Counting Beans

Dr. Timothy BenderPsychology DepartmentMissouri State University901 S. National AvenueSpringfield, MO 65897

Counting Beans

In 1871, Jevons wanted to determine how many items he could perceive accurately in one brief glance at a stimulus. Specifically, he wanted to know how many items he could detect without consciously counting them. He assumed that the mind engaged in parallel processing of the number of objects, at least if the number was small enough. At that time, the estimates ranged from 4 to 6 items.

Counting Beans

In order to study this question, Jevons would throw a handful of beans at a small box. He would then glance swiftly at the box and try to estimate how many beans were in the box. He then counted the actual number and recorded his estimate with the real number. He did this more than 1,000 times!

Counting Beans

We will try something similar. However we first need to operationally define what a ‘glance’ will be. In this demonstration there are two glance times. Some occur for 167 milliseconds and some for 333 milliseconds. This will allow us to compare a short glance with a slightly longer glance.

Counting Beans

Please prepare a response sheet consisting of the numbers 1 through 40 written on your paper.

Counting Beans

For each of the next 40 slides you will see a + sign in the middle of the screen for about 1 second. That will be followed by an image of one or more beans. The image will appear for either 167 milliseconds or 333 milliseconds. Record the number of beans you think you saw.

OPERATING HINT: To continue from trial to trial make sure your cursor is near one side of the slide before you click for the next stimulus.

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

Trial 6

Trial 7

Trial 8

Trial 9

Trial 10

Trial 11

Trial 12

Trial 13

Trial 14

Trial 15

Trial 16

Trial 17

Trial 18

Trial 19

Trial 20

Trial 21

Trial 22

Trial 23

Trial 24

Trial 25

Trial 26

Trial 27

Trial 28

Trial 29

Trial 30

Trial 31

Trial 32

Trial 33

Trial 34

Trial 35

Trial 36

Trial 37

Trial 38

Trial 39

Trial 40

Counting Beans

The following are the correct answers for the 167 millisecond slides. Count the number of times students were correct. Record those scores.1. 2 beans 7. 3 beans 12. 7 beans 22. 5 beans

2. 9 beans 8. 6 beans 15. 7 beans 28. 8 beans

4. 9 beans 9. 3 beans 16. 5 beans 29. 4 beans

5. 10 beans 10. 4 beans 17. 10 beans 30. 8 beans

6. 1 bean 11. 2 beans 21. 1 bean 40. 6 beans

Counting Beans

The following are the correct answers for the 333 millisecond slides. Count the number of times students were correct for each number. Each student could be correct twice for each. Record those numbers.3. 1 bean 20. 5 beans 27. 3 beans 35. 7 beans

13. 2 beans 23. 9 beans 31. 3 beans 36. 6 beans

14. 1 bean 24. 9 beans 32. 6 beans 37. 4 beans

18. 2 beans 25. 7 beans 33. 10 beans 38. 5 beans

19. 4 beans 26. 8 beans 34. 8 beans 39. 10 beans

Counting BeansThis table shows Jevons’ percentage correct when the actual number of beans ranged from 3 to 15. (Sorry about that 120 percent . I have no idea how to

tell PowerPoint not to do that!)

0

20

40

60

80

100

120

3 4 5 6 7 8 9 10 11 12 13 14 15

Actual Number of Beans

Perc

en

tag

e o

f C

orr

ect

Esti

mate

s

Counting Beans

Jevons felt that the number of items a person could perceive in a single glance probably would vary from person to person. However, his own data suggested that an estimate of from 4 to 6 items was likely. His own limit was between 4 and 5, which is very close to the estimate offered by Sperling (1960), based on data collected using the whole report method.

Counting Beans

Jevons also tended to over-estimate the smaller numbers and under-estimate the larger ones.

Counting Beans

If you compare the number of times students in class were correct to Jevons’ own data, you will probably find a similar curve. For small numbers, many students were correct. For larger numbers, very few students were correct.

Counting Beans

Finally, if you compare the data for the 167 millisecond ‘glance’ with those from the 333 millisecond ‘glance,’ you might see better performance for the longer glance. It is possible that with the longer glance, you were able to group the larger sets of beans into smaller sets of 3, 4, or 5. In other words, you had time to engage in some basic chunking of the perceptual information.

Counting Beans

Data such as these do not tell us how much information we can perceive in a single glance, but they do suggest that we can perceive small numbers of stimuli as a single unit and that we may not have to consciously count the stimuli in order to discriminate quantity.

References

Jevons, W. S. (1871). The power of numerical discrimination. Nature, 3, 281-282.

Sperling, G. (1960). The information available in brief visual presentations. Psychological Monographs: General and applied, 74, 1-29.