0.2 - The Dalton Multipurpose Statistic

0.2 – The 'Dalton Multipurpose statistic'

By Dr Clive Dalton

Cranking handles in the 1950s

As a student in the 1950s, we did statistics labs on small Brunsviga hand-cranked calculators with tiny levers pulled down to select the numbers wanted. You cranked the handle clockwise until a bell rang (I think when dividing), and then cranked it anticlockwise for a reason I’ve forgotten.

In a class of 20, you could not tell when your bell had rung!

Then for my PhD at Bangor University, the Agriculture Department had one electric Facit machine shared among students and staff. Inside it was a mass of robust little German cogs that whizzed around when you pressed the keys. We thought it was magic, and I pounded it for three years without problems. When I finished, there were rumours that the University was about to get a ‘computer’ to take up the entire space of an old chapel.

The computer age -1960s

In my early lecturing days at Leeds University, the Facit and American Marchant machines (see the interior of a Marchant XL at left) with a massive bank of keys ruled supreme, and were hammered by students for their projects and higher degrees.

A computer had arrived at Leeds and filled a retired church hall, and some of us started to learn to program in a mystery language called Algol, and then punch tape to get simple exercises done that took as long (if you added our errors) as using a calculator.

But our kids loved the reels of error-ridden punched tape that I took home after my failed forays into computing.

What did the end value mean?

The point was, that by the time you got to the end of a calculation, and you hadn’t botched things up a few times on the way, so had to start all over again, you were far too exhausted to think much about what the final values meant. Did they make any sense? Were they of any practical use?

Statistical magicians

When I went into full time research in New Zealand, I started to have suspicions about statistics because we had very bright professional statisticians to give advice at all stages of projects – in my case animal breeding trials. This was both interesting and frustrating.

When the statistician had ‘run your data’, and the miles of ‘line flow’ paper spewed out of the research station computer (that filled a whole room), you needed to go into a scientific trance to work out how to get ‘the results you wanted’ – so the imagined published paper would blow the scientific community away and you would be for ever famous! It was here the statisticians came into their own.

What you wanted?

It was wonderful if the results (explained by the statistician) confirmed your preconceived expectations (which you were not supposed to have), or if you were positively surprised with them. In other words you didn’t expect those results but you would have not trouble getting them published.

What was really bad news was when you were negatively surprised, as when the results went the opposite way to what you wanted and you couldn’t explain why – and would be lucky if any journal would publish the results.

The real pits were when after years of work, you got no result at all, and there was no way you could claim this as a ‘positive surprise’ that was publishable.

Hazards of long-term trials

In long-term trials, we could easily have the services of two or three statisticians as they came and went to further their careers. This could be really nasty as a newly-qualified statistician fresh from University with all A++ papers, would look at the analysis and ask why his predecessor hadn’t used the new XYZ package? It was inevitable that the new chum recommended the whole years of data be reanalyzed –his way.

The other statistician’s comment to bring on a sweat was ‘oh that’s interesting, I wonder what would happen if we put the data through the new ZYX package? I’ll give it a go’.

As the years went on, I found it hard not to scream – ‘for hell’s sake, just leave things alone’, as what came out of these packages became more and more unintelligible, and harder for us oldies to work out what it meant in practical terms. Statistical significance at different levels of probability to prove the null hypothesis was one thing, but making farming sense was very much another.

The trick was to feign knowledge of what all the statistical analysis meant. At times the blank pages in the line-flow printout were the most useful part of the output - for the kids to draw on!

Delays, delays

You knew that extra analysis meant delays in publication of a paper by at least another 12 months and sometimes more. They also meant more questions from editorial committees, whose job you very soon realised were a pack of nitpickers and/or jealous colleagues hell bent on stopping you publishing and having more published papers than they had. In a world of ‘publish or perish’, these antics didn’t help your next application for advancement with the research director.

0.2

So it was in this environment that I realised the value of 0.2 and claimed it as my own ‘Dalton Multipurpose Statistic’. This simple little value has four massive advantages, that I strongly recommend to you:

1. It is extremely versatile.
2. It is non-confrontational.
3. It can be grossly misinterpreted without causing serious harm.
4. It can bring relief and satisfaction to the needy.
   

Correlation coefficients

These are values that tell you how much one thing is related to another, and their interpretation is more abused that anything else on the planet.

• If you need a low correlation coefficient, then 0.2 can be called “low” and will support your case.
• If you need a “low and non significant” correlation to suit a case, then all you need are the numbers of observations (n) below about 60.
• Getting rid of observations is not difficult as there are plenty of reasons to classify values as ‘aberrant’. Animals die, they get pregnant before they should, they give birth before they should, they change sex half way through trials, and so on.
• If on the other hand you have a desperate need for things to be statistically significance at say r = 0.2, then increase the number of observations to over 100, and significance will be easily reached at 5% probability (P<0.05) which is respectable.
• The fact that it is “statistically significant” carries the day, rather than its probability, and not the fact that its practical implications may be total nonsense.
• Squaring a correlation coefficient (r²) should be avoided, as this can so often show how meaningless a correlation coefficient can be.
  

Repeatability and heritability estimates

Repeatability measures how things keep appearing and heritability is how strongly traits are inherited.

• If you need a ‘low’ estimate of either estimate, then 0.2 can be called low.
• This would be, for example, to show breeders that they were wasting their time in selecting for what they thought were important traits. In this case 0.2 could also be called ‘very low’.
• If however you needed it to support your own research, or a new trait that you wanted to claim a reputation from such as:
  

(Muzzle width/teat length) x √heart girth

then a repeatability and heritability of 0.2 could be squeezed from a ‘low’ into the ‘medium’ classification.

