Reaction Times Essay Example

Reaction Times Essay Example Reaction Times Essay Reaction Times Essay Hypotheses: 1) Boys are faster than girls are 2) Right-handed students are faster than left-handed students are 3) Right-handed boys are faster than right-handed girls are Possible methods of testing 1. Hit the mole (arcade game)- I would time how many moles they could hit in one minute, repeat this 3 times to get a fair result and then find an average. This would be read as the higher the number of moles that are hit, the faster the reaction. However you would have to travel to an arcade to carry this test out and it would be extremely expensive. 2. Stopwatch- I would tell the student to stop it at a certain time e.g. 2 minutes, and however many seconds before or after they stopped the stopwatch, would be their reaction time, the closer the number of seconds it is to 2 minutes, the faster the reaction. This would of course be repeated 3 times to get a fair result and then the average found. However the stopwatch buttons may get stuck, therefore altering results. 3. Dropping a ruler- I would take a 30cm ruler and make sure that the zero is inline with the index finger. I would then drop the ruler, which would be caught by the student (who is standing), then the number of cms nearest to the index finger where the zero was lined up with, would be taken down as the reading for their reaction times. The results would be read as, the lower the number of cms, the quicker the reaction. This would be repeated 3 times for each student, to get a fair result, and then the mean found. This is the best method of testing, because it doesnt cost money, you dont need to travel and no errors can be found with a ruler. How is it a fair test? I will make this a fair test by: * Using the same 30cm ruler * Making sure the students are standing * Making sure the zero on the ruler is in line with the index finger of the student * Standing the students in the same position * Testing all students at the same time of day * Repeating each test 3 times * Using only year 10 students Note: All Reactions are measured in cms Methods of sampling Hypothesis 1 Boys are faster than girls are There are 307 year 10 students in this school, of which I need 50. I will use stratified sampling to find a fair number of girls and boys. Out of 307 students, 156 are girls and 151 are boys. To pick the 25 girls and 25 boys from the data bank, I will use systematic sampling whereby I will role a dice, then take the number it lands on and then pick every nth person on the list. I have rolled a 4, so I will pick every 4th person on the list, until I have my complete total of 25 girls and boys. I will use 4 to select the people for all 3 hypotheses. Hypothesis 2 Right-handed students are faster than left-handed students are I will again use stratified sampling, to find a fair number of left-handed and right-handed students that I need to total 50, out of the 307 year 10 students. There are 234 right-handed students, and 73 left-handed people. To select the 38 right-handed students and the 12 left-handed students, I will pick every 4th person, as I did for hypothesis 1. Hypothesis 3 Right-handed boys are faster than right-handed girls are Out of the 307 year 10 students, 127 are right-handed boys, and 107 and right-handed girls. To find the proportion of right-handed boys and girls that I need to make 50 I will again use stratified sampling. To select my 27 right-handed boys and 23 right-handed girls, I will pick every 4th person from the data bank. Testing Hypothesis 1 Boys are faster than girls are I found the averages for my sample of 50 students, and decided to arrange the results into grouped-data tables for convenience and accuracy. My groups were decided as: Reaction (cms) 0-5 extremely fast 5-10 fairly fast 10-20 average 20-25 slow 25-30 Very slow The results for boys were as follows- Reaction Tally Frequency Cumulative Frequency 0 ; r ; 5 0 0 5 ; r ; 10 12 12 10 ; r ; 20 12 24 20 ; r ; 25 1 25 25 ; r ; 30 0 25 The results for girls were as follows- Reaction Tally Frequency Cumulative Frequency 0 ; r ; 5 0 0 5 ; r ; 10 5 5 10 ; r ; 20 16 21 20 ; r ; 25 03 24 25 ; r ; 30 01 25 I will use a cumulative frequency graph with the inter-quartile range and box-plots. I will use A Cumulative Frequency Graph as I will be able to compare ranges (I.Q.R.), find the median and aid with boxplots to identify outliers and show skewness. As I expect the boys reaction to be faster than the girls I will expect the line representing the boys to be steeper than the line representing the girls. Testing Hypothesis 2 Right-handed students are faster than left-handed students I found the averages for my sample of 50 students, and decided to arrange the results into grouped-data tables for convenience and accuracy. My groups were decided as: Reaction (cms) 0-5 extremely fast 5-10 fairly fast 10-20 average 20-25 slow 25-30 very slow The