of Fisher and Yates and Finney and put them into a single framework so that any design could be described in terms of two formulas. The first was for the block structure, which was the structure of the experimental units before you inserted the treatments. The second was the treatment structure—the treatments that were put on these units. The specification was completed by the data matrix showing which treatments went on to which unit. [12] (P125)

I have quoted this at length because it leaves me little else to say. John was able to unify the developments of Fisher and Yates and others, (David Finney is mentioned) so that a wide range of experimental designs could be analysed using a single general approach. The results were published in two papers in the Proceedings of the Royal Society [13], [14] in 1965, one of which did, indeed cover block structure and the other treatment structure.

Was that it?

No. Not at all. What Nelder established was that a general algorithm could be used and that hence a computer package could be written to implement it. After his arrival as head of statistics at Rothamsted, he was able to direct the development of Genstat, the software that was designed to implement his theory. However, many others worked on this [15], particularly notable being the contributions of Roger Payne, who continues to develop it to this day. An irony is that whereas one of John Nelder’s other seminal contributions to statistics, Generalised Linear Models, has been taken up by every major statistical package, (as far as I am aware) Genstat is the only one to have implemented the Rothamsted School approach to analysing designed experiments. Thus, when the Genstat user proceeds to analyse such an experiment by first declaring a BLOCKSTRUCTURE and then a TREATMENTSTRUCTURE before proceeding to request an ANOVA they are using software that is still ahead of its time but based on a theory with a century of tradition.

About the author

Professor Stephen Senn has worked as a statistician but also as an academic in various positions in Switzerland, Scotland, England and Luxembourg. From 2011-2018 he was head of the Competence Center for Methodology and Statistics at the Luxembourg Institute of Health. He is the author of Cross-over Trials in Clinical Research (1993, 2002), Statistical Issues in Drug Development (1997, 2007,2021), and Dicing with Death (2003). In 2009 he was awarded the Bradford Hill Medal of the Royal Statistical Society. In 2017 he gave the Fisher Memorial Lecture. He is an honorary life member of PSI and ISCB. 

Stephen Senn: Blogs and Web Papers http://www.senns.uk/Blogs.html

References

1.      Wood TB, Stratton F. The interpretation of experimental results. The Journal of Agricultural Science. 1910;3(4):417-440. 

2.      Airy GB. On the Algebraical and Numerical Theory of Errors of Observations and the Combination of Observations. MacMillan and Co; 1862.

3.      Student. The probable error of a mean. Biometrika. 1908;6:1-25. 

4.      Pfanzagl J, Sheynin O. Studies in the history of probability and statistics .44. A forerunner of the t-distribution. Biometrika. Dec 1996;83(4):891-898. 

5.      Dyke G. Obituary: Frank Yates. Journal of the Royal Statistical Society Series A (Statistics in Society. 1995;158(2):333-338. 

6.      Finney DJ. Remember a pioneer: Frank Yates (1902‐1994). Teaching Statistics. 1998;20(1):2-5. 

7.      Yates F. Complex Experiments (with discussion). Supplement to the Journal of the Royal Statistical Society. 1935;2(2):181-247. 

8.      Yates F. Incomplete randomized blocks. Annals of Eugenics. Sep 1936;7:121-140. 

9.      Yates F. Sir Ronald Fisher and the design of experiments. Biometrics. 1964;20(2):307-321. 

10.    Fisher RA. Statistical Methods for Research Workers. Oliver and Boyd; 1925.

11.    Fisher RA. Statistical Methods for Research Workers. In: Bennett JH, ed. Statistical Methods, Experimental Design and Scientific Inference. Oxford University; 1925.

12.    Senn SJ. A conversation with John Nelder. Research Paper. Statistical Science. 2003;18(1):118-131. 

13.    Nelder JA. The analysis of randomised experiments with orthogonal block structure I. Block structure and the null analysis of variance. Proceedings of the Royal Society of London Series A. 1965;283:147-162. 

14.    Nelder JA. The analysis of randomised experiments with orthogonal block structure II. Treatment structure and the general analysis of variance. Proceedings of the Royal Society of London Series A. 1965;283:163-178. 

15.    Senn S. John Ashworth Nelder. 8 October 1924—7 August 2010. The Royal Society Publishing; 2019.

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The VSNi Team

9 months ago

What is a p-value?

