## Some human biases in conditional reasoning

Tracking down coding mistakes is a common developer activity (for which training is rarely provided).

Debugging code involves reasoning about differences between the actual and expected output produced by particular program input. The goal is to figure out the coding mistake, or at least narrow down the portion of code likely to contain the mistake.

Interest in human reasoning dates back to at least ancient Greece, e.g., Aristotle and his syllogisms. The study of the psychology of reasoning is very recent; the field was essentially kick-started in 1966 by the surprising results of the Wason selection task.

Debugging involves a form of deductive reasoning known as conditional reasoning. The simplest form of conditional reasoning involves an input that can take one of two states, along with an output that can take one of two states. Using coding notation, this might be written as:

if (p) then q       if (p) then !q
if (!p) then q      if (!p) then !q

The notation used by the researchers who run these studies is a 2×2 contingency table (or conditional matrix):

OUTPUT
1    0

1   A    B
INPUT
0   C    D

where: A, B, C, and D are the number of occurrences of each case; in code notation, p is the input and q the output.

The fertilizer-plant problem is an example of the kind of scenario subjects answer questions about in studies. Subjects are told that a horticultural laboratory is testing the effectiveness of 31 fertilizers on the flowering of plants; they are told the number of plants that flowered when given fertilizer (A), the number that did not flower when given fertilizer (B), the number that flowered when not given fertilizer (C), and the number that did not flower when not given any fertilizer (D). They are then asked to evaluate the effectiveness of the fertilizer on plant flowering. After the experiment, subjects are asked about any strategies they used to make judgments.

Needless to say, subjects do not make use of the available information in a way that researchers consider to be optimal, e.g., Allan’s index (sorry about the double, , rather than single, vertical lines).

What do we know after 40+ years of active research into this basic form of conditional reasoning?

The results consistently find, for this and other problems, that the information A is given more weight than B, which is given by weight than C, which is given more weight than D.

That information provided by A and B is given more weight than C and D is an example of a positive test strategy, a well-known human characteristic.

Various models have been proposed to ‘explain’ the relative ordering of information weighting: , e.g., that subjects have a bias towards sufficiency information compared to necessary information.

Subjects do not always analyse separate contingency tables in isolation. The term blocking is given to the situation where the predictive strength of one input is influenced by the predictive strength of another input (this process is sometimes known as the cue competition effect). Debugging is an evolutionary process, often involving multiple test inputs. I’m sure readers will be familiar with the situation where the output behavior from one input motivates a misinterpretation of the behaviour produced by a different input.

The use of logical inference is a commonly used approach to the debugging process (my suggestions that a statistical approach may at times be more effective tend to attract odd looks). Early studies of contingency reasoning were dominated by statistical models, with inferential models appearing later.

Debugging also involves causal reasoning, i.e., searching for the coding mistake that is causing the current output to be different from that expected. False beliefs about causal relationships can be a huge waste of developer time, and research on the illusion of causality investigates, among other things, how human interpretation of the information contained in contingency tables can be ‘de-biased’.

The apparently simple problem of human conditional reasoning over two variables, each having two states, has proven to be a surprisingly difficult to model. It is tempting to think that the performance of professional software developers would be closer to the ideal, compared to the typical experimental subject (e.g., psychology undergraduates or Mturk workers), but I’m not sure whether I would put money on it.

## A study of deceit when reporting information in a known context

A variety of conflicting factors intrude when attempting to form an impartial estimate of the resources needed to perform a task. The customer/manager, asking for the estimate wants to hear a low value, creating business/social pressure to underestimate; overestimating increases the likelihood of completing the task within budget.

A study by Oey, Schachner and Vul investigated the strategic reasoning for deception/lying in a two-person game.

