With so few results, a single result of useless data may alter my outcomes significantly. Because of this, I will be forced to make sure the correct information type is written on the questionnaire. I will place myself next to each of the surveyed while they fill out their details and information to ensure that non-responsive data is not entered. If anything is left out, I will be able to contact the person again, as I will have their name and class.
Bias: To subconsciously influence the outcome of results through wording or through sampling is bias, and it will alter the outcome of the entire investigation. To prevent this as best I can, I will survey each student personally, to ensure that s/he is not influence by his or her peers nor has any access to measuring equipment. I mainly chosen these odd figures, as people often give inaccurate guesses by simply rounding off estimates. This from of bias was not realised before the investigation. As the three classes are taught to the same standard of mathematics, neither of the classes will be more familiar to a measurement. I am introducing bias, as I am ignoring staff members, those in any other Year and those who are not in Jerudong International School. However, due to limitations and time frames, I could not deal with a larger population.
Sampling: As I must question each of the mathematics classes within relative proportions, to ensure that an accurate amount of students is measured. For this, I will use stratified sampling to obtain the correct proportions, however each class (strata) contains 20 students exactly, which is to my advantage, as I only need to calculate once. For the gender issue, I have simply chosen to ask 50% male and 50% female subjects. I will also use systematic sampling for the actual subjects
(See below).
To obtain the names of the subjects, class registers will be placed in alphabet and divided into males and females. From the calculation above, I have worked out that I need every second student, as 10/20 is half of the sample. I will choose every 2nd name on each list to get my candidates. To produce graphical outcome, I will use a computer-based spreadsheet program. Microsoft Excel was chosen, as it ideally calculates and process data more effectively than people, as well as its ideal graph making utilities.
Data Collection cont’d: The data will be collected twice, for accuracy and efficiency. The subject will be handed out a sheet of paper (Fig 1) with an angle (69 degrees) and a line (13.9cm) drawn, without the measurements, and they will be required to estimate to the best of their ability. I will stand next to each one to record the estimates on my own data collection sheet (Fig 2) for efficiently in results processing, as well as to disallow any cheating, which is a form of bias.
In any doubt, the respondents’ questionnaire paper will be used as the correct answer.
Fig.1 Data Collection Sheet for Respondent
Subject No. 1
Name: _____________ Class: A B C
Gender: Male Female
Please estimate the following line and angle, to the best of your ability.
Fig. 2 Data Collection Sheet for me
Etc..
Table of Results: Note: Placed in Descending Order
Gender not included, as of c no importance
The estimation data has been ranked into descending order for the cumulative frequency table.
Hypothesis i: The estimation of the line will be more accurate than the estimation of the angle. The following tables were used to construct a cumulative frequency graph. Using the inter-quartile range, (calculations on Graph 1), you can see that the measure of spread on the length estimation is closer together than the angle estimation. This shows that, overall, the lines were estimated and grouped closer to the right answer than the angle estimates. I use the inter-quartile range (See graph 1) to ignore any extreme or boundary data, which these results can be anomalous. To include them in my calculations may severely alter my results. The anomalies are circled.
I will also use the mean difference to determine which was most accurate. As they use two different units, the only way of comparing results would be to compare the two as percentages of inaccuracy. The following calculations do this:
The accuracy of the line estimates was at a higher level than the angle estimates when I used the percentage comparison results, as well the cumulative frequency graph.
My hypothesis was correct, which is proven from both the cumulative frequency graph, as well as the percentile of accuracy of both.
Hypothesis 2: The female angle estimation will be more closely populated to the correct answer than the male estimations. The measure of spread is the range of data and is to be calculated to prove my hypothesis. Standard deviation will be used, with the following key fact in mind:
68% of the estimations lies within one standard deviation.
The formula for standard deviation is
Symbols:
is the sum of …
is the average of x and is worked out through the averaging of the total estimation errors.
The tables (See attached sheets) are broken down to show the progress of calculating standard deviation. The following calculations for have not been shown on the table.
is worked out through the averaging of the total estimation errors.
= Total inaccuracy ÷ number of candidates
Male: = 93.5 ÷ 15 = 6.23
Female: = 105 ÷ 15 = 7
The graphs show that the female estimation was more closely population than the male estimation, which is shown through the smaller standard deviation. This means that the females had overall estimated closer to the correct answer
I reject my hypothesis, as the opposite was in fact true. From the work above, I have deduced the following:
The Year 10 male angle estimation is more closely populated to the correct answer than the male estimations (in JIS).
Conclusion:
Hypothesis i: Correct. The estimation of the line is more accurate than the estimation of the angle. The two methods of proving my hypothesis both proved me right. The cumulative frequency graph shows how the line estimation was estimated better than the angles, generally. Anomalies were not considered in the final results. The percentage of accuracy was also proving to my advantage.
Hypothesis ii: Corrected. The Year 10 male angle estimation is more closely populated to the correct answer than the female estimations (in JIS). The male angle estimations (S.D. = 3.0) calculated to a figure almost twice as small as the female angle estimations (S.D. = 4.7). The spread of data was smaller for the boys, which shows that their range of data was closer to the correct answer.
My investigation only examined the Year 10 mathematics classes, which is effective enough it is mandatory to take mathematics as a subject. Therefore I correctly the Year levels estimation skills, however I investigated only half of the students, as time was disallowing larger samples from being collected. Another limitation was the students who did not take the survey seriously and thus, gave untrue estimates from the best of their ability. This would have led to anomalies.
To improve my investigation, I would add another measurement for comparison, possibly volume, however this would be more appropriate for higher students. I would ask staff members and other Year level students to widen my range. Due to this increase of candidates, I would simply pass around two sheets of paper, one with the diagrams and the other with a space for their answers. However bias would again be introduced as they may look at previous estimates and change their own estimate. I would individually survey everyone to prevent bias results.