Statistics - the absolute basics and when to ignore numbers

Average - this is a number we choose to best represent others. There are 3 kinds of average. I learnt this in primary school.

- mean: this is the most used. It is simply the sum of all the numbers divided by the no. of values (I mean the numbers, not the ones your mom should have given you). The mean is useful in achieving equity. It is most representative when there are no extreme numbers that deviate from the rest.

- median: this simply refers to the middle value when all the numbers are arranged in sequence. If there are an even no. of values, we use the mean of the middle two. Given a median, you know that there are an equal number of values greater and smaller than it. A median is useful when there are some outlying values (values that are uncharacteristically large) that might distort your average value if you use the mean. Eg if you calculate the prices of public housing around the world, the median and the mean may be quite different because of Singapore HDB prices. The median would likely be more representative.

- mode: this refers to the value that happens most often. There can be more than one mode or none at all (ie. all values occur the same no. of times). Ideally, given a number from that set, it is most likely to be the mode.

Using all three can tell us different things about the data set.


Deviation - this tells us how much the various values differ from the mean. Usually, standard deviation is used.
eg {5, 10, 15} and {0, 10, 20} both have a mean of 15 but drastically different deviation.


Statistical Significance - this tells us how sure we are that a particular result is true and not due to randomness. For example,
if we throw a dice 6 times and we get "three" 4 out of the 6 times, how confident are we that the dice is biased rather than it being a matter of 'luck'.
Conversely, how many more people should we find have borrowed from the romance section than the cookery section for us to be 95% sure that cookery books are really more popular.

This calculation is needed because typically we cannot obtain all the data (eg survey every single person) but use a sampling, so randomness comes into the picture.

Caution: Statistical significance depends on a true random sample. Otherwise the sigificance level can be misleading. If we are obtaining feedback from all participants, there is no need for this, unless we are using their feedback to infer the preferences of the population at large. Then more will need to be done statistically.

Examples of Applications:
1) The use of deviation in loans or in-library collection size can help us figure out how much shelf space we really need. After all, the amount of shelf space depends more directly on how many books are left the library at any time rather than the overall collection size.

2) We may receive feedback that a particular timing is preferred for a programme. Given that the feedback is from a random sample, how sure are we that the indicated timing is really better for the community?

3) Librarians are told to pick 5 children from every session of a programme for feedback (because it is logistically impossible to poll everyone). If the resulting positive feedback has a 0.05 significance level (ie 95% confidence) can we be sure the programme is good? This actually depends on how randomly the librarian selected the children. Usually bias to pick favourable and more forthcoming children will come into play.

4) There seems to have been a recent rise in loans. Can we be 99% sure that this is a trend rather than a 'random' variation?


Ignoring Statistics
Limits of Statistics - There will be times when we wish to ignore statistics given. This may be times when broad strokes alone are not helpful. For example, the parent of a child whose child was murdered won't care if their neighbourhood is actually very safe and that their child's death does not add significantly to the mortality rate. To do otherwise is to allow a tyranny of the majority over the needs of the minority. Some needs are so important that zero tolerance may be the way to go.
Statistics are descriptive. Just because something is statistically significant or not does not affect reality, it only describes how sure we are that it reflects reality. Statistically, it is impossible to be hundred percent sure unless we use the entire population as a sample. Thus there can be occasions when the best statistics are wrong and the worse may prove to be right. Thus assessing purely by statistics alone is to play a game purely on probability. But a strategy that is very likely to succeed can still fail (see below). All things being equal, the larger the sample size thre more sure we can be but the flip side is that cost rises exponentially.

Moreover, the brain is more complex than mere statistics and is capable of heuristics that can be chillingly more efficient and accurate depending on the relevant experience he/she has. Humans as a group can exhibit irrationality that defy simplistic mathematical models and the seemingly improbable is not impossible. Quantum mechanics and the normal curve includes an implicit awareness of this. Statistically air travel is safer than land but planes still crash ever so often. It is near impossible for an individual to strike the lottery yet we know there must be a winner at every draw. Marketing is deeply aware of this so you will never see an ad that appeals by logic. Every marketing technique I've read about appeals to intuition and emotions (That is how many make decisions). The statistics they use are direct results from testing the effectiveness of various methods. So while statistics can be helpful, making purely logical inferences from it can be misleading. I have no examples here: this is an area I am only beginning to explore. This is the limit of my understanding so far.

Incomplete picture - One typical manner in which statistics can be misleading is when only certain sides are presented. We may say that a particular organisation only has a 5% penetration rate in a particular section of the market. But what's missing is how large and profitable the market is and what the ROI is for various products. And how saturated the market is. Typically, time and manpower (including training hours) are sometimes neglected when computing costs. The scalability and replicability of a model is important and are currently not included in most calculations used.

Beware of probability - we have all heard of how a dice gives an equal chance for any number to appear. Yet we have all had times when we threw a succession of 6's or 1's. The skinny on probability is that it is ultimately a statistics assuming that the event occurs infinite times. Thus any programme based solely on probability can be dangerous unless there are enough resources and time to run it many, many times. Even then, there may often be better ways. And many types of events are independant ie, past performance does not and never will predict future events. You could have thrown 100 6's on a dice and the probability of getting a 6 (or any numer from 1 to 5) on the next throw is still 1 in 6.