A game involved a Sender and Receiver, with the two players alternating between the roles. The game started with both subjects seeing a picture of a box containing red and blue marbles (the percentage of red marbles was either 20%, 50%, or 80%). Ten marbles were randomly selected from this ‘box’, and shown to the Sender. The Sender was asked to report to the Receiver the number of red marbles appearing in the random selection, (there was an incentive to report higher/lower, and punishment for being caught being inaccurate). The Receiver could accept or reject the number of red balls reported by the Sender. In the actual experiment, unknown to the human subjects, one of every game’s subject pair was always played by a computer. Every subject played 100 games.

In the inflate condition: If the Receiver accepted the report, the Sender gained points, and the Receiver gained points.

If the Receiver rejected the report, then:

• if the Sender’s report was accurate (i.e., == ), the Sender gained points, and the Receiver gained points (i.e., a -5 point penalty),
• if the Sender’s report was not accurate, the Receiver gained 5 points, and the Sender lost 5 points.

In the deflate condition: The points awarded to the Sender was based on the number of blue balls in the sample, and the points awarded to the Received was based on the number of red balls in the sample (i.e., the Sender had in incentive to report fewer red balls).

The plot below shows the mean rate of deceit (i.e., the fraction of a subject’s reports where , averaged over all 116 subject’s mean) for a given number of red marbles actually seen by the Sender; vertical lines show one standard deviation, calculated over the mean of all subjects (code+data):

Subjects have some idea of the percentage of red/blue balls, and are aware that their opponent has a similar idea.

The wide variation in the fraction of reports where a subject reported a value greater than the number of marbles seen, is likely caused by variation in subject level of risk aversion. Some subjects may have decided to reduce effort by always accurately reporting, while others may have tried to see how much they could get away with.

The wide variation is particularly noticeable in the case of a box containing 80% red. If a Sender’s random selection contains few reds, then the Sender can feel confident reporting to have seen more.

The general pattern shows subjects being more willing to increase the reported number when they are supplied with few.

There is a distinct change of behavior when half of the sample contains more than five red marbles. In this situation, subjects may be happy to have been dealt a good hand, and are less inclined to risk losing 5-points for less gain.

Estimating involves considering more factors than the actual resources likely to be needed to implement the task; the use of round numbers is one example. This study is one of few experimental investigations of numeric related deception. The use of students having unknown motivation is far from ideal, but they are better than nothing.

When estimating in a team context, there is an opportunity to learn about the expectations of others and the consequences of over/under estimating. An issue for another study

## Clustering source code within functions

The question of how best to cluster source code into functions is a perennial debate that has been ongoing since functions were first created.

Beginner programmers are told that clustering code into functions is good, for a variety of reasons (none of the claims are backed up by experimental evidence). Structuring code based on clustering the implementation of a single feature is a common recommendation; this rationale can be applied at both the function/method and file/class level.

The idea of an optimal function length (measured in statements) continues to appeal to developers/researchers, but lacks supporting evidence (despite a cottage industry of research papers). The observation that most reported fault appear in short functions is a consequence of most of a program’s code appearing in short functions.

I have had to deal with code that has not been clustered into functions. When microcomputers took off, some businessmen taught themselves to code, wrote software for their line of work and started selling it. If the software was a success, more functionality was needed, and the businessman (never encountered a woman doing this) struggled to keep on top of things. A common theme was a few thousand lines of unstructured code in one function in a single file

Adding structural bureaucracy (e.g., functions and multiple files) reduced the effort needed to maintain and enhance the code.

The problem with ‘born flat’ source is that the code for unrelated functionality is often intermixed, and global variables are freely used to communicate state. I have seen the same problems in structured function code, but instances are nowhere near as pervasive.

When implementing the same program, do different developers create functions implementing essentially the same functionality?

I am aware of two datasets relating to this question: 1) when implementing the same small specification (average length program 46.3 lines), a surprising number of variants (6,301) are created, 2) an experiment that asked developers to reintroduce functions into ‘flattened’ code.

The experiment (Alexey Braver’s MSc thesis) took an existing Python program, ‘flattened’ it by inlining functions (parameters were replaced by the corresponding call arguments), and asked subjects to “… partition it into functions in order to achieve what you consider to be a good design.”