A way to decide whether to reject the null hypothesis (H0) against our alternative hypothesis (H1) is to determine the probability of obtaining a test statistic at least as extreme as the one observed under the assumption that H0 is true. This probability is referred to as the “p-value”. It plays an important role in statistics and is critical in most biological research.

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What is the true meaning of a p-value and how should it be used?

P-values are a continuum (between 0 and 1) that provide a measure of the strength of evidence against H0. For example, a value of 0.066, will indicate that there is a probability that we could observe values as large or larger than our critical value with a probability of 6.6%. Note that this p-value is NOT the probability that our alternative hypothesis is correct, it is only a measure of how likely or unlikely we are to observe these extreme events, under repeated sampling, in reference to our calculated value. Also note that this p-value is obtained based on an assumed distribution (e.g., t-distribution for a t-test); hence, p-value will depend strongly on your (correct or incorrect) assumptions.

The smaller the p-value, the stronger the evidence for rejecting H0. However, it is difficult to determine what a small value really is. This leads to the typical guidelines of: p < 0.001 indicating very strong evidence against H0, p < 0.01 strong evidence, p < 0.05 moderate evidence, p < 0.1 weak evidence or a trend, and p ≥ 0.1 indicating insufficient evidence [1], and a strong debate on what this threshold should be. But declaring p-values as being either significant or non-significant based on an arbitrary cut-off (e.g. 0.05 or 5%) should be avoided. As Ronald Fisher said:

“No scientific worker has a fixed level of significance at which, from year to year, and in all circumstances he rejects hypotheses; he rather gives his mind to each particular case in the light of his evidence and his ideas” [2].

A very important aspect of the p-value is that it does not provide any evidence in support of H0 – it only quantifies evidence against H0. That is, a large p-value does not mean we can accept H0. Take care not to fall into the trap of accepting H0! Similarly, a small p-value tells you that rejecting H0 is plausible, and not that H1 is correct!

For useful conclusions to be drawn from a statistical analysis, p-values should be considered alongside the size of the effect. Confidence intervals are commonly used to describe the size of the effect and the precision of its estimate. Crucially, statistical significance does not necessarily imply practical (or biological) significance. Small p-values can come from a large sample and a small effect, or a small sample and a large effect.

It is also important to understand that the size of a p-value depends critically on the sample size (as this affects the shape of our distribution). Here, with a very very large sample size, H0 may be always rejected even with extremely small differences, even if H0 is nearly (i.e., approximately) true. Conversely, with very small sample size, it may be nearly impossible to reject H0 even if we observed extremely large differences. Hence, p-values need to also be interpreted in relation to the size of the study.

References

[1] Ganesh H. and V. Cave. 2018. P-values, P-values everywhere! New Zealand Veterinary Journal. 66(2): 55-56.

[2] Fisher RA. 1956. Statistical Methods and Scientific Inferences. Oliver and Boyd, Edinburgh, UK.

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The VSNi Team

9 months ago

Evolution of statistical computing

It is widely acknowledged that the most fundamental developments in statistics in the past 60+ years are driven by information technology (IT). We should not underestimate the importance of pen and paper as a form of IT but it is since people start using computers to do statistical analysis that we really changed the role statistics plays in our research as well as normal life.

In this blog we will give a brief historical overview, presenting some of the main general statistics software packages developed from 1957 onwards. Statistical software developed for special purposes will be ignored. We also ignore the most widely used ‘software for statistics’ as Brian Ripley (2002) stated in his famous quote: “Let’s not kid ourselves: the most widely used piece of software for statistics is Excel.” Our focus is some of the packages developed by statisticians for statisticians, which are still evolving to incorporate the latest development of statistics.

Ronald Fisher’s Calculating Machines

Pioneer statisticians like Ronald Fisher started out doing their statistics on pieces of paper and later upgraded to using calculating machines. Fisher bought the first Millionaire calculating machine when he was heading Rothamsted Research’s statistics department in the early 1920s. It cost about £200 at that time, which is equivalent in purchasing power to about £9,141 in 2020. This mechanical calculator could only calculate direct product, but it was very helpful for the statisticians at that time as Fisher mentioned: "Most of my statistics has been learned on the machine." The calculator was heavily used by Fisher’s successor Frank Yates (Head of Department 1933-1968) and contributed to much of Yates’ research, such as designs with confounding between treatment interactions and blocks, or split plots, or quasi-factorials.

