Investigate peoples judgement of measurements Essays

Investigate peoples judgement of measurements Essays Investigate peoples judgement of measurements Essay Investigate peoples judgement of measurements Essay I have decided to investigate peoples 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 candidates 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) Right handed people Left handed people Right hand Left hand Right hand Left hand 22.5 44 98 35 63 31 21 17 43 42 45 26 83 73 36 48 81 50 25.5 46 38 115 4 9 7 7 42 54 46 24 13 30 82 59 24 22 43 9 23 21 0 2 53 100 10.5 20 34 30 15 12 31 11 50 34 34.5 5 34 18.5 40 33 21 28 25 22 32 31 56 61 78 22 10 30 13 47 18 12 22 24 16 36 39 22 42 53 40 29 28 7 29 36 3 3.5 38 17 94 75 17 23 36 53 TOTAL: 947 819.5 852 839.5 MEAN: 37.88 32.78 34.08 33.58 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) Table 2 Stem and Leaf diagram for Right handed people Right hand estimates Left hand estimates 7,0 0 2,7,9 7,5,3,0.5 1 2,7,8.5 9,2.5,2,1 2 0,2,2,3,4,4,8,9 9,8,8,4,2 3 1,1,4,6 6,3,3,0 4 2,4,7 0 5 0,9 3 6 8 7 3 3,2,1 8 9 10 11 5 1QR: (25 + 1) = 6.5 4 1QR: (25 + 1) = 6.5 4 Therefore 48 19 = 29 Therefore 43 19.25 = 23.75 Median = 38 Median = 28 Mean = 37.88 Mean = 32.78 Table 3 Stem and Leaf diagram for Left handed people Right hand estimates Left hand estimates 4,3 0 3.5,5,7,9 8,6,3,0 1 1,2,7 8,5.5,5,4,3,1 2 1,2,2,6 6,6,4.5,4,1 3 0,0,0,3,5,6 5,2,2,0 4 6,8 6,3 5 3,4 6 1 7 5 8 8,4 9 10 0 1QR: (25 + 1) = 6.5 4 1QR: (25 + 1) = 6.5 4 Therefore 42 19.5 = 22.5 Therefore 47 14.5 = 32.5 Median = 31 Median = 30 Mean = 34.08 Mean = 33.58 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 using their favoured hand only for marking. The summed results are displayed in table 4. I will then transfer this data into a scatter graph, plotting data with glasses on against data without. This transfer is to demonstrate whether my prediction is valid. If it is correct there will be a positive correlation and the line of best fit will have a gradient less than 45à ¯Ã‚ ¿Ã‚ ½. The prediction will not have been validated if there is no correlation or a line of best fit is above 45à ¯Ã‚ ¿Ã‚ ½. Table 4 Distance judgement of spectacle wearers (sum of 3 estimates in mm) With Glasses on Without Glasses on 14 7 17 38 41 23 20 23 10 8 23.5 33.5 41 42 20 6 9.5 19 4 3 7 7 12 9 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 candidates judgement of distance, it is their eyes. As you can see from my results this apparently is the case. There is no conclusive difference between Left or Right handed people. There is more variation between the hand being used to estimate than there is between Left or Right handedness. The Right handed sample shows both the best and worst results. Another point that my data sample shows is that in both cases the mean result is less with the left hand (whether that is the candidates preferred hand or not). However this could be explained by the fact that the trial with the candidates left hands was made after that of their right. Because it is after I can put this down to the fact that they have realised if they are aiming too far or falling too short and therefore they adjust using common sense so they improve their score. This is not true in all cases and in future trial the candidates should: a) Not be allowed to stand up between estimates (or potentially view the table). This could be prevented by screening the table top and only having eye holes in the screen at the viewing level. b) Not be told what their previous Right hand result was. This should combat the problem and make the way for a fairer test. To help verify my original prediction, I shall take a different sample of right handed candidates (I can not do this for the left handed people as there arent enough) and repeat the comparison with the original Left Handed results. In this sample, instead of taking every sixth persons results I shall sample every fifth right handed candidates data. The results have been tabulated in Table 8 in the same way as table 1 and the data displayed in the same Stem and Leaf format in Table 9. From the two sets of data I will be able to confirm these conclusions by comparing the data samples. Table 8 2nd Test: Sample 1 Right handed people Left handed people Right hand Left hand Right hand Left hand 6 8 98 35 81 69 21 17 21 23 45 26 22 30 36 48 76 18 25.5 46 11 12 4 9 46 10 42 54 14 2 13 30 10 3 24 22 13 7 23 21 12 12 53 100 16 40 34 30 6 8 31 11 29 32 34.5 5 14 25 40 33 11 49.5 25 22 11 5 56 61 27 17 10 30 5 6 18 12 31 22 16 36 11 25 42 53 4 3 28 7 24 8 3 3.5 60.5 45.5 94 75 42 17 36 53 TOTAL 603.5 497 852 839.5 AVERAGE 24.14 19.88 34.08 33.58 Table 9 2nd Test. Sample 1: Stem and Leaf diagram for Right handed people Right eye Left eye 6,6,5,4 0 2,3,3,5,6,7,8,8,8 6,4,4,3,2,1,1,1,1,0 1 0,2,2,7,7,8 9,7,4,2,1 2 2,3,5,5 1 3 0,2 6,2 4 0,5.5,9.5 5 0.5 6 9 6 7 1 8 1QR: (25 + 1) = 6.5 4 1QR: (25 + 1) = 6.5 4 Therefore 30 11 = 19 Therefore 27.5 7.5 = 20 Median = 14 Median = 17 Mean = 24.14 Mean = 19.88 The Stem and Leaf formats clearly show the shape of the distributions and, because I was comparing the distance from the target point with both the left and right hand I felt it was more explanatory to display the comparison in this way. The data that was