h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Right, bit of a convoluted one this, here goes...

As mentioned below in earlier journal I did an experiment as part of my OU course that was designed to clarify some elements of how human beings compare 2-digit numbers represented externally on a computer screen.

I've now had a chance to analyse the data and been able to pull some further information out.

One of the main motivators in this study was to see whether when doing the comparisons we compared the individual digits in parallel and then combine at the end to com up with a result. So comparing 41 with 45 would compare 4 with 4 and 1 with 5. 4 with 4 is not clear but 1 with 5 is less so we combine them and decide that 41 is less than 45.

Equally comparing 21 with 45. Compare 2 with 4 and we see it is less. Compare 1 with 5 and we see it is less. Combine the two and we conclude that 21 is less than 45.

However, the theory behind all this indicates that in the case of number comparisons such as 29 with 45 or 61 with 45 we have a different problem. Since 2 is less that 4 but 9 is greater than 5 when we compare them we have to work out that the 2 < 4 result is more important than the 9 > 5 result in order to conclude that 29 is less than 45. And vice versa for 61 with 45.

The study I did showed that in these later cases there is indeed a delay in response time (and one that is statistically significant with p<0.001). This looks great and indicates that we do indeed compare 2-digit numbers by looking at the individual digits and then combining the results and applying a weighting where the individual digit results differ (ie the 25 result).

However, I then worked out that I could add a further check in. I could look at how the response times differed when the comparison was between numbers of the same decade (ie 41 with 45) or different decade (ie 21 with 45). And I could look and see how that interacted with the previous effect (know as a stroop like effect).

Now it probably won't surprise anyone outside the university of the bleedin' obvious that comparing numbers of different decades (21 with 45) is faster than comparing numbers of the same decade (41 with 45) because you can ignore the units and just look at the decade digit. Half the processing, faster response time.

BUT what is interesting is the combined effect, and this is also statistically significant.

What I mean is that comparing 41 with 45 is faster than comparing 49 with 45. And this is regardless of the order the numbers are shown in (ie as 49 45 or 45 49, makes little difference and no statistically significant difference).

I can understand why 21 with 45 is faster than 29 with 45 because of the stroop like effect where in 21 with 45 the two comparisons reinforce each other and in 29 with 45 they clash and weighting has to be added to decide.

But in 49 with 45 the 4 is essentially irrelevant since it provides no help in determining which is larger. So why should 49 with 45 be slower than 41 with 45?
We're talking a difference, in average, of about 60ms. Approx 830ms compared with 890ms for same decade comparisons.

For outside decade comparisons the values are more like 760ms (for 21 with 45) vs. 780ms (for 29 with 45) so the within decade is clearly having an effect.

Or could it be that I modeled my data incorrectly? I specified that 49 with 45, 59 with 55 and 69 with 65 as being stroop like but that 41 with 45, 51 with 55 and 61 with 65 as non stroop). Maybe I was wrong to do that and something else is going on here that has been hidden by this assignment?

I realise this is probably so much nonsense to most readers but any comments welcome. I'm confused!

If you're confused we have no chance! Dunno. I'm going to read it through again and see if anything comes up. but it'll probably be nothing useful

No worries Mr. Penguin!

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maybe the brain is trying to get useful information from the 4 even though it's not useful?

Or maybe its because 49 is almost 50 so the brain tries to work ot if 50 is bigger than 45, kinda lik rounding up. and then there's the whole stroop effect thingy. I dunno, that doesn;t make sense to me why the brain would do it that way. But maybe the brain tries to round things up to make life easier for itself.

Consider the possibility this delay is related to visual processing, rather than cognitive processing.

For example, the numeral "1" may be quicker to process than "9", because of its dissimilarity to all other numerals.

Contrariwise, "9" is visually similar to both "7" and "6". In fact, it is common to substitute "6", for "9". So common that Hendrix even sang about it!

hmmm, yes, could have an impact. And since all the comparisons are -9 or -1 with -5 (where - is whatever) that could have an effect.

But that is, as you say, going to be a visual encoding issue. I still feel something else must be happening.

I wonder if it could be a further comparison issue whereby we find it easier to compare smaller numbers than large? It is know, for example, that 4 or 5 objects are the maximum amount that can be recognised in a glance without counting (as a general rule). And similarly it is know that even babies seem to be able to recognise the difference of 1,2 or 3 items. Maybe our brains have a specialised or more practiced comparator routine for small numbers?