The 23 rows in the plot below show the start/end (green/brown delimited by blue lines) of each function created by the 23 subjects; red shows code not within a function, and right axis is percentage of each subjects’ code contained in functions. Blue line shows original (currently plotted incorrectly; patched original code+data):

There are many possible reasons for the high level of agreement between subjects, including: 1) the particular example chosen, 2) the code was already well-structured, 3) subjects were explicitly asked to create functions, 4) the iterative process of discovering code that needs to be written did not occur, 5) no incentive to leave existing working code as-is.

Given that most source has a short and lonely existence, is too much time being spent bike-shedding function contents?

Given how often lower level design time happens at code implementation time, perhaps discussion of function contents ought to be viewed as more about thinking how things fit together and interact, than about each function in isolation.

Analyzing each function in isolation can create perverse incentives.

## Shopper estimates of the total value of items in their basket

Agile development processes break down the work that needs to be done into a collection of tasks (which may be called stories or some other name). A task, whose implementation time may be measured in hours or a few days, is itself composed of a collection of subtasks (which may in turn be composed of subsubtasks, and so on down).

When asked to estimate the time needed to implement a task, a developer may settle on a value by adding up estimates of the effort needed to implement the subtasks thought to be involved. If this process is performed in the mind of the developer (i.e., not by writing down a list of subtask estimates), the accuracy of the result may be affected by the characteristics of cognitive arithmetic.

Humans have two cognitive systems for processing quantities, the approximate number system (which has been found to be present in the brain of many creatures), and language. Researchers studying the approximate number system often ask subjects to estimate the number of dots in an image; I recently discovered studies of number processing that used language.

In a study by Benjamin Scheibehenne, 966 shoppers at the checkout counter in a grocery shop were asked to estimate the total value of the items in their shopping basket; a subset of 421 subjects were also asked to estimate the number of items in their basket (this subset were also asked if they used a shopping list). The actual price and number of items was obtained after checkout.

There are broad similarities between shopping basket estimation and estimating task implementation time, e.g., approximate idea of number of items and their cost. Does an analysis of the shopping data suggest ideas for patterns that might be present in software task estimate data?

The left plot below shows shopper estimated total item value against actual, with fitted regression line (red) and estimate==actual (grey); the right plot shows shopper estimated number of items in their basket against actual, with fitted regression line (red) and estimate==actual (grey) (code+data):

The model fitted to estimated total item value is: , which differs from software task estimates/actuals in always underestimating over the range measured; the exponent value, , is at the upper range of those seen for software task estimates.

The model fitted to estimated number of items in the basket is: . This pattern, of underestimating small values and overestimating large values is seen in software task estimation, but the exponent of is much smaller.

Including the estimated number of items in the shopping basket, , in a model for total value produces a slightly better fitting model: , which explains 83% of the variance in the data (use of a shopping list had a relatively small impact).

The accuracy of a software task implementation estimate based on estimating its subtasks dependent on identifying all the subtasks, or having a good enough idea of the number of subtasks. The shopping basket study found a pattern of inaccuracies in estimates of the number of recently collected items, which has been seen before. However, adding to the Shopping model only reduced the unexplained variance by a few percent.

Would the impact of adding an estimate of the number of subtasks to models of software task estimates also only be a few percent? A question to add to the already long list of unknowns.

Like task estimates, round numbers were often given as estimate values; see code+data.

The same study also included a laboratory experiment, where subjects saw a sequence of 24 numbers, presented one at a time for 0.5 seconds each. At the end of the sequence, subjects were asked to type in their best estimate of the sum of the numbers seen (other studies asked subjects to type in the mean). Each subject saw 75 sequences, with feedback on the mean accuracy of their responses given after every 10 sequences. The numbers were described as the prices of items in a shopping basket. The values were drawn from a distribution that was either uniform, positively skewed, negatively skewed, unimodal, or bimodal. The sequential order of values was either increasing, decreasing, U-shaped, or inversely U-shaped.

