Investigate people's judgement of measurements.

Authors Avatar

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. The closer to the pin they are allowed to get, the less individual judgement is involved and the more likely cheating will occur. To combat these effects I have elected to enforce a minimum of 100mm between the target pin and the candidates mark.
  3. Candidates must keep their eyes at the level of the tabletop

The experimental set up is shown in Figure 1.

The results of the individual estimates will be recorded and compiled into a computer database.


Figure 1 :  Experimental  Set up

Hypothesis

To predict outcomes in an investigation such as this is very difficult as individuals vary markedly in their ability to judge distances. However a few predictions are possible albeit rather sketchy and basic.

I predict:

  1. whether the individual is right or left handed will have no effect on judgement of distance
  2. individuals who wear spectacles, other than for reading, will have better judgement when wearing those spectacles than without
  3. on average girls will be more accurate than boys because girls tend to be more precise, thoughtful and careful

There will be individual anomalies to the above predictions as peoples judgement is a personal attribute and also luck will be a random factor.


Sample 1

Data: Right or Left handedness

I have calculated from the database that there are 25 left handed and 150 right handed people. As this is a ratio of 1:6 then to have equal sample populations I have sampled every sixth right handed person. Each candidate’s three results, using both eyes individually and together, when using both their right and left hand have been recorded, and the sums of results are displayed in this table.

Table 1 Distance estimates in mm (sum of estimates from left, right and both eyes)

My initial inspection of Table 1 results suggested that the average results in each column supported my first prediction that there would be no significant difference between right or left handed people. However inspection of the component results reveals such a wide spread of values that such a conclusion is unsafe. I have therefore decided to display my results in a ‘stem and leaf’ diagram. From this presentation I can calculate inter-quartile ranges and transfer the data into a ‘box and whisker’(see Fig 2 and Fig 3)

Join now!

Table 2   Stem and Leaf diagram for Right handed people

Table 3   Stem and Leaf diagram for Left handed people


Sample 2

Data: Effect of wearing spectacles

To test my second prediction that those who wear spectacles, other than for reading, will better judge distance whilst wearing their glasses than when not, I will take every candidate who wears spectacles, 30 in total, and compare their data measured both with and without their spectacles on. Again this test used three estimates ie when using both and individual eyes (right first) but ...

This is a preview of the whole essay