All very interesting.

Having briefly considered this, is there any way of knowing which number is assessed first? This is presumably going to be related to eye scanning.
Could this have any relation to R/L handedness, RT/L eye dominance, any other factors eg dyslexia

Thinking particularly about the comparison 41/45 compared with 45/49, if the two 4s are quickly dismissed, perceiving 1 indicates that this is likely to be the lower number (only 0 will be less). Perceiving 5 is too open to gauge, whereas 9 must be the highest (so why was this assessment slower?)

I suspect there are other factors involved here.

"is there any way of knowing which number is assessed first?"
depends what you mean.
One of the things we checked for was whether the order of display had any effect.
I.e. is the response time for evaluating
45 49
different to the response for
49 45

and the answer is no - well, slight difference but not statistically significant. I guess it would be interesting to see if that changed with distance between the numbers so that both were not in the fiueld of view, but then you are testing for peoples preference of whether to look left or right first and there may be a degree of 'anything for a change' to that decision!

Just a thought, but the physical representations of the numbers themselves (font and kerning) may affect their perceived assessment?

Your assumption that the decade doesn't matter when comparing 41 to 45 and 45 to 49 is one that demands to be tested. Yeah, logically it's irrelevant but psychology wouldn't be half as interesting nor half as fun as it is if the brain worked logically all the time.

One idea that occurs to me is that in comparing 41 with 45, both four and one are smaller than five, whereas comparing 49 with 45 the four is smaller but the nine larger, which could result in a Stroop-like effect. You quote average response times for out-of-decade comparisons, is the 20ms difference statistically significant? It's interesting that even in that example, comparing 21 with 45 (where both digits smaller than 4 and 5) takes less time than comparing 29 with 45 (where one digit is smaller and one larger than both 4 and 9), suggesting that the unit figures are not totally disregarded and the Stroop-like effect is working on multiple levels.

Have you got data for other in-decade comparisons, e.g. 51 and 59 with 55, and 61 and 69 with 65?

hmmm, yes, I had wondered about cross interference between decade and unit comparisons like you suggest. Not sure why this would happen but as we don;t know the mechanics it could well be the case. I could phrase it in the discussion as further research

" You quote average response times for out-of-decade comparisons, is the 20ms difference statistically significant?"
Not sure, ain't got access to my results at the moment (shame really, have the file but not SPSS!) I don't think it is but can't recall the figures at the moment. When i originally did the analysis I only looked for significance of the stroop like effect ignoring the within/without decade difference and the result of that was significant. I think the analysis I did was purely whether or not the within decade/without decade difference was significant and it was.

I know that the interaction between the stroop-like and within decade categories is significant.

"Have you got data for other in-decade comparisons, e.g. 51 and 59 with 55, and 61 and 69 with 65?"
Yep, the results above are averaged across all 6 comparisons.

"comparing 21 with 45 (where both digits smaller than 4 and 5) takes less time than comparing 29 with 45 (where one digit is smaller and one larger than both 4 and 9), suggesting that the unit figures are not totally disregarded and the Stroop-like effect is working on multiple levels."

Very true, but that is the main stroop like effect we were investigating where 9>5 conflicts with the 2<4 giving the stroop like effect.

I think your comment though about decade less than unit and unit greater than unit is worth some further thought though and see if I can tease any more detail out of the results. Really needs another experiment though.

I'm trying to have a think about this, but I have a few questions first.

What were the participants actually told to do? What were you asking them to respond to?

Was the presentation order of the number pairs the same for all participants or did you randomise/counterbalance? How many pairs did each person look at?

I've had to summarise but it makes sense to me this way!

----------------------------
Aim: To investigate factors involved in how human beings compare 2-digit numbers represented externally on a computer screen to decide which number is smallest.

Hypothesis: There will be a difference in response time when comparing a pair of two different 2 digit numbers to decide which is smaller. (non directional) Comparison between numbers from the same decade will be faster than those from different decades. (directional)

Method:


Results: There is significant delay in response time when deciding which of two 2 digit numbers from a pair is smaller if the pair is from the same decade.
There is further significant delay in response time when deciding which of two 2 digit numbers from a pair from the same decade is smaller, if the individual digits that are second in the number vary in the opposite direction to the first digit.