The low down on statistics and surveys

As the strip shows, results from such surveys can be interpreted in different ways. The reason is because such surveys (or "studies") only show association rather than cause and effect.
Sometimes, the interpretation fails to consider tertiary conditions or a larger perspective. To give an example bordering on the ridiculous, all murderers pee but it doesn't mean that peeing results in murderous tendencies although if you stand in the way of someone looking urgently for a restroom, you may get different ideas. Likewise, it is also conceivable that a survey may show more smokers eat more ice-cream. This may not mean that smoking causes a craving for dessert or vice-versa (unless it's nicotine flavoured ice-cream. Thank goodness the industry is still above this.) Rather it may just show that both are choice stress relievers for many people.

A recent "study" by SMU Psychology Professor Norman Li shows that Singapore women are more materialistic than their American counterparts while men on both continents went for looks first. (http://sg.news.yahoo.com/blogs/singaporescene/pore-girls-materialistic-smu-study-092109660.html; and http://www.smu.edu.sg/news_room/smu_in_the_news/2011/sources/ST_20110615_2.pdf) Now before women join hands to go up in arms (while others secretly visit surgeons) and some Singapore men toast each other in agreement, a closer look at the study will reveal much. Actually, even a casual look will do. The study surveyed "400 psychology students aged between 19 and 21, studying at the SMU and the Northern Illinois University near Chicago in the United States, on their attitudes towards marriage, children and preferences when it comes to choosing a partner."

So perhaps a more accurate conclusion would be: young SMU female psychology students are more materialistic than than their NIU counterparts while young male psychology students in both varsities are equally superficial. After all, the last time I checked, SMU psychology students aren't representative of our population. And in view of the much recognised fact that self-reporting is one of the most inaccurate methodologies, we may wish to add "self-alleged" somewhere in there. But otherwise, I'd say this study is worrying -- it seems our future psychology workers are either materialistic or superficial. Perhaps the study went through because it largely corroborates conventional results from other surveys. Men tend to filter subjects by looks first and women by power & status (ie security factors) when looking for partners. But again, as far as I know, most of these studies also take the form of self-reporting surveys. And of course, we know that we are always honest when talking about ourselves and we always know ourselves best. That's why some live in mental insitutes and see psychiatrists.

What does this have to do with the library?

Well, how are customer satisfaction surveys done? They are usually done by interviews, a methodology which is just a step above self-reporting surveys -- or not, depending on how trained the interviewers are. Otherwise, we have the bias of the interviewee filtered through the interviewer's lens.
And how representative are the people interviewed? Well, I often received results based on a survey of 3-4 people. In this case, it should really be treated more as feedback than a generalisable finding. And in the past, I had feedback about children programmes given by adults... right.

The other thing we can learn from the "study" is on measuring things. For example, what did the study conclude as materialism? It defined it as looking for social status. The last time I checked, status and material wealth can be closely related but not equivalent. One only needs to look at Mother Therea, Gandhi (later in his life), and many non-Singapore politicians. And conversely, look at the many secret millionaires we don't know about? Who are they you say? Didn't I just say we don't know?

Now how do we measure readership in the library? The primary measure is loans. The two are very closely related but not the same. I would say it is analogous to Newton's and Einstein's laws of physics. It is now widely spread (alright, only among science geeks) that Newton was wrongly thought to be right till Einstein came along. It is obvous that Einstein was smarter because he was uglier and we all know looks + brains = constant. The closer truth is that Newton hit upon a very close approximation of the truth (or what we currently think is right) -- so close that on Earth, it is much simpler and better to use his computations. So unless you are migrating to the milky way or negotiating at light speeds, Newton would pretty much be a worthy guide.

So for us, the question is: when does loans approximate readership? Logically, loans would be consistently lesser than readership (some may browse but not borrow, other may read non-library materials. And assuming humans are creatures of habit this difference should be fairly constant - under normal circumstances). Thus loan trends can mimic readership trends. However, when we throw in loan promotions, this premise can fail -- mainly because we are promoting just loans. Most of us will have encountered people who keep buying McDonald's meals to get the full set of toys - perhaps not because they like the food but because their child likes the toy. If the library equivalent exists, this is when loans deviates from readership and no longer mimics its trends. Part of it now measures greed or obsession.

The upshot is that this also skews our collection statistics. Previously, we may use borrowing trends as a guide to reading preferences. But under such circumstances, it may become more of a guide on what some people can borrow when they don't really want to read. Thus my take is that a poorly conceived promotion is akin to using television to nanny your kids. Effective in the short run, destructive in the larger scheme of things.

The borrowing trends on a poorly developed or organised collection can also exhibit a bit of this anomaly. It may reflect instead what people borrow when they can't find what they want but don't want to leave empty handed.

How can we circumvent this then? I'm taking this to the grave with me.... no seriously, it is simplyto start with a good norm or failing that do constant development and analysis of the statistics to monitor changes based on the development.

But of course, this is also an oversimplification of the situation. Or overthinking. After all, most people end up doing the same thing anyway.