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Frank Yates

Rothamsted Annual Report for 1952: "The analytical work has again involved a very considerable computing effort." 

Beginning of the Computer Age

From the early 1950s we entered the computer age. The computer at this time looked little like its modern counterpart, whether it was an Elliott 401 from the UK or an IBM 700/7000 series in the US. Although the first documented statistical package, BMDP, was developed starting in 1957 for IBM mainframes at the UCLA Health Computing Facility, on the other side of the Atlantic Ocean statisticians at Rothamsted Research began their endeavours to program on an Elliot 401 in 1954.

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Programming Statistical Software

When we teach statistics in schools or universities, students very often complain about the difficulties of programming. Looking back at programming in the 1950s will give modern students an appreciation of how easy programming today actually is!

An Elliott 401 served one user at a time and requested all input on paper tape (forget your keyboard and intelligent IDE editor). It provided the output to an electric typewriter. All programming had to be in machine code with the instructions and data on a rotating disk with 32-bit word length, 5 "words" of fast-access store, 7 intermediate access tracks of 128 words, 16 further tracks selectable one at a time (= 2949 words – 128 for system).

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Computer paper tape

fitting constants to main effects and interactions in multi-way tables (1957), regression and multiple regression (1956), fitting many standard curves as well as multivariate analysis for latent roots and vectors (1955).

Although it sounds very promising with the emerging of statistical programs for research, routine statistical analyses were also performed and these still represented a big challenge, at least computationally. For example, in 1963, which was the last year with the Elliott 401 and Elliott 402 computers, Rothamsted Research statisticians analysed 14,357 data variables, and this took them 4,731 hours to complete the job. It is hard to imagine the energy consumption as well as the amount of paper tape used for programming. Probably the paper tape (all glued together) would be long enough to circle the equator.

Development of Statistical Software: Genstat, SAS, SPSS

The above collection of programs was mainly used for agricultural research at Rothamsted and was not given an umbrella name until John Nelder became Head of the Statistics Department in 1968. The development of Genstat (General Statistics) started from that year and the programming was done in FORTRAN, initially on an IBM machine. In that same year, at North Carolina State University, SAS (Statistical Analysis Software) was almost simultaneously developed by computational statisticians, also for analysing agricultural data to improve crop yields. At around the same time, social scientists at the University of Chicago started to develop SPSS (Statistical Package for the Social Sciences). Although the three packages (Genstat, SAS and SPSS) were developed for different purposes and their functions diverged somewhat later, the basic functions covered similar statistical methodologies.

The first version of SPSS was released in 1968. In 1970, the first version of Genstat was released with the functions of ANOVA, regression, principal components and principal coordinate analysis, single-linkage cluster analysis and general calculations on vectors, matrices and tables. The first version of SAS, SAS 71, was released and named after the year of its release. The early versions of all three software packages were written in FORTRAN and designed for mainframe computers.

Since the 1980s, with the breakthrough of personal computers, a second generation of statistical software began to emerge. There was an MS-DOS version of Genstat (Genstat 4.03) released with an interactive command line interface in 1980.

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Genstat 4.03 for MSDOS

Around 1985, SAS and SPSS also released a version for personal computers. In the 1980s more players entered this market: STATA was developed from 1985 and JMP was developed from 1989. JMP was, from the very beginning, for Macintosh computers. As a consequence, JMP had a strong focus on visualization as well as graphics from its inception.

The Rise of the Statistical Language R

The development of the third generation of statistical computing systems had started before the emergence of software like Genstat 4.03e or SAS 6.01. This development was led by John Chambers and his group in Bell Laboratories since the 1970s. The outcome of their work is the S language. It had been developed into a general purpose language with implementations for classical as well as modern statistical inferences. S language was freely available, and its audience was mainly sophisticated academic users. After the acquisition of S language by the Insightful Corporation and rebranding as S-PLUS, this leading third generation statistical software package was widely used in both theoretical and practical statistics in the 1990s, especially before the release of a stable beta version of the free and open-source software R in the year 2000. R was developed by Ross Ihaka and Robert Gentleman at the University of Auckland, New Zealand, and is currently widely used by statisticians in academia and industry, together with statistical software developers, data miners and data analysts.