• Once it is into the “medium” group – then it can be squeezed into the “medium-high” group.
• Thus ‘low’ could be 0-0.19; ‘medium’ would be 0.20-0.40.
  
• Now 0.4 is really getting ‘high’, so 0.20-0.40 must be in a ‘medium-high’ group. You have created a winner - if that’s what you wanted.
  

Genetic and phenotypic correlations between traits

Again, these are values that tell you how much one thing is related to another. The genetic ones are about what’s inside the animal and the phenotypic ones are things you can see on the outside of the animal.

• Again 0.2 is very valuable.
• If you need a value to support a case, especially if you don’t know or can’t remember the actual value, or if you don't have one and need one, adopt the following rule:
• If you feel unsure or your job or reputation could be under threat, then use 0.19-0.20.
• If you feel confident, then really go for it and use 0.20-0.21
  

General percentages

• Whenever you need a percentage, 20% can be used with enormous confidence.
• If for example you need to show that a major fact is of minor importance, (e.g. the number of geneticists who have not written up their lifetime work), then 20% can be interpreted as small. This will take the heat out of the discussion.
  
• However, if you need to generate some heat, (e.g. to highlight the percentage of geneticists who are homosexuals or atheists, or both), then you can make 20% sound deliciously high!
• The 20% statistic is of course, the core of the 80:20 rule, which has certainly stood the test of time. You can use this rule for anything that comes to mind where you need to prove that 80% of something is caused by 20% of something else.
• Some visionary must have carefully researched this rule, who could see that the 20% part of the ratio was the clincher and would never be questioned, Have you ever met anyone who questioned it?
• If you do meet anyone doubters, simply drop it to 18-20%. If you feel cocky, raise it to 20-25%. But don’t every push it up to 20-30% as the ice gets too thin.
  

General Correction Factors

These are things that are used to get people to believe that mountainous playing fields can been made level by a bit of mathematical manipulation. A better name for them would be ‘Fudge Factors’. Geneticists need them all the time - described below.

• The effects on an animal of both Genetics (G) and the Environment (E) is the big worry.
• E can make a real fool of all your pontifications about G, as there are so many variables involved in the environment.
• But we love these variables, as it can so often save our bacon, especially in arguments with farmers where we use the trick of telling them what they know already, and that the problem is complex. By using the word ‘multifactorial’ – you can sound as if you know what you are talking about!
• You always need to find a plausible reason (excuse) why your years of work and money spent have resulted in a lemon.
• We also have to deal with what is called the ‘G x E interaction’ which is great fun where some animals do well in one environment but not in others. It adds delicious complexity to the situation – which only a host of fudge factors can help disguise.
• So here again, good old 0.2 is comes to the rescue and is perfect for the job.
  

Standard errors and standard deviations

These are tricky things to explain. You use a standard error (SE) to describe how accurate a mean is because of variation around it, and a standard deviation (SD) to describe the variation in a range of data. This is what they used to be anyway!

• 0.2 suits most needs and can be used freely if you do not have one of these statistics, or you forget to work one out, or especially if you don’t really understand what they are.
• Such is the case of a “residual standard error” which few ever knew that they were - 0.2 is ideal.
  
• The ± symbol which appears before these values fools most folk, as they are not sure what it is so move on searching for a heading that says ‘summary’ or ‘conclusions’ or both.
• Have no fear that 0.2 will get you through most editorial committees, that because of their age will ignore statistics because they won’t understand them.
• And the real coup is that they won’t dare to admit it, and stoop to ask some young smart whipper-snapper what it all means. The young always had learned from the old, and never vice versa.
• These old codgers could concentrate on checking if the author had written “data is” instead of “data are”, and if their name was in the list of references.
  

Missing values in a matrix

A matrix is a mass of little squares (cells) with figures in them all joined together in a big table with headings along the top and down the side.

• You need a matrix to show the relationships (correlations) between a host of things, and in all their possible combinations.
• You can’t have empty cells as it looks bad.
  
• It also risks putting a stop to your entire work, as some greater being will declare that things will have to wait, ‘until more data become available’. This is the kiss of death.
• All the meetings you have been attending for the last 18 months or more (expenses paid plus fudge factors) to finish the project will end.
• Never fear though as here again 0.2 can come to the rescue, simply because it can be used with confidence and without causing serious problems – at least problems where you could be blamed for.
• The reason why you don’t need to worry is that there are so many errors and generalities in a matrix that a dusting of 0.2s in empty cells won’t cause any serious damage to the outcome.
• But don’t put 0.2 in every empty cell. Break it up a bit by putting 0.19 in some and 0.21 in others. It’s not prudent go outside this range.
  

Acknowledgements

I have to thank many colleagues over the years, some of whom were distinguished geneticists and statisticians, for stimulating my thoughts in smoke-filled rooms, confirming my fears and excitement about 0.2.

The punched tape the kids loved.

They could throw the role and it would unwind for miles.

The boxes were very useful too.

I owe special thanks to Chris Dyson, Biometrician at the Ruakura Agricultural Research Centre when I worked there in 1980. Chris bristled with Yorkshire wisdom and common sense, and drew my attention to the fact that if you ever needed ‘a number’ - for anything , then 153 was the one to go for.

Chris pointed out that if you take the reciprocal of the natural logarithm of 153, this comes out as 0.199, which rounds up to 0.2. So there’s the magic 0.2 coming to the surface again for air and respect. It’s magic. QED!

Thanks also for comments by Dr Harold Henderson, veteran statistician at Ruakura whose statistical skills were only eclipsed by his patience with non-mathematical scientists like me.

I must also credit a wonderful website where images and information about old calculators abounds - http://www.oldcomputers.arcula.co.uk/calc1.htm#marchant_xl