Fitting a regression model to the lab data finds that the distribution used had very little impact on performance, and the sequence order had a small impact; see code+data.

## Impact of number of files on number of review comments

Code review is often discussed from the perspective of changes to a single file. In practice, code review often involves multiple files (or at least pull-based reviews do), which begs the question: Do people invest less effort reviewing files appearing later?

TLDR: The number of review comments decreases for successive files in the pull request; by around 16% per file.

The paper First Come First Served: The Impact of File Position on Code Review extracted and analysed 219,476 pull requests from 138 Java projects on Github. They also ran an experiment which asked subjects to review two files, each containing a seeded coding mistake. The paper is relatively short and omits a lot of details; I’m guessing this is due to the page limit of a conference paper.

The plot below shows the number of pull requests containing a given number of files. The colored lines indicate the total number of code review comments associated with a given pull request, with the red dots showing the 69% of pull requests that did not receive any review comments (code+data):

Many factors could influence the number of comments associated with a pull request; for instance, the number of people commenting, the amount of changed code, whether the code is a test case, and the number of files already reviewed (all items which happen to be present in the available data).

One factor for which information is not present in the data is social loafing, where people exert less effort when they are part of a larger group; or at least I did not find a way of easily estimating this factor.

The best model I could fit to all pull requests containing less than 10 files, and having a total of at least one comment, explained 36% of the variance present, which is not great, but something to talk about. There was a 16% decline in comments for successive files reviewed, test cases had 50% fewer comments, and there was some percentage increase with lines added; number of comments increased by a factor of 2.4 per additional commenter (is this due to importance of the file being reviewed, with importance being a metric not present in the data).

The model does not include information available in the data, such as file contents (e.g., Java, C++, configuration file, etc), and there may be correlated effects I have not taken into account. Consequently, I view the model as a rough guide.

Is the impact of file order on number of comments a side effect of some unrelated process? One way of showing a causal connection is to run an experiment.

The experiment run by the authors involved two files, each containing one seeded coding mistake. The 102 subjects were asked to review the two files, with file order randomly selected. The experiment looks well-structured and thought through (many are not), but the analysis of the results is confused.

The good news is that the seeded coding mistake in the first file was much more likely to be detected than the mistake in the second file, and years of Java programming experience also had an impact (appearing first had the same impact as three years of Java experience). The bad news is that the model (a random effect model using a logistic equation) explains almost none of the variance in the data, i.e., these effects are tiny compared to whatever other factors are involved; see code+data.

What other factors might be involved?

Most experiments show a learning effect, in that subject performance improves as they perform more tasks. Having subjects review many pairs of files would enable this effect to be taken into account. Also, reviewing multiple pairs would reduce the impact of random goings-on during the review process.

The identity of the seeded mistake did not have a significant impact on the model.

Review comments are an important issue which is amenable to practical experimental investigation. I hope that the researchers run more experiments on this issue.

## Estimating quantities from several hundred to several thousand

How much influence do anchoring and financial incentives have on estimation accuracy?

Anchoring is a cognitive bias which occurs when a decision is influenced by irrelevant information. For instance, a study by John Horton asked 196 subjects to estimate the number of dots in a displayed image, but before providing their estimate subjects had to specify whether they thought the number of dots was higher/lower than a number also displayed on-screen (this was randomly generated for each subject).

How many dots do you estimate appear in the plot below?

Estimates are often round numbers, and 46% of dot estimates had the form of a round number. The plot below shows the anchor value seen by each subject and their corresponding estimate of the number of dots (the image always contained five hundred dots, like the one above), with round number estimates in same color rows (e.g., 250, 300, 500, 600; code+data):

How much influence does the anchor value have on the estimated number of dots?