Conclusion: Comparing numbers of different decades (eg 21 with 45) is significantly faster than comparing numbers of the same decade (eg 41 with 45). This delay is significantly enhanced where the individual digits that are second in the number vary in the opposite direction to the first digit (eg 29 with 45).

It is suggested that individuals compare 2-digit numbers by comparing the individual digits in parallel and then combine at the end to come up with a result - looking at the individual digits and then combining the results and applying a weighting where the individual digit results differ (ie the 25 result).

Further research:
_______________________________


There's a lot of speculation so your further research would have to be some kind of physiological method of tracking eye movement. Complicated but possible!

Also, did you use all numbers? Would a Stroop like effect be more noticable if you compared more visually similar first and secoind numbers, say 67 and 91?

Another thought. How long were the numbers displayed? Iconic memory is just that, a very brief store in the same sense as it was presented, so it would be possible to "see" the numbers after the display had gone. So,would you expect the same findings if the numbers were aurally presented? This would prevent parallel processing.

Oh but I hate writing the method and design section!

Participants - 24 individuals selected randomly from the attendees at the ou resi school. No balancing for age or male/female or anything else except to check for any dyslexia or dyscalculia.

Each participant sat in front of a computer screen and keyboard. The computer was running the experiment using ePrime.
Actual process:
Pairs of numbers were displayed on screen. The numbers were displayed in a yellow arial 24pt font on a black background (for contrast/visibility and to reduce strain on the eyes). After some intro screens and a 'press space to start' Number pairs were displayed side by side with approx 3 inches or so between them
(ie. 45 41 but scaled up as it were).

Participant had to then decide which number was larger and press the 'x' key for larger on the left or 'm' for larger on the right.
Response time from display of the numbers to pressing of a key was recorded.
When a key was pressed a blank screen was displayed for 500ms and then the next number pair.

The number pairs consisted of a list 3 targets and 16 comparators.
The three targets were 45, 55 and 65.
The comparators were 19,21,29,31,39,41,49,51,59,61,69,71,79,81,89,91

The reason for this is that the -9/-1 choices would offer the greatest numerical distance from the -5 of the target and thus provided the strongest stroop like interaction (should it be there).
The range of 11-99 was chosen as a) don;t want to use 09 or similar and b) because 55 is midway between 11 and 99 thus we wouldn't skew the results by having more numbers 'higher' than 'lower' than the median target. Equally 45 and 65 were chosen as alternative balancing targets and because where 45 had more above than below, 65 had equally more below than above (ie on average all the targets had as many above as below).

Each comparator was paired up with each of the targets generating 3 lists - one with each comparator with 45, then with 55, then with 65 giving 48 pairings.

Two versions of these 3 lists were prepared - one with the target on the left (so 45 21) and one with the target on the right (so 21 45). This gives 96 pairings.
These lists were then duplicated so each one of them was presented twice giving 192 pairings.

For presentation the 196 pairings were split up into 4 blocks - (can't quite remember how they were divided up but the upshot was that you'd get a mix of left/right I think).

Between each block of 48 pairings there was a break so the participant could rest and stretch and the experiment only started again when they hit the space bar (although it did then jump straight in - would have been better with a count down or something to prep them).

Equally it would have been better to counter the fatigue effect by having the 4 blocks of unequal size so that they got shorter as you progressed.

Design was within-participants so each participant did exactly the same set of number comparisons (all 192 of them) although due to the random presentation they will have done them in a different order within each of the 4 blocks.

Each sitting took between 5 and 10 mins depending on speed of response and familiarity with computer.

Thanks for that coelacanth, very helpful, will reply properly in a moment as doing something convoluted at work!

Ictoan working?

yeah, yeah, I know, I have to sometimes

Was going to post the actual averages for the three IVs (sequential order (ie biggest L or R), Stroop like (or not) and in-decade (or not)) so you could see the averages coelacanth - but it appears that SPSS .spo files are proprietry format and I can't read them here at work. Ah well.

If you are interested, let me know and I'll post them later.

Sssh, I'm supposed to be working too! Of course I'd be interested, but I don't get to check here much, so if it looks like I'm ignoring it for a few days, it's because I'm getting ready for the new term.

ah, fair enough, no probs!

darn, never posted the detail, ah well. Thanks for the input all anyway.

Only 437 words to delete and I'm there. Time to delete all the posh words, explanations in parentheses and waffle! Or at least all the 'a' 'it' 'is' 'and' and so on. Will read like txt speak by the time I've done I think!