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# Investigate people's judgement of measurements.

Extracts from this document...

Introduction

Nathan Hart        Maths Coursework        22 FEB 2003

Statistics Coursework:

Judgement of

Distance

By Nathan Hart

Judgement of Measurements

Object

I have decided to investigate people’s judgement of measurements as the subject for my Statistics Coursework.

Before starting this experiment I needed to define guidelines that would establish the fairness of the tests method of assessment. The method I chose to fulfil this requirement was to:

1. Place the test candidates at one end of a table with their eyes level with the table-top
2. Ask the candidates to look horizontally across the table at a pin located at a fixed position in the middle of a sheet of graph-paper [see diagram 1].
3. Require the candidate to mark (on the graph-paper) that distance where they thought the pin was located (firstly marking using their right hand, and then their left). Viewing, per hand, is firstly using both eyes followed by each eye individually, right first.  The difference between the estimated and the actual position of the target pin is measured for each of the eye conditions. These 3 results are added together to give the final result.

This method creates two problems:

1. How the candidate should mark the point which they feel is in line with the pin. I have chosen to use a pin as a marker since I feel it both represents the object they were viewing and gives a greater degree of accuracy than a pencil mark.
2. How far to the side from the target pin should the candidate mark the graph-paper.

Middle

3

2

17

8

12

6

15

10.5

13

15

26

15

12

6

11

22

* Denotes anomalous results which have been disregarded for the purposes of the graph, table totals and averages. This was thought a result of ‘seeing’ the target between tests with and without glasses on.

22

23

21

8

131*

8*

13.5

18.5

44

14

3

9

3

9

20

9

16

20

5

5

TOTAL:

344.5

410.5

MEAN:

11.9

14.2

Sample 3

Data: Girls judgement compared with that of Boys

To test whether girls are better judges of distance than boys I will compare every fifth boy and girl results when using their favoured hand. Candidates must not be spectacle wearers, as we would then be introducing another variable. The data shown is the total score of the candidates three estimates using their preferred hand.

Table5   Distance judgement by Girls compared with Boys (Sum of estimates mm)

 Boys Girls 52 81 21 44 13 14 29 6 33 9 19 5 19 20 16 4 22 12 18 50 11 19 20 5 39.5 40 6.5 14 27 6.5 20 16 40 16 20 11 0 11 53 5 1 4 6 12 4 17 76 40 18 3 5 12 59 13 4 11 28 8 27 20 TOTAL: 707 528.5 MEAN: 23.6 17.6

The data from table 5 has been grouped here into a second table 6. The reason for me doing this is so that I am able to then transfer the data in table 6, firstly into a frequency density graph, and then cumulative frequency graphs from table 7.

Table 6  Boys vs Girls grouped into 10mm increments

 Mm Boys(f) Girls(f) x (midpoint) Boys(fx) Girls(fx) 0 – 10 7 10 5 35 50 -20 10 15 15 150 225 -30 6 0 25 150 0 -40 3 2 35 105 70 -50 0 2 45 0 90 -60 3 0 55 165 0 -70 0 0 65 0 0 -80 1 0 75 75 0 -90 0 1 85 0 85 Sum fx 30 30 ∑ fx 680 520

Table 7  Cumulative frequency

 mm Boys Cf Girls Cf 0 – 10 7 10 0 – 20 17 25 0 – 30 23 25 0 – 40 26 27 0 – 50 26 29 0 – 60 29 29 0 – 70 29 29 0 – 80 30 29 0 – 90 30 30

Cf – Cumulative frequency

Conclusions for Sample 1

1. Whether the individual is right or left handed

For this sample I predicted that handedness will have no effect on judgement of distance.

I made this prediction because the hands have nothing to do with a candidate’s judgement of distance, it is their eyes. As you can see from my results this apparently is the case.

Conclusion

The tests I applied examined:

• Firstly, the effect of an individuals handedness. My measurements, including a repeat second test, when analysed by tables of comparison, stem and leaf and box and whisker diagrams confirmed my prediction 1. There is no conclusive difference dependant on handedness. There was however considerable individual variability between candidates confirming my hypothesis that estimation of distance is an individual attribute.
• Secondly, estimates of distance by candidates requiring spectacles would be better when wearing their spectacles than when not. My measurements did indicate estimation of distance was better when wearing their spectacles. A line of best fit from a scatter graph supported this conclusion although again there was considerable variation of estimates.
• Thirdly, that girls would be better than boys at estimating distances. My measurements, including a second test, clearly supported this conclusion. The results were probably the most conclusive of all the tests. Superimposed graphs of the two tests for the Boys and Girls showed very good reproducibility of these results although individual estimates varied widely in both groups. However the Boys showed the greatest variation further supporting the conclusion that, on average, girls are better at estimating distance.

Whilst the indications are all my predictions have been shown to be apparently correct, the degree of variability from individual results makes absolute conclusions difficult. In any extension of the work I would try and increase the size of the test population database. This would increase the confidence in the conclusions.

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