One way of measuring the anchor’s influence is to model the estimate based on the anchor value. The fitted regression equation explains 11% of the variance in the data. If the higher/lower choice is included the model, 44% of the variance is explained; higher equation is: and lower equation is: (a multiplicative model has a similar goodness of fit), i.e., the anchor has three-times the impact when it is thought to be an underestimate.

How much would estimation accuracy improve if subjects’ were given the option of being rewarded for more accurate answers, and no anchor is present?

A second experiment offered subjects the choice of either an unconditional payment of \$2.50 or a payment of \$5.00 if their answer was in the top 50% of estimates made (labelled as the risk condition).

The 196 subjects saw up to seven images (65 only saw one), with the number of dots varying from 310 to 8,200. The plot below shows actual number of dots against estimated dots, for all subjects; blue/green line shows , and red line shows the fitted regression model (code+data):

The variance in the estimated number of dots is very high and increases with increasing actual dot count, however, this behavior is consistent with the increasing variance seen for images containing under 100 dots.

Estimates were not more accurate in those cases where subjects chose the risk payment option. This is not surprising, performance improvements require feedback, and subjects were not given any feedback on the accuracy of their estimates.

Of the 86 subjects estimating dots in three or more images, 44% always estimated low and 16% always high. Subjects always estimating low/high also occurs in software task estimates.

Estimation patterns previously discussed on this blog have involved estimated values below 100. This post has investigated patterns in estimates ranging from several hundred to several thousand. Patterns seen include extensive use of round numbers and increasing estimate variance with increasing actual value; all seen in previous posts.

## Most percentages are more than half

Most developers think …

Most editors …

Most programs …

Linguistically most is a quantifier (it’s a proportional quantifier); a word-phrase used to convey information about the number of something, e.g., all, any, lots of, more than half, most, some.

Studies of most have often compared and contrasted it with the phrase more than half; findings include: most has an upper bound (i.e., not all), and more than half has a lower bound (but no upper bound).

A corpus analysis of most (432,830 occurrences) and more than half (4,857 occurrences) found noticeable usage differences. Perhaps the study’s most interesting finding, from a software engineering perspective, was that most tended to be applied to vague and uncountable domains (i.e., there was no expectation that the population of items could be counted), while uses of more than half almost always had a ‘survey results’ interpretation (e.g., supporting data cited as collaboration for 80% of occurrences; uses of most cited data for 19% of occurrences).

Readers will be familiar with software related claims containing the most qualifier, which are actually opinions that are not grounded in substantive numeric data.

When most is used in a numeric based context, what percentage (of a population) is considered to be most (of the population)?

When deciding how to describe a proportion, a writer has the choice of using more than half, most, or another qualifier. Corpus based studies find that the distribution of most has a higher average percentage value than more than half (both are left skewed, with most peaking around 80-85%).

When asked to decide whether a phrase using a qualifier is true/false, with respect to background information (e.g., Given that 55% of the birlers are enciad, is it true that: Most of the birlers are enciad?), do people treat most and more than half as being equivalent?

A study by Denić and Szymanik addressed this question. Subjects (200 took part, with results from 30 were excluded for various reasons) saw a statement involving a made-up object and verb, such as: “55% of the birlers are enciad.” They then saw a sentence containing either most or more than half, that was either upward-entailing (e.g., “More than half of the birlers are enciad.”), or downward-entailing (e.g., “It is not the case that more than half of the birlers are enciad.”); most/more than half and upward/downward entailing creates four possible kinds of sentence. Subjects were asked to respond true/false.

The percentage appearing in the first sentence of the two seen by subjects varied, e.g., “44% of the tiklets are hullaw.”, “12% of the puggles are entand.”, “68% of the plipers are sesare.” The percentage boundary where each subjects’ true/false answer switched was calculated (i.e., the mean of the percentages present in the questions’ each side of true/false boundary; often these values were 46% and 52%, whose average is 49; this is an artefact of the question wording).