results for right-handed students were as follows- Reaction Tally Frequency Frequency density 0 r 5 0 0/5=0 5 r 10 11 11/5=2.2 10 r 20 23 23/10=2.3 20 r 25 3 3/5=0.6 25 r 30 1 1/5=0.2 The results for left-handed students were as follows- Reaction Tally Frequency Frequency density 0 r 5 0 0/5=0 5 r 10 0 0/5=0 10 r 20 12 12/10=1.2 20 r 25 0 0/5=0 25 r 30 0 0/5=0 I will use a Histogram, to find the median. As I expect the right-handed students to be faster, I will expect the median for the right-handed students to be lower than for the left-handed students. Right-handed Median = 13.5 Left-handed Median = 15 Conclusion for Hypothesis 2 The medians again prove that my 2nd hypothesis is correct. Right-handed students are faster than left-handed students because the right-handed students achieved a median of 13.5 whereas the left-handed students achieved a median of 15, making the right-handed students average faster. Testing Hypothesis 3 Right-handed boys are faster than right-handed girls are I found the averages for my sample of 50 students, and decided to arrange the results into grouped-data tables for convenience and accuracy. My groups were decided as: Reaction (cms) 0-5 extremely fast 5-10 fairly fast 10-20 average 20-25 slow 25-31 very slow The results for right-handed boys were as follows- Reaction Tally Frequency Mid-point Mid-point x Frequency 0 r 5 0 2.5 0 x 2.5=0 5 r 10 10 7.5 10 x 7.5=75 10 r 20 15 15 15 x 15=225 20 r 25 02 22.5 2 x 22.5=45 25 r 30 0 27.5 0 x 27.5=0 27 345 The results for right-handed girls were as follows- Reaction Tally Frequency Mid-point Mid-point x Frequency 0 r 5 0 2.5 0 x 2.5=0 5 r 10 7 7.5 7 x 7.5=52.5 10 r 20 13 15 13 x 15=195 20 r 25 2 22.5 2 x 22.5=45 25 r 30 1 27.5 1 x 27.5=27.5 23 320 The estimated mean for right-handed boys is 13 The estimated mean for right-handed girls is 14 Conclusion for Hypothesis 3 The estimated mean for the right-handed boys is 13 whereas the estimated mean for the right-handed girls is 14, this means that the boys are faster because they have a faster average than the girls do. This proves my 3rd hypothesis correct I used the estimated mean in order to get an immediate result of who is faster out of everybody. It also means I will be able to find the standard deviation (page 7 7a). Testing Hypothesis 3 (continued) Although I have already proved the 3rd hypothesis correct, I am going to put the data into a histogram, to secure my conclusion. The tables of results were arranged in the same way Right-handed boys- Reaction Tally Frequency Frequency density 0 r 5 0 0/5=0 5 r 10 10 10/5=2 10 r 20 15 15/10=1.5 20 r 25 2 2/5=0.4 25 r 30 0 0/5=0 27 Right-handed girls- Reaction Tally Frequency Frequency density 0 r 5 0 0/5=0 5 r 10 7 7/5=1.4 10 r 20 13 13/10=1.3 20 r 25 2 2/5=0.4 25 r 30 1 1/5=0.2 23 The Medians Right-handed boys = 12 Right-handed girls = 13.5 Conclusion for 2 for hypothesis 3 I can see from the Medians, which I read off of the histograms, that Right-handed boys are faster than Right-handed girls are. The right-handed boys median was 12 whereas the girls median was 13.5 making the right-handed girls slightly less- faster than the boys are. This proves my 3rd and final hypothesis right for the second time. Testing Hypothesis 3 (continued 2) The estimated mean for boys = 13 The estimated mean for girls = 14 The method of how I found the estimated means, is on page 5 Mid Point (x) Frequency (f) Mid point Estimated mean (x-x) (Mid point Estimated mean) à ¯Ã‚ ¿Ã‚ ½ (x-x) à ¯Ã‚ ¿Ã‚ ½ Frequency x (Mid point Estimated mean) à ¯Ã‚ ¿Ã‚ ½ f(x-x) à ¯Ã‚ ¿Ã‚ ½ 2.5 0 2.5-13= -10.5 -10.5à ¯Ã‚ ¿Ã‚ ½ = 110.25 0 x 110.25= 0 7.5 10 7.5-13= -5.5 -5.5à ¯Ã‚ ¿Ã‚ ½= 30.25 10 x 30.25= 302.5 15 15 15-13= 2 2à ¯Ã‚ ¿Ã‚ ½= 4 15 x 4= 60 22.5 2 22.5-13= 9.5 9.5à ¯Ã‚ ¿Ã‚ ½= 90.25 2 x 90.25= 180.5 27.5 0 27.5-13= 14.5 14.5à ¯Ã‚ ¿Ã‚ ½= 210.25 0 x 210.25= 0 ? =27 ? =543 The standard deviation for the right-handed boys is (to 3 s.f.): 4.48 Mid Point (x) Frequency (f) Mid point Estimated mean (x-x) (Mid point Estimated mean) à ¯Ã‚ ¿Ã‚ ½ (x-x) à ¯Ã‚ ¿Ã‚ ½ Frequency x (Mid point Estimated mean) à ¯Ã‚ ¿Ã‚ ½ f(x-x) à ¯Ã‚ ¿Ã‚ ½ 2.5 0 2.5 14 = -11.5 -11.5à ¯Ã‚ ¿Ã‚ ½ = 132.25 0 x 132.25 = 0 7.5 7 7.5 14 = -6.5 -6.5à ¯Ã‚ ¿Ã‚ ½ = 42.25 7 x 42.25 = 295.75 15 13 15 14 = 1 1à ¯Ã‚ ¿Ã‚ ½ = 1 13 x 1 = 13 22.5 2 22.5 14 = 8.5 8.5à ¯Ã‚ ¿Ã‚ ½ = 72.25 2 x 72.25 = 144.5 27.5 1 27.5 14 = 13.5 13.5à ¯Ã‚ ¿Ã‚ ½ = 182.25 1 x 182.25 = 182.25 ? =23 ? =635.5 The standard deviation for the right-handed girls is (to 3 s.f.): 5.26 Conclusion 3 for Hypothesis 3 The standard deviation value of the right-handed boys is lower, which means that the right-handed boys are more consistant Also I can see from the Standard deviation methods on page 7a, that 95% of the right-handed boys reaction ranged between 4.04cm and 21.96cm whereas 95% of the right-handed girls ranged between 3.48cm and 24.52cm, this again shows that the boys are more consistent. I expect to find the