# How are numbers related to your body movements? Depends on how you read words

The SNARC effect is a fascinating phenomenon (and no, it has nothing to do with cheeky one-off blog posts). When asked to recognize numbers, people react faster with their left hand for low numbers, and faster with their right hand for high numbers. Take a look at this graph:

This shows the results of an experiment led by Samuel Shaki: Twelve Canadian university students were shown a series of single-digit numbers. Their task was simple: as quickly as possible, press one button if the number is odd, and another button if the number is even. This graph charts reaction time of the right hand minus the reaction time of the left hand (the odd-even buttons were switched halfway through the experiment, so each hand had an equal number of tries with each number).

It takes a little explanation to understand what you're seeing here. For the number "1", the difference in reaction time is a little over 50 milliseconds, meaning the right hand is slower than the left hand. For "9" the difference is a little more than negative 60 milliseconds, meaning the right is faster than the left hand. The pattern across the span of the digits is similar: respondents are better with their left hand for low numbers, and better with the right hand for high numbers.

This result has been replicated in dozens of studies, one of which we've discussed on Cognitive Daily. What's less clear is exactly why the result occurs. It's possible that because we're accustomed to seeing number-lines with lower values on the left (like on the graph above), we respond more quickly with the left hand to low values. But it's also possible that left-to-right reading of words is what leads to the effect. In fact, Japanese readers (who typically read top-to-bottom) have been tested with a vertical arrangement of buttons, and they respond faster to lower numbers with the top button.

So Shaki's team decided to test 11 Palestinian students who read only Arabic text and Arabic-Indic digits, both of which are read from right-to-left instead of left-to-right. Here are the results:

For Palestinians, there's still a SNARC effect, but it's reversed from the Canadian SNARC effect: They're faster with the right hand for smaller numbers, and faster with the left hand for larger numbers. That's powerful evidence that there's no left-to-right number line in everyone's head; the effect seems to depend on how you learned to read words and numbers.

But Shaki's team wasn't finished. Most Israeli students learn to read Hebrew text (right-to-left), but also learn Arabic numbers, which are read left-to-right. Here are the results for 16 Israeli students on the same test:

Now there's no SNARC effect at all -- the results show no significant difference in response time for the right or left hand for any portion of the number range. Even when the researchers split the Israeli students into groups with slightly positive and slightly negative slopes, they couldn't find an orderly effect in either group, so it doesn't appear to be the case that some Israelis have a left-right SNARC effect while others have a right-left effect.

The researchers say this probably means that the SNARC effect is a result of the combination of left-right (or right-left) reading and left-right/right-left numbering -- but there may be other contributors, such as preferred order for finger-counting or for counting real objects.

Shaki, S., Fischer, M., & Petrusic, W. (2009). Reading habits for both words and numbers contribute to the SNARC effect Psychonomic Bulletin & Review, 16 (2), 328-331 DOI: 10.3758/PBR.16.2.328

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I notice that the number seven is frequently higher than the surrounding numbers. I wonder: do the number of syllables in the word effect the response rate?

By Gary Godfrey (not verified) on 04 May 2009 #permalink

I suspect the mentioned Japanese results are not connected to this. Japanese read top-to-bottom, but also left-to-right (and even right-to-left, though that is rare today). In fact, you may even have a mix of top-bottom and left-right in the same body of text (a mix of newspaper articles on a page, for instance) and books may be published either way. Even more confusingly, when the text is right-to-left (rare today, as I mentioned), Arabic numbers are still written left-to-right while Kana numbers follow the text right-to-left.

I'd like to see the top-bottom arrangement tested for other groups, and the left-right arrangement for Japanese. I strongly suspect that non-Japanese show the same bias on top-bottom tests, and that Japanese follow Western left-right bias, since left-right reading order is much more common than right-left today.

Some questions about the SNARC effect in general. What happens if you include larger numbers rather than just single-digit ones? What difference does it make whether or not you reveal the range of possible numbers in advance? What happens if you start with some small numbers, then throw in a few larger ones, and then small ones again - does the brain recallibrate how big is big?

As shown, intriguing, but hard to evaluate.

In Canadians, there is essentially no difference between numbers 3, 4, 6, and 8, and almost none with 7.

In Palestinians, little difference between 1,3,4, and 6.

In both there is no number 5 shown. Reason?

No error bars, no r values. n < 17 seems to low to me to conclude too much. But you do say SNARC shown in other papers, so... Well, interesting.

CM: 5 was not one of the numbers presented, I'm guessing so that there was a clear distinction between smaller and larger numbers. As to your other questions, if you want that level of analysis, you're going to have to read the original article. The results are statistically significant.

Adrian: My understanding is that it works with larger numbers too; I haven't read the studies myself but here's one summary. I'd guess the effect would disappear with roman numerals, especially since most people don't process them very quickly.