The plot below shows the number of subjects whose true/false boundary occurred at a given percentage (code+data):

When asked, the majority of subjects had a 50% boundary for most/more than half+upward/downward. A downward entailment causes some subjects to lower their 50% boundary.

So now we know (subject to replication). Most people are likely to agree that 50% is the boundary for most/more than half, but some people think that the boundary percentage is higher for most.

When asked to write a sentence, percentages above 50% attract more mosts than more than halfs.

Most is preferred when discussing vague and uncountable domains; more than half is used when data is involved.

## Study of developers for the cost of a phase I clinical drug trial

For many years now, I have been telling people that software researchers need to be more ambitious and apply for multi-million pound/dollar grants to run experiments in software engineering. After all, NASA spends a billion or so sending a probe to take some snaps of a planet and astronomers lobby for \$100million funding for a new telescope.

What kind of experimental study might be run for a few million pounds (e.g., the cost of a Phase I clinical drug trial)?

Let’s say that each experiment involves a team of professional developers implementing a software system; call this a Project. We want the Project to be long enough to be realistic, say a week.

Different people exhibit different performance characteristics, and the experimental technique used to handle this is to have multiple teams independently implement the same software system. How many teams are needed? Fifteen ought to be enough, but more is better.

Different software systems contain different components that make implementation easier/harder for those involved. To remove single system bias, a variety of software systems need to be used as Projects. Fifteen distinct Projects would be great, but perhaps we can get away with five.

How many developers are on a team? Agile task estimation data shows that most teams are small, i.e., mostly single person, with two and three people teams making up almost all the rest.

If we have five teams of one person, five of two people, and five of three people, then there are 15 teams and 30 people.

How many people will be needed over all Projects?

15 teams (30 people) each implementing one Project
5 Projects, which will require 5*30=150 people (5*15=75 teams)

How many person days are likely to be needed?

If a 3-person team takes a week (5 days), a 2-person team will take perhaps 7-8 days. A 1-person team might take 9-10 days.

The 15 teams will consume 5*3*5+5*2*7+5*1*9=190 person days
The  5 Projects will consume              5*190=950 person days

How much is this likely to cost?

The current average daily rate for a contractor in the UK is around £500, giving an expected cost of 190*500=£475,000 to hire the experimental subjects. Venue hire is around £40K (we want members of each team to be co-located).

The above analysis involves subjects implementing one Project. If, say, each subject implements two, three or four Projects, one after the other, the cost is around £2million, i.e., the cost of a Phase I clinical drug trial.

What might we learn from having subjects implement multiple Projects?

Team performance depends on the knowledge and skill of its members, and their ability to work together. Data from these experiments would be the first of their kind, and would provide realistic guidance on performance factors such as: impact of team size; impact of practice; impact of prior experience working together; impact of existing Project experience. The multiple implementations of the same Project created provide a foundation for measuring expected reliability and theories of N-version programming.

A team of 1 developer will take longer to implement a Project than a team of 2, who will take longer than a team of 3.

If 20 working days is taken as the ballpark period over which a group of subjects are hired (i.e., a month), there are six team size sequences that one subject could work (A to F below); where individual elapsed time is close to 20 days (team size 1 is 10 days elapsed, team size 2 is 7.5 days, team size 3 is 5 days).

Team size    A      B      C      D      E      F
1      twice   once   once
2                     once  thrice  once
3             twice                twice   four

The cost of hiring subjects+venue+equipment+support for such a study is likely to be at least £1,900,000.

If the cost of beta testing, venue hire and research assistants (needed during experimental runs) is included, the cost is close to £2.75 million.

Might it be cheaper and simpler to hire, say, 20-30 staff from a medium size development company? I chose a medium-sized company because we would be able to exert some influence over developer selection and keeping the same developers involved. The profit from 20-30 people for a month is not enough to create much influence within a large company, and a small company would not want to dedicate a large percentage of its staff for a solid month.

Beta testing is needed to validate both the specifications for each Project and that it is possible to schedule individuals to work in a sequence of teams over a month (individual variations in performance create a scheduling nightmare).