Software like Genstat, SAS, SPSS and many other packages had to deal with the challenge from R. Each of these long-standing software packages developed an R interface R or even R interpreters to anticipate the change of user behaviour and ever-increasing adoption of the R computing environment. For example, SAS and SPSS have some R plug-ins to talk to each other. VSNi’s ASReml-R software was developed for ASReml users who want to run mixed model analysis within the R environment, and at the present time there are more ASReml-R users than ASReml standalone users. Users who need reliable and robust mixed effects model fitting adopted ASReml-R as an alternative to other mixed model R packages due to its superior performance and simplified syntax. For Genstat users, msanova was also developed as an R package to provide traditional ANOVA users an R interface to run their analysis.

What’s Next?

We have no clear idea about what will represent the fourth generation of statistical software. R, as an open-source software and a platform for prototyping and teaching has the potential to help this change in statistical innovation. An example is the R Shiny package, where web applications can be easily developed to provide statistical computing as online services. But all open-source and commercial software has to face the same challenges of providing fast, reliable and robust statistical analyses that allow for reproducibility of research and, most importantly, use sound and correct statistical inference and theory, something that Ronald Fisher will have expected from his computing machine!

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Dr. John Rogers

10 months ago

50 years of bioscience statistics

Earlier this year I had an enquiry from Carey Langley of VSNi as to why I had not renewed my Genstat licence. The truth was simple – I have decided to fully retire after 50 years as an agricultural entomologist / applied biologist / consultant. This prompted some reflections about the evolution of bioscience data analysis that I have experienced over that half century, a period during which most of my focus was the interaction between insects and their plant hosts; both how insect feeding impacts on plant growth and crop yield, and how plants impact on the development of the insects that feed on them and on their natural enemies.

Where it began – paper and post

My journey into bioscience data analysis started with undergraduate courses in biometry – yes, it was an agriculture faculty, so it was biometry not statistics. We started doing statistical analyses using full keyboard Monroe calculators (for those of you who don’t know what I am talking about, you can find them here).  It was a simpler time and as undergraduates we thought it was hugely funny to divide 1 by 0 until the blue smoke came out…

After leaving university in the early 1970s, I started working for the Agriculture Department of an Australian state government, at a small country research station. Statistical analysis was rudimentary to say the least. If you were motivated, there was always the option of running analyses yourself by hand, given the appearance of the first scientific calculators in the early 1970s. If you wanted a formal statistical analysis of your data, you would mail off a paper copy of the raw data to Biometry Branch… and wait.  Some months later, you would get back your ANOVA, regression, or whatever the biometrician thought appropriate to do, on paper with some indication of what treatments were different from what other treatments.  Dose-mortality data was dealt with by manually plotting data onto probit paper. 

Enter the mainframe

In-house ANOVA programs running on central mainframes were a step forward some years later as it at least enabled us to run our own analyses, as long as you wanted to do an ANOVA…. However, it also required a 2 hours’ drive to the nearest card reader, with the actual computer a further 1000 kilometres away.… The first desktop computer I used for statistical analysis was in the early 1980s and was a CP/M machine with two 8-inch floppy discs with, I think, 256k of memory, and booting it required turning a key and pressing the blue button - yes, really! And about the same time, the local agricultural economist drove us crazy extolling the virtues of a program called Lotus 1-2-3!

Having been brought up on a solid diet of the classic texts such as Steele and Torrie, Cochran and Cox and Sokal and Rohlf, the primary frustration during this period was not having ready access to the statistical analyses you knew were appropriate for your data. Typical modes of operating for agricultural scientists in that era were randomised blocks of various degrees of complexity, thus the emphasis on ANOVA in the software that was available in-house. Those of us who also had less-structured ecological data were less well catered for.

My first access to a comprehensive statistics package was during the early to mid-1980s at one of the American Land Grant universities. It was a revelation to be able to run virtually whatever statistical test deemed necessary. Access to non-linear regression was a definite plus, given the non-linear nature of many biological responses. As well, being able to run a series of models to test specific hypotheses opened up new options for more elegant and insightful analyses. Looking back from 2021, such things look very trivial, but compared to where we came from in the 1970s, they were significant steps forward.