displayed in the Stem and Leaf diagrams can be transferred into Box and whisker diagrams to display the spread of data and how it is distributed across the range. The 1st test of sample 1 is shown in Fig 2 for Right handed candidates and Fig 3 for the Left handed. The 2nd test of sample 1 is shown in Fig 4 for Right handed candidates only. These confirm the spread of results is such that any effect of handedness affecting judgement of distance is inconclusive. Conclusions for Sample 2 2. Whether the candidate wears glasses For this example I predicted individuals who wear spectacles, other than for reading, will have better judgement when wearing those spectacles From the table alone it is clear to see that my prediction has been proved correct, this is evident from both the total, and the mean result: With Glasses On Without Glasses On TOTAL: 344.5 410.5 MEAN: 11.9 14.2 It is shown by this that on average spectacle wearers estimates are over 2mm closer with their spectacles on. Despite my predictions being proved correct I am a bit surprised to see that the effect of spectacles is only (on average) 2mm better. I would expect them to have a greater influence. Maybe glasses influence the clearness of objects more the further they are away. Alternatively it may be influenced by the individuals optical deficiency being either long, short or asymmetric. However, as I do not wear spectacles I can not be sure of this effect. As an extension to this I could see who was most greatly influenced on the judgement of distance, long sighted people or short sighted people. Unfortunately the occurrence of suitable sighted candidates from this database would be too small to draw any significant conclusions. The data from Table 4 was plotted as a scatter graph as Figure 5. To transfer the data from table to graph I did not need to draw any other tables or charts. The reason I chose to plot a scatter graph is because I wanted to show whether glasses influenced a persons judgement of measurement. I knew that if the line of best fit was of less than 45à ¯Ã‚ ¿Ã‚ ½ gradient my prediction would be proved correct. This proved to be the case although considerable scatter (variability of results) was evident. Conclusions for Sample 3 3. Girls are more accurate than boys For this sample I predicted that on average girls will be more accurate than boys because girls tend to be more precise and careful From the table 5 it is evident once more that my prediction has been proved correct as shown by both the total, and the mean: Boys Girls TOTAL: 707 528.5 MEAN: 23.6 17.6 The results show that girls are (from the mean result) 6mm better than boys. From the table I have plotted the following graphs: Fig 6 Frequency density diagrams, showing the spread of data across the range for both male and female candidates, this also made a comparison possible. Figs 7 Cumulative frequency diagram, displaying how the frequency changes as the data values increase. I could also use this to get a closer value for the median. From Fig 6 it is evident that there is a higher frequency density of closer estimates for girls than boys. This is followed by a lower frequency density for the girls than boys, further away from the target. This is more apparent from Fig 7 where the girls cumulative frequency is well separated from the boys I am able, in this case, to take another sample (as there are enough boy and girl candidates) and confirm or disprove my prediction and first set of results. If this second sample agreed with my first I could conclude that my prediction is true. On the other hand if this second sample went against my prediction I could investigate this further, possibly by creating a different database. The results of this second test are shown in Table 10. 2nd Test: Sample 3 Table 10 Distance judgement by Girls compared with Boys (Sum of estimates mm) Boys Girls 6 8 4 20 13 13 29 6 33 8 19 13 19 23 16 12 22 50 4 4 3 34 63 5 20 10 42 6.5 24 16 13 16 13 11 12 11 3 31 53 12 1 5 34 20 44 19 15 5 46 40 10 14 35 3 39 10 14 12 7 14 TOTAL: 656 451.5 MEAN: 21.8667 15.05 Boys(fx) Girls(fx) Sum Boys (fx) Sum Girls (fx) 0 10 8 11 8 11 -20 10 14 18 25 -30 3 1 21 26 -40 4 3 25 29 -50 3 1 28 30 -60 1 0 29 30 -70 1 0 30 30 -80 0 0 30 30 -90 0 0 30 30 Sum fx 30 30 The cumulative frequency for this data has been plotted in Fig 8 with a similar result to that shown in Fig 7. The results appear so consistent I have compared both sets of girls data in Fig 9 and of boys in Fig 10. As can be seen, the respective lines of best fit agree very well between the tests. This would indicate also that the investigation on the whole was a success, due to the consistency shown throughout the data. Overall Conclusions I have carried out three tests of candidates Judgement of Distance. By summing the three estimates, using both eyes together and the eyes individually, I have eliminated any preference candidates may have for a favoured viewing technique. Usually both eyes together by focusing on a single target from two sides should give a better estimate than each of the eyes used individually. This would enable an extension to the work by comparing estimates using each of the three viewing conditions. 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.