## Estimation experiments: specification wording is mostly irrelevant

Existing software effort estimation datasets provide information about estimates made within particular development environments and with particular aims. Experiments provide a mechanism for obtaining information about estimates made under conditions of the experimenters choice, at least in theory.

Writing the code is sometimes the least time-consuming part of implementing a requirement. At hackathons, my default estimate for almost any non-trivial requirement is a couple of hours, because my implementation strategy is to find the relevant library or package and write some glue code around it. In a heavily bureaucratic organization, the coding time might be a rounding error in the time taken up by meeting, documentation and testing; so a couple of months would be considered normal.

If we concentrate on the time taken to implement the requirements in code, then estimation time and implementation time will depend on prior experience. I know that I can implement a lexer for a programming language in half-a-day, because I have done it so many times before; other people take a lot longer because they have not had the amount of practice I have had on this one task. I’m sure there are lots of tasks that would take me many days, but there is somebody who can implement them in half-a-day (because they have had lots of practice).

Given the possibility of a large variation in actual implementation times, large variations in estimates should not be surprising. Does the possibility of large variability in subject responses mean that estimation experiments have little value?

I think that estimation experiments can provide interesting information, as long as we drop the pretence that the answers given by subjects have any causal connection to the wording that appears in the task specifications they are asked to estimate.

If we assume that none of the subjects is sufficiently expert in any of the experimental tasks specified to realistically give a plausible answer, then answers must be driven by non-specification issues, e.g., the answer the client wants to hear, a value that is defensible, a round number.

A study by Lucas Gren and Richard Berntsson Svensson asked subjects to estimate the total implementation time of a list of tasks. I usually ignore software engineering experiments that use student subjects (this study eventually included professional developers), but treating the experiment as one involving social processes, rather than technical software know-how, makes subject software experience a lot less relevant.

Assume, dear reader, that you took part in this experiment, saw a list of requirements that sounded plausible, and were then asked to estimate implementation time in weeks. What estimate would you give? I would have thrown my hands up in frustration and might have answered 0.1 weeks (i.e., a few hours). I expected the most common answer to be 4 weeks (the number of weeks in a month), but it turned out to be 5 (a very ‘attractive’ round number), for student subjects (code+data).

The professional subjects appeared to be from large organizations, who I assume are used to implementations including plenty of bureaucratic stuff, as well as coding. The task specification did not include enough detailed information to create an accurate estimate, so subjects either assumed their own work environment or played along with the fresh-faced, keen experimenter (sorry Lucas). The professionals showed greater agreement in that the range of value given was not as wide as students, but it had a more uniform distribution (with maximums, rather than peaks, at 4 and 7); see below. I suspect that answers at the high end were from managers and designers with minimal coding experience.

What did the experimenters choose weeks as the unit of estimation? Perhaps they thought this expressed a reasonable implementation time (it probably is if it’s not possible to use somebody else’s library/package). I think that they could have chosen day units and gotten essentially the same results (at least for student subjects). If they had chosen hours as the estimation unit, the spread of answers would have been wider, and I’m not sure whether to bet on 7 (hours in a working day) or 10 being the most common choice.

Fitting a regression model to the student data shows estimates increasing by 0.4 weeks per year of degree progression. I was initially baffled by this, and then I realized that more experienced students expect to be given tougher problems to solve, i.e., this increase is based on self-image (code+data).

The stated hypothesis investigated by the study involved none of the above. Rather, the intent was to measure the impact of obsolete requirements on estimates. Subjects were randomly divided into three groups, with each seeing and estimating one specification. One specification contained four tasks (A), one contained five tasks (B), and one contained the same tasks as (A) plus an additional task followed by the sentence: “Please note that R5 should NOT be implemented” (C).

A regression model shows that for students and professions the estimate for (A) is about 1-2 weeks lower than (B), while (A) estimates are 3-5 weeks lower than (C) estimated.

