Study the effects of number characteristics on human response

1. Study the effects of number characteristics on human response Group 10 Zhaoxueming Sunda JiangYiqing WangBing ZhangBingfeng

2. Guinness world record for sudoku(数独): • Is the completing time totally determined by the IQ or response of • humans? • Is there any potential unfair factors?

4. In the three sudoku games, if the color, size or font of numbers are different, can it influence the response of people? • At last, we determine our experiment is: Study the effects of number characteristics on human response

5. number Related Articles • 2003/6《Nature Neuroscience》 Fisher If the number is 1 or 2, people react quicker to the left box If the number is 8 or 9, people react quicker to the right box

6. Human factors in Engineering and Design, seventh edition In the fourth chapter, it tells about how color, size, font and layout can influence human’s visual perception and response. • The color psychology shows that color can affect the emotion and the brain's reaction of human.

7. The conceive of our experiment • We will use java to randomly generate 1 to N, then remove a number. The order of the numbers is random. • The experimenter must write out the absent number in the shortest time. So, why do we choose java to do our experiment?

8. Reasons to use java • We can accurately record the response time: use timer in the java • We can store the data automatically, reducing the human error of copying data. • The experiment is expandable. • It is convenient for experimenters, just pressing the keyboard is ok.

9. Fish-bone diagram

10. Response variable

11. Control variable

12. “Held constant" variables

13. Nuisance factor

14. A full factorial design

15. Descriptive analysis • Almost all experimenters can have a correction ration of 100% or 97.9%. • There are only one whose correction ratio is less than 90%.

16. Descriptive analysis • For all the experimenters,the average response time is nearly normally distributed. • It is mostly distributed between 3200 and 5600ms.

17. Descriptive analysis • The fastest three experimenters • Blocking Effects: From the descriptive analysis, we can predict that blocking will play an important role in the data analysis.

18. Analysis for response time • There are two response variables : response time and correction ratio • First, we do the analysis for the response time Residual Plot of response time

19. Box-Cox transform Lamda=0: y  lny

20. After transformation The residuals is normally and iid distributed.

21. Main effects plot for ln(response time)

22. Interaction plots for ln(response time)

23. The effect analysis

24. In our experiment, every experimenter is a block. • The blocking effects is important. If we construct the linear model, it can just fit the 24 experimenters. • At first, we want to calculate the average value of the block coefficients and contain it into the constant. But asking Pro. Wang, we know this is not scientific.

25. The purpose of model Interpretation Prediction

26. Analysis for accuracy rate • Box-cox plot Lamda = 5 y  y^5

27. Main effects for (accuracy ratio)^5

28. Interaction effects for (accuracy ratio)^5

29. Robust Analysis Why I always meet some strange lost numbers while playing Sudoku?

30. Robust Analysis • Our goal is to find the optimal combination of different factors, so that the influence of lost numbers will be minimized. • Minimize the reaction time • Archive higher correctness rate

31. Robust Analysis • Taguchi Method • Control factors: color, size, font, arrange style • Noise factors: the lost number

32. Robust Analysis • The interaction may exist • Fonts and the lost number • Size and the lost number • Color and the lost number

33. Robust Analysis • Fonts and the lost number • Can you tell which number is lost? 60541973

34. Robust Analysis • Size of numbers 123489605 123489605 • Color of numbers 723489605132468907

35. Robust Analysis • Inner array color: 4 levels size : 3 levels font : 2 levels arrange style: 2 levels • Outer array Lost numbers: 10 levels • Total experiment time: 4*3*2*2*10=480

36. Robust Analysis • Descriptive statistics • We have found two brave volunteers! • Some compare

37. Robust Analysis • Descriptive statistics • Larger numbers may need more time • Great differences can be found between individuals

38. Robust Analysis • Taguchi Method • We want to minimize the response • SN ratio : smaller is better

39. Robust Analysis • Main Effects Plot for Means(小A)

40. Robust Analysis • Main Effects Plot for Means(小B)

41. Robust Analysis • Main Effects Plot for Means • The most important factor :color

42. Robust Analysis • Main Effects Plot for SN ratios(小A)

43. Robust Analysis • Main Effects Plot for SN ratios (小B)

44. Robust Analysis • SN ratios • We need to max the SN ratio. Using Excel, we got some combination quite like that suggested by the main effects plot. • Still too few samples : we need more data for better explanation.

45. Thanks!