Do People Know More About Their Life Aspirations As They Progress Through High School?

 

A study comparing two Proportions in order to discover if as people go into higher grades in high school, do they know more about what they want to do when they grow up.

 

By Chris Markham

Buckingham Browne & Nichols School

Cambridge MA

 

5/24/2002

Pre-Study

The purpose of this study is to discover if the 11th and 12th graders at Buckingham Browne and Nicholes School know which profession they would like to go in to when they grow up more so than the 9th and 10th graders. The population being sampled is the Upper School (grades 9, 10, 11 and 12) at Buckingham Browne and Nicholes school. A simple random sample of the two groups was taken and a p-value was computed. The population of 9th and 10th graders was 234, with the proportion of my sample who knew what they wanted to do when they grew up as 4/22. The population of 11th and 12th graders was 231, with the proportion of my sample who knew what they wanted to do when they grew up as 10/20. The p-value came out to be .014 through a 2 proportion Z-test of significance. Before this study was done it was predicted that the students in grades 11 and 12 would know which profession they wanted to go into when they grew up more than the students in grades 9 and 10 did. Though this was true, and the p-value was statistically significant, the non-response factor may have created uncontrollable bias. Due to the small population size the sample sizes were to small and the non-response factor may have created bias. I do not believe that these findings could be used to extrapolate to other schools across the country because BB&N is unique in its learning environment, though other Independent School League schools may be able to have these findings applied because they are so similar to BB&N.

Sampling

This study attempted to discover if the students in grades 11 and 12 new which profession they would like to go into when they grew up more so than the students in grades 9 and 10. This was done by taking a random sample from each group of kids (grades 9,10 and grades 11,12) and asking them if they knew which profession they wanted to go into when they grew up. The way this data was collected is as follows. The Buckingham Browne and Nicholes telephone book has a list of all the people in the upper school, sorted by grade and in alphabetical order. I took the lists of 11th graders and 12th graders and numbered them consecutively, having the 12th grader who is first in alphabetical order in his grade as number 1. Once I was finished numbering all the 12th graders I continued the numbering process starting with the first 11th grader in alphabetical order, and so on having the last 11th grader in alphabetical as the last number . The total number of grade 11 kids and grade 12 kids was 231, and because the population has to be 10 times the sample size in order to do a test of significance with proportions, the sample size was 23. To get these 23 kids, 23 random numbers between 1 and 231 were generated and used as the sample. The same thing was done for the grade 9 and 10 kids. In total there were 234 grade 9 and 10 kids, so again because of the technical conditions for the two-proportion test of significance, the sample size was 23. For every person in each of these 2 groups of 23 I put a questionnaire in their mail box asking them "Do you know what profession you want to go into when you grow up?" and prompted them to circle either "yes" or "no". I compared the answers of the 9th and 10th graders to the answers of the 11th and 12th graders in a two-proportion z-test of significance.

Significance Test of Equality of q (11,12) and q (9,10)

Ho: q (11,12) = q (9,10) The proportion of 11th and 12th graders who know what

Ha: q (11,12) > q (9,10) The proportion of 11th and 12th graders who know what

Requirements: Both of these samples are independently selected (meaning the outcome of one sample does not effect the outcome of the other) simple random samples from the population of interest (students at BB&N). Also phatC = 14/42 = 1/3 n(11,12) = 20 n(9,10) = 22

n(11,12) * phatC = 6.66 > 5 n(11,12) * (1-phatC) = 13.33 > 5

n(9,10) * phatC = 7.33 > 5 n(9,10) * (1-phatC) = 14.66 > 5

( Where: n(11,12) = The number of 11th and 12th graders sampled n(9,10) = The number of 9th and 10th graders sampled phat(11,12) = The predicted proportion of 11th and 12th graders who answered "Yes" phat(9,10) = The predicted proportion of 9th and 10th graders who answered "Yes" phatC = phat(11,12) + phat(9,10) , a weighted average )