Janne: According to the BPS article linked above, the up/down effect holds for non-Japanese.

While the single digit numbers seem to be biased by the direction we read, it would be interesting to see differences in body movement between English and, for example, German speakers who reversely say two digit numbers by saying the lower number first, i.e., "91" is literally translated as 'one and nity' ("einundneunzig").
Initially, do both hands go up at the same time? Or first the right and then the left hand or vice versa? Do German speakers take longer because they have to switch the (verbal/visual) mental coding, i.e,. "19", into perceptual coding "91"?

I'd be interested in seeing how English-speaking Yeshiva students would do. Many Yeshiva students learn to read Hebrew (right to left) first, in Nursery and Kindergarten, but speak English as a first language. Presumably, they would perform in a manner similar to that of the Israelis. I wonder if which language is learned first has any bearing on the results, if equal competence is achieved in both.

By E. Wrotslavsky (not verified) on 05 May 2009 #permalink

"Arabic text and Arabic-indic digits, both of which are read from right-to-left instead of left-to-right" - umm, no. Arabic text is right-to-left, but Hindi numerals (which I assume is what's meant by "Arabic-indic") are left-to-right. Or at least, in my limited experience in Arabic classes, in Saudi Arabia, in Egypt, and in the UAE that's how it works. I suppose it could be different in Palestine, but it seems unlikely. It's one of the things that makes driving computer displays for Arabic particularly amusing.

Yeah, what Bob said; numbers in Arabic are written in exactly the same way as in European languages, except (in the Middle East, at least) using different symbols. That is, the lowest-valued digit is placed at the extreme right. So I don't really get this article.

By WyattEarp (not verified) on 05 May 2009 #permalink

In Arabic, numbers are written in the same system as in English (even though the symbols are different)- high digits on the left, low on the right. This is why we call our numerals in English "Arabic" numerals - as they came to us via Arabs from India. So, if there is an effect, it can't be due to the way numbers are read.

(One thing though that has not occurred to me before. Do Arabic readers somehow "read" the numbers differently, given that interpreting the high digits first runs counter to the direction of the surrounding text? I taught science to Arab students for five years, so it's a bit embarrassing that I never thought about this.)

However, I'm sceptical about the whole post, and agree with another comment about the lack of error bars. I think the "effect" needs further testing before time is wasted on explanations for it.

I type higher numbers with my right hand, lower with my left. It's the way my keyboard is laid out, and I've been typing for over 40 years It's habit.

By GeekGoddess (not verified) on 06 May 2009 #permalink

According to the original journal article, most Arabic numerals are indeed read left-to-right, as in America and Europe. The researchers took special care to find a population that read Arabic text and used Arabic-Indic numerals (also called Eastern Arabic), which they read from right to left. Look around Wikipedia for a discussion of the various numeral systems currently in use. There are lots, and just because you're familiar with one system doesn't mean you understand every system.

I'm with GeekGoddess - it immediately struck me that when typing we use our left hand to indicate lower numbers and right hand for higher numbers. I don't know how keyboards are laid out for other languages though.

I'd be curious if similar results, consistent with keyboard layout, would be seen with letters of the alphabet. Obviously the experiment would be set up differently (no such thing as "odd" and "even" letters) - perhaps the letters could appear as one of two colors, and the hand used to push a button would depend on the letter's color.

Thinking about the arrangement of piano keys, perhaps people would respond to high pitches more quickly with their right hands, and low pitches with their left...

I agree that some visualization of the distribution of responses would be good here, but error bars probably aren't the ideal solution. This is a within-subject design, so the relation between error bars and significance is non-intuitive. It might have been better if there was a data point for every single respondent's average difference.

But none of that contradicts the fact that the results are significant. For Canadians and Palestinians, the slopes were significantly different from zero, with p < .01. Results for all three groups were significantly different from each other as well.

I guess the results mean that generally our right hand is more likelz to respond. Is it the same for left+handed?
What number is the break point for both hands?

I wonder how a typists vs non-keyboarders distribution would look?

Dear Madam/Sir: There is a fundamental problem with the literature of SNARC and STROOP effects, i.e. the assumption that the reaction times of dominant and nondominant hands (right and left, in vast majority of people) are equal. This assumption is wrong. This is because our handedness is a rough reflection of the closeness of the command center (the hemisphere of speech) to the dominant hand; in turn a reflection of the fact the moving the nondominant side of the body requires the command to travel the width of the corpus callosum (the bridge between hemispheres) to make the minor hemisphere to move the nondominant side (left, in most people). Thus, no matter how hard one tries, the dominant hand is always ahead of the nondominant by an interhemispheric transfer time (IHTT).
This arrangement vitiates all conclusions arrived at in experiments of SNARC effect. More on this issue may be read in my website: www.mimickingman.com