Enter Genstat

My first exposure to Genstat, VSNi’s stalwart statistical software package, was Genstat for Windows, Third Edition (1997). Simple things like the availability of residual plots made a difference for us entomologists, given that much of our data had non-normal errors; it took the guesswork out of whether and what transformations to use. The availability of regressions with grouped data also opened some previously closed doors. 

After a deviation away from hands-on research, I came back to biological-data analysis in the mid-2000s and found myself working with repeated-measures and survival / mortality data, so ventured into repeated-measures restricted maximum likelihood analyses and generalised linear mixed models for the first time (with assistance from a couple of Roger Payne’s training courses in Hobart and Queenstown). Looking back, it is interesting how quickly I became blasé about such computationally intensive analyses that would run in seconds on my laptop or desktop, forgetting that I was doing ANOVAs by hand 40 years earlier when John Nelder was developing generalised linear models. How the world has changed!

Partnership and support

Of importance to my Genstat experience was the level of support that was available to me as a Genstat licensee. Over the last 15 years or so, as I attempted some of these more complex analyses, my aspirations were somewhat ahead of my abilities, and it was always reassuring to know that Genstat Support was only ever an email away. A couple of examples will flesh this out. 

Back in 2008, I was working on the relationship between insect-pest density and crop yield using R2LINES, but had extra linear X’s related to plant vigour in addition to the measure of pest infestation. A support-enquiry email produced an overnight response from Roger Payne that basically said, “Try this”. While I slept, Roger had written an extension to R2LINES to incorporate extra linear X’s. This was later incorporated into the regular releases of Genstat. This work led to the clearer specification of the pest densities that warranted chemical control in soybeans and dry beans (https://doi.org/10.1016/j.cropro.2009.08.016 and https://doi.org/10.1016/j.cropro.2009.08.015).

More recently, I was attempting to disentangle the effects on caterpillar mortality of the two Cry insecticidal proteins in transgenic cotton and, while I got close, I would not have got the analysis to run properly without Roger’s support. The data was scant in the bottom half of the overall dose-response curves for both Cry proteins, but it was possible to fit asymptotic exponentials that modelled the upper half of each curve. The final double-exponential response surface I fitted with Roger’s assistance showed clearly that the dose-mortality response was stronger for one of the Cry proteins than the other, and that there was no synergistic action between the two proteins (https://doi.org/10.1016/j.cropro.2015.10.013

The value of a comprehensive statistics package

One thing that I especially appreciate about having access to a comprehensive statistics package such as Genstat is having the capacity to tease apart biological data to get at the underlying relationships. About 10 years ago, I was asked to look at some data on the impact of cold stress on the expression of the Cry2Ab insecticidal protein in transgenic cotton. The data set was seemingly simple - two years of pot-trial data where groups of pots were either left out overnight or protected from low overnight temperatures by being moved into a glasshouse, plus temperature data and Cry2Ab protein levels. A REML analysis, and some correlations and regressions enabled me to show that cold overnight temperatures did reduce Cry2Ab protein levels, that the effects occurred for up to 6 days after the cold period and that the threshold for these effects was approximately 14 Cº (https://doi.org/10.1603/EC09369). What I took from this piece of work is how powerful a comprehensive statistics package can be in teasing apart important biological insights from what was seemingly very simple data. Note that I did not use any statistics that were cutting edge, just a combination of REML, correlation and regression analyses, but used these techniques to guide the dissection of the relationships in the data to end up with an elegant and insightful outcome.

Final reflections

Looking back over 50 years of work, one thing stands out for me: the huge advances that have occurred in the statistical analysis of biological data has allowed much more insightful statistical analyses that has, in turn, allowed biological scientists to more elegantly pull apart the interactions between insects and their plant hosts. 

For me, Genstat has played a pivotal role in that process. I shall miss it.

Dr John Rogers

Research Connections and Consulting

St Lucia, Queensland 4067, Australia

Phone/Fax: +61 (0)7 3720 9065

Mobile: 0409 200 701

Email: john.rogers@rcac.net.au

Alternate email: D.John.Rogers@gmail.com

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