What are subjects to make of an experimental situation where the specification includes a task that they are explicitly told to ignore?

How would you react? My first thought was that the ignore R5 sentence was itself ignored, either accidentally or on purpose. But my main thought is that Relevance theory is a complicated subject, and we are a very long way away from applying it to estimation experiments containing supposedly redundant information.

The plot below shows the number of subjects making a given estimate, in days; exp0to2 were student subjects (dashed line joins estimate that include a half-hour value, solid line whole hour), exp3 MSc students, and exp4 professional developers (code+data):

I hope that the authors of this study run more experiments, ideally working on the assumption that there is no connection between specification and estimate (apart from trivial examples).

## Where are we with models of human learning?

Learning is an integral part of writing software. What have psychologists figured out about the characteristics of human learning?

A study of memory, published in 1885, kicked off the start of modern psychology research. At the start of the 1900s, learning research was still closely tied to the study of the characteristics of what we now call working memory, e.g., measuring the time taken for subjects to correctly recall sequences of digits, nonsense syllables, words and prose. By the 1930s, learning was a distinct subject in its own right.

What is now known as the power law of learning was first proposed in 1926. Wikipedia is right to use the phrase power law of practice, since it is some measure of practice that appears in the power law of learning equation: , where: is the time taken to do the task, is some measure of practice (such as the number of times the subject has performed the task), and , , and are constants fitted to the data.

For the next 70 years some form of power law did a good job of fitting the learning data produced by researchers. Then in 1997 a paper pointed out that researchers were fitting aggregate data (i.e., one equation fitted to all subject data), and that an exponential equation was a better fit to individual subject response times: . The power law appeared to be the result of aggregating the exponential response performance of multiple subjects; oops.

What is the situation today, 25 years later? Do the subsystems of our brains produce a power law or exponential improvement in performance, with practice?

The problem with answering this question is that both equations can fit the available data quite well, with one being a technically better fit than the other for different datasets. The big difference between the two equations is in their tails, however, it is costly and time-consuming to obtain enough data to distinguish between them in this region.

When discussing learning in my evidence-based software engineering book, I saw no compelling reason to run counter to the widely cited power law, but I did tell readers about the exponential fit issue.

Studies of learnings have tended to use simple tasks; subjects are usually only available for a short time, and many task repetitions are needed to model the impact of learning. Simple tasks tend to be dominated by one primary activity, which means that subjects can focus their learning on this one activity.

Complicated tasks involve many activities, each potentially providing distinct learning opportunities. Which activities will a subject focus on improving, will the performance on one activity improve faster than others, will the approach chosen for one activity limit the performance on a second activity?

For a complicated task, the change in performance with amount of practice could be a lot more complicated than a single power law/exponential equation, e.g., there may be multiple equations with each associated with one or more activities.

In the previous paragraph, I was careful to say “could be a lot more complicated”. This is because the few datasets of organizational learning show a power law performance improvement, e.g., from 1936 we have the most cited study Factors Affecting the Cost of Airplanes, and the less well known but more interesting Liberty shipbuilding from the 1940s.

If the performance of something involving multiple people performing many distinct activities follows a power law improvement with practice, then the performance of an individual carrying out a complicated task might follow a simple equation; perhaps the combined form of many distinct simple learning activities is a simple equation.

Researchers are now proposing more complicated models of learning, along with fitting them to existing learning datasets.

Which equation should software developers use to model the learning process?

I continue to use a power law. The mathematics tend to be straight-forward, and it often gives an answer that is good enough (because the data fitted contains lots of variance). If it turned out that an exponential would be easier to work with, I would be happy to switch. Unless there is a lot of data in the tail, the difference between power law/exponent is usually not worth worrying about.

There are situations where I have failed to successfully add a learning (power law) component to a model. Was this because there was no learning present, or was the learning not well-fitted by a power law? I don’t know, and I cannot think of an alternative equation that might work, for these cases.