2 Proportion Z-Test:

(phat(11,12) - phat(9,10)) / sq.rt. [ phatC * (1- phatC) * (1/ n(11,12) + 1/ n(9,10) ]

( 10/20 - 4/22 ) / sq.rt. [ 1/3 * ( 1 —1/3) * (1/ 20 + 1/22)]

( 140/440 ) / sq.rt. [ 2/9 * 42/ 440 ]

= 2.1846

Standard Deviation = .145643

 

This test of significance shows that the difference between the proportion of 11th and 12th graders who know what they want to do when they grow up compared to the proportion of 9th and 10th graders has a p-value of .01445 (where the p-value is the probability of this event happening by chance variation alone). This p-value is very low at 1.4%, and would in many cases, without response bias, be sufficient evidence to conclude that Phat(11,12) is significantly larger than Phat(9,10). Due to the non-response factor in this study we can not necessarily conclude that the difference between the two proportions is this large, but still, do to how small the p-value is, there is most likely a difference.

Weaknesses

This observational study had very large problems, which may have greatly affected the results and the conclusions coming from the results of this study.

The first problem I came across when in doing this study was the wording in which I put my question. The was I stated my question was "Do you know what profession you want to go into when you grow up?" and then had them either circle "yes" or "no"(see appendix 2). Though I tried my best to make my question the least wordy and confusing as possible, there still is a chance for different interpretations. For example, one person may know that they want to be a lawyer when they group up, but they are not sure whether they want to be a defense attorney or a prosecutor. Some people may consider this as knowing what they want to do when they grow up (because they want to be a lawyer), while others may say they do not know what they want to do when they grow up (because they do not know if they want to be a prosecutor or a defense attorney).

Another problem I came across that I was unable to change was the small sample size that I had to use. Because the two populations I was using to take my sample from (grade 9,10 kids and grade 11,12 kids) were small, one being 234 and the other being 231, I could not have a large sample because of the technical conditions for the two-proportion z-test of significance. This made it hard, especially after the people who did not respond, to have a sufficient sample size.

The final problem I came across, and the most major, was the issue of non-response. Due to the fact that my sample was taken by distributing a questionnaire, people had a choice whether to respond or not. Four people did not respond, and this created a possible bias that I was unable to control. This bias meant that no matter what my p-value came out to be I would have to question the validity of my study. This non-response also made my sample size smaller than I had originally planned which created more problems when looking at the two-proportion z-test of significance.

With more time I would have been able to do this study better. I could have spent more time finding the perfect question, and creating more specific directions, in order to eliminate any confusion when in answering the question. The issue on non-response could have possibly been dealt with easier, and with less people who did not respond, if I had done it at a time when 12th graders were not on break and the rest of the school was not preoccupied with exams (at the end of the year). If given the chance there are many follow up studies I could do. I could find the differences between all grades to see if the amount of people who know what they want to do when they grow up gradually increases with age. Also I would try doing this study at other, larger schools, and possibly compare those results to the ones I obtained at BB&N.

Extrapolation and Conclusions

It seems probable that at most high schools people would be more likely to know what they want to do when they grow up as they get older. Realistically the only population I would be comfortable extrapolating to would be other ISL schools. The reason for this is that many of the ISL schools seem to be very similar while other schools across the country could have completely different learning styles and atmospheres.

This is not an experiment, it is an observational study, and because of this causation cannot be implied. There was no treatment that was imposed and there was no attempt to control lurking variables. Many factors could have possibly changed the outcome of my study, and whether they seem reasonable or not, we can still not say that at BB&N, your grade affects if you know what you want to do when you grow up.

This study set out to find if you are an 11th or 12th grader, are you more likely to know what you want to do when you grow up, then if you are a 9th or 10th grader. This was done by taking simple random samples of both groups and performing a 2-proportion Z-test of significance of which the p-value was .014. These finding, though very significant, could not necessarily be trusted due to the fact that the non-response may have created uncontrollable bias.