PSYCHOLOGY CORNER

Ryan Ocampo (Psychology Correspondent)

Table of Contents:

The Law of Small Numbers

or in nerd terms "The Law of Small Numbers"

Like most people, I consider myself reasonably smart. I can usually figure out which way doors open after two tries, how to read an analog clock, and I haven’t failed any of my classes. Jokes aside, my point is that most people (or at the very least, me) consider themselves decently intelligent and can trust themselves to make simple assumptions. Just like how you could easily come to the conclusion that the following sentence means that senior citizens are more likely to support the current president.

“In a telephone poll of 300 senior citizens, 67% expressed support for the president. 13% were undecided and 20% expressed disapproval for the president.”

Yet this sentence is nearly meaningless. If not for the fact that you had already prepared for me to try to trick you, you wouldn’t have considered the background information. “A telephone poll of 300 seniors”. Your assumption about the meaning of this sentence would have been the same even if the sample size hadn’t. Yet, you should have had a different assumption and identified the fact that the sample is far too small, but neither you nor I would figure that out intuitively.

The Law of Small Numbers is a statistical bias where people underestimate the effect of a small sample size and exaggerate the coherence of what we see. It is the effect seemingly originating from the first of these two statements, despite both meaning the same thing.

More precise results are received with larger samples
Smaller samples are more likely to have extreme results.

We know these two statements mean the same thing and this can be seen logically with a simple example. If you have a bucket of red and green finger biting toads, arranged randomly, identical in all ways except color.When you stick two fingers in, you’re more likely to be bitten by toads of only one color, as compared to if you stick your entire hand in. (simply using marbles as an example bores me). The reason for this is just basic probability. You have a (½ x ½) 25 percent chance to get bitten by two green toads putting two fingers in, while only a (½ x ½ x ½ x ½ x ½) 3.125 percent likelihood of getting bitten by only green toads if you put five fingers in.

The problem is that people don’t consider the fundamentals of probability theory when they make decisions. If I ask you which of these sequences of male/female births in a hospital is most likely…

GGGBBB, GGGGGG, BGGBGB

You will probably say the third option, intuitively, even though all of these sequences are equally likely since the outcomes are independent, and B and G are (approximately) equal in likelihood. Yet, most people don’t realize this. For example, there was an uproar when someone discovered that no girls had been born in 132 villages in the small Himalayan state of Uttarakhand in the months between April and June of 2019. (See BBC 25 July 2019 issue). While India has struggled with sex-selective abortions, savvy readers like yourself may have realized that probability, not sexism, may have caused the no-girl villages. As BBC also pointed out, “officials found 180 girls and no boys were born during the same period in 129 different villages. And to complete the mixed picture, 88 girls and 78 boys were born in another 166 villages.” Sometimes things are simply random and that’s all there is to it.

As I’ve written about before, people tend to naturally exaggerate the coherence of random events. Even Bill Gates has fallen for the Law of Small Numbers. Billy’s foundation once gave $1.7 billion to explore the fact that the most successful schools, on average, are small. As seen, when we look at the 1,662 schools in Pennsylvania, 6 of the top 50 are small, which is overrepresentation by a factor of 4. The Gates foundation then proceeded to invest in small schools, in some cases even cutting up larger schools. As many things do, this made sense on the surface level. We can easily think up explanations, like how the students are more likely to receive more personalized teaching. But as I hope you’ve learned, intuitive predictions matter for little. The data also says that the worst schools in the state are also smaller.

So What Does This Mean for Daily Life?

Remember to have a massive sample size when you conduct your experiments! But as I’m sure you’re thinking, I’m not going to be doing an experiment with sample size unless my science teacher forces me to. So take it out of the context of science. Any time you get an impression of something, or someone, remember that this could just be an outlier. So Montgomery seems like a jerk the first time you meet him, but then all your friends have told you how much they like him. Maybe it was just a bad day for him. (Or he just really dislikes you). The main point of this article is to appreciate the random, wait to gather more information before coming to a conclusion where you won’t change your mind. Think of this article as an extension of the Halo effect.

Works Cited

1. Biswas, Soutik. “Have No Girls Been Born in 132 Villages in India?” BBC News, BBC, 25 July 2019, www.bbc.com/news/world-asia-india-49109767.

The Halo Effect

or in nerd terms “Exaggerated Emotional Coherence”

School has already been happening for a few weeks and you have undoubtedly met some new people. Who’s the one person you’ve met recently that seems friendly? Do you think they’d be willing to donate a small sum of money to charity that is really important to you if you asked them (assuming that they have the time to grab some money from home)? Personally, people have either no money, or at least $100. If you’re like the majority of us, you probably assumed that the person would be generous. You likely recall how you like the person, and since you don’t have any specific examples of generosity to draw upon, you assume that that they are generous because it fits with the theme of friendliness. Simply put, the Halo Effect occurs when you don’t have the evidence to answer a question, where your brain will replace analytical reasoning with a snap emotional judgment. In the pursuit of simplicity, you will often like, or dislike, all of a person.

The oversimplification of a person is also in effect when you slowly gather evidence about a person’s personality. A classic of psychology is the experiment presented by Solomon Asch: a subject is presented with descriptions of two people and asked to say what they think of the people’s personality. You can do the same.

Alan: intelligent-industrious-impulsive-critical-stubborn-envious

Ben: envious-stubborn-critical-impulsive-industrious-intelligent

You likely automatically liked Alan more than Ben. Despite being portrayed by the same adjectives, the previous words influenced the effect of the subsequent words. An intelligent person is good, an envious person who is intelligent is dangerous. The Halo Effect allows ambiguous descriptions such as stubborn to be influenced. Did you think that stubborn trait was a respectable or negative trait, for Alan and Ben?

There is a principle underlying the Halo Effect, confirmation bias. When asked a question such as, “is Aidan friendly?” you will think of extremely different examples compared to those if you were asked “is Aidan unfriendly?”. Your mind deliberately searches for confirming evidence to judge a theory. This fits into the theory of psychologist Danial Gilbert: to begin to comprehend a statement you first try to imagine the statement was true. Only after that can you proceed to judge whether you actually believe the statement. Even with a ridiculous example, “Look, there’s a dead bird in the sky”, you must first imagine what that would mean if it were true. You were probably aware of vague impressions of birds, sky, and death. You associate bird with sky, but then your mind frantically tries to connect the concept of dead. You must first try to make sense of nonsense before you can identify it as such. Thus, it is much easier to have new information conform to previous beliefs, because we are wired to.

What does this mean in daily life?

You should question your first impressions of people and ideas. Next time you are asked whether something is true, deliberately think of the inverse of the question, is this untrue? Perhaps then you will be able to truly think objectively? Yeah no. There are always biases. Yet if you can make a positive impact with minimal impact, in this case simply by thinking of the inverse, you should take it. Or if I put it into the words that would actually convince me: If you think of the inverse you are more likely to see the more complete story. Therefore your opinion will be closer to the objective truth, and I can’t speak for you, but I like being right.

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