median and expect of the boys to be lower than the girls. Further improvements If I were to do this investigation again, I would re-do Hypothesis 1. I would find and remove the outliers from the data, and re-construct my cumulative frequency graph, to see if it altered the results, which I have found. Also I would place the data for each hypothesis, into other forms of graphs (i.e. histograms for hypothesis 1, cumulative frequency for hypothesis 2 etc). This would ensure that my conclusions are more precise and correct, as I did for hypothesis 3 where I used the estimated mean, a histogram and then found the standard deviation. Furthermore, I would test other hypotheses such as Right-handed girls are faster than Left-handed boys are etc. I could also change the age group, and see if I get different results to what I have, for each hypothesis. Another thing I could change is the form of test, so instead of dropping the ruler I could try the stopwatch experiment. Overall Conclusion After analyzing all of the results from the tests for all 3 hypotheses, I can see that my hypotheses were correct. For hypothesis 1, the Median for the boys was 10 whereas the median for the girls was 13. This meant that the boys were faster than the girls were. Also the box plots and the steepness of the lines from cumulative frequency graph showed the boys were faster. For hypothesis 2, the Right-handed students proved to be faster than left-handed students because the right-handed students had a median of 13.5 whereas the left-handed students achieved a median of 15. This meant that right-handed students average was faster. For the 3rd hypothesis the boys estimated mean was 13 whereas the girls estimated mean was 14. This showed that the right-handed boys average was faster than the right-handed girls was, making the right-handed boys faster. I also put the data into a histogram. The Median for the right-handed boys was 12 whereas the right-handed girls, was 13.5. This proves again that the right-handed boys were faster than the right-handed girls were. I found the standard deviations for the right-handed girls and boys. It showed that the boys were more consistent than the girls were. Conclusion for Hypothesis 1 The Median for the boys is 10 whereas the median for the girls is 13. This already proves my hypothesis correct boys are faster than girls are. Also, on the box-plots 3/4 of the boys have a reaction between 10 and 13 whereas 3/4 of the girls have a reaction between 13 and 17, so the majority of boys are faster than the girls are. I can also see from the whiskers of the box plots that there are outliers. There is a boy who is extremely slow in comparison to the majority of the boys and a girl who is also extremely slow in comparison to the majority of the girls. The steepness of the boys graph proves again that the boys have a faster reaction than the girls do. Furthermore, I can see from the inter-quartile ranges, (which represent the middle-half of the sample) that the girls are slower, the reaction of the middle half being 6.5 and the boys being 4.5. In addition to this, I can see from the inter-quartile ranges that the boys are more consistent as their range is closer together 8.5 13 compared to the girls ranging from 10.5 17 Maths Statistics Coursework: Reaction times

A Piece On Wanting to Take Credit

A Piece On Wanting to Take Credit Publishing is hard. No doubt about it. But sometimes authors get so caught up in the publishing aspect of the profession that we forget the reader doesnt give a darn how the book was made, researched, written, published, or promoted. The point is for a reader to find a good story and feel that it is theirs. Theyve allowed this story into their life, committed hours and days to reading it, in hope that its memorable enough to improve their quality of existence. As a minimum, provide a wonderful experience to remember . . . hopefully a book to recommend to others. While this may sound weird to you, after infusing so much time and effort into the story, the end game is not to get credit for the book. Its to give the world a great story experience. â€Å"It is amazing what you can accomplish if you do not care who gets the credit.†Ã‚  ~Harry Truman For instance, books that Ill usually pass up, are  promoted  as: 1) free 2) cheap 3) self-published 4) five years in the making (or other number) 5) an authors greatest achievement 6) a great first book Books Ill give a second glance at, are promoted as: 1) a great story about 2) an award-winning story about 3) a poignant story about 4) recommended 5) a wonderful beach read, I want the author to care that I have a great time reading. I want the author to promise me a treat for investing my time. I want the author to make my life better. This is why we write. To fulfill a promise to the reader. To know even one life has breathed easier because you have lived. This is to have succeeded.   Ralph Waldo Emerson