Evidence of Research
I conducted my research in the form of a poll on the social networking website Facebook.com. After creating the poll on the website, it was posted where all of my Facebook friends were able to see it and answer in a quick and convenient manner. Every one of my friends was able to see this poll, but in the designated description space, I provided this supplemental information: “I’m asking only IB students, so please only post if you are in it. For IB students, please post your weighted GPA! Use the GPA on your first marking period report card. If you would like for you GPA to remain confidential, just send me a private message- you will be anonymously put into my data. No one’s identity will be disclosed in my final data. Thank you!!” For security purposes, I am unable to replicate this data, but a table with the collected data is composed below.
Mathematical Investigation
Data Collection
Table A: IB student dominant hand when writing and current GPA
Graph A: Number of Left Handed Students vs. Left-Handed Students’ Current GPA
This histogram depicts the GPAs of left-handed students and the frequency of the number of students with that GPA. It is represented in a bar graph of the frequency distribution of the various GPAs of left-handed students such that the height of the bar corresponds to the number of students with that GPA. It is significant in depicting which averages are the most and least common for left-handed students for the purpose of comparison with the right-handed counterparts.
Graph B: Number of Right-Handed Students vs. Right-Handed Students’ GPA
This histogram depicts the GPAs of right-handed students and the frequency of the number of students with that GPA. It is represented in a bar graph of the frequency distribution of the various GPAs of right-handed students such that the height of the bar corresponds to the number of students with that GPA. It is significant in depicting which averages are the most and least common for left-handed students for the purpose of comparison with the right-handed counterparts.
Graph C: Right-Handed Students’ GPA vs. Left-Handed Students’ GPA
This histogram combines the two preceding histograms in order to compare the frequency of the GPAs of right and left-handed students. It is represented in a bar graph of the frequency distribution of both left and right-handed students such that the height of the bar corresponds to the number of students who currently have that GPA. It depicts the frequencies of the various GPAs of left and right-handed students in a singular unifying histogram so as to clearly compare the data attained from both groups.
Graph D: Percentage Distribution of Left-Handed Students’ GPA
This pie chart creates a visual aid to depict the percentage distribution of the GPAs of left-handed students. It serves as another way to display the frequency and distribution of the GPAs of left-handed IB students.
Graph E: Percentage Distribution of Right-Handed Students’ GPA
This pie chart creates a visual aid to depict the percentage distribution of the GPAs of right-handed students. It serves as another way to display the frequency and distribution of the GPAs of right-handed IB students.
Calculation of Chi-Squared () Test
Chi-squared tests evaluate the observed and expected frequencies of a set of collected data in order to determine if there is a significant difference between then. It is determined with the equation:
Observed Values (variables)
Expected Values (variables)
Null Hypothesis:
Students’ GPA and dominant hand when writing are independent.
Alternative Hypothesis:
Students’ GPA and dominant hand when writing are not independent.
Table D: Observed Values
Calculation of Expected Values
Table F: Expected Values
The expected values in the table above are shown as rounded to the nearest whole number for the purpose of maintaining a simple and concise table. However, in the chi-squared calculations done by hand () in Table G, the values were used to three significant figures (see Calculation of Expected Values, page 11) for more accurate data.
Degrees of Freedom
The degree of freedom dictates the acceptable amount of variance in the final statistical calculation. It is determined with the equation:
Calculation of Degrees of Freedom
Table G: Calculation of Chi-Squared (
Values are shown exact or rounded to 3 significant figures when necessary. Exact values were used for all numbers when doing calculations in a TI-84 calculator.
Rounded to 3 significant figures:
Chi-Squared Test Verification
To verify my chi-squared level of significance result, I preformed a second -test () in my TI-84 calculator. To do this, I first went to 2nd + to get to the Matrix screen. I arrowed over to the right 2 times, to the Edit column, and entered my observed values, seen in Table D, into a 2x5 matrix in Matrix [A]. I then went to 2nd + 0 to get to the Catalog screen, and arrowed down until I found -test, which I selected. In my calculator screen, I think hit 2nd + to get back to the Matrix screen. I selected [A], and then went back to the Matrix screen and selected [B] in order for the chi-squared test to be performed in both of the matrices. The calculator gave me the answers , which is an insignificant 0.03 difference from my manually attained value of 8.07, and which agrees with my manually attained degree of freedom. It is reasonable to assume that the slight difference in numbers is due to the fact that the manual -test was calculated to 3 significant figures and the calculator -test was calculated to further decimal places, making the answer slightly more accurate. Furthermore, it is logical to use the more accurate of the two values, , and henceforth assume that .
Chi-Squared Analysis
At a 5% level of significance, the critical value with 4 degrees of freedom is 9.49. The critical value is therefore less than the determined value, 8.04>9.49, so the null hypothesis is accepted; thus, it can be assumed that students’ handedness when writing and GPA are independent.
Discussions and Validity
Limitations
In the course of my investigation, there were a number of variables that could have affected the data.
One limitation is that the only data reflected is from my personal friends on Facebook. Students who do not have Facebook and/or are not friends with me on the social networking site would not have been able to submit their data into my survey.
Secondly, because only my personal Facebook friends were privy to my data collection, the data comes solely from student who attend my high school. This entails that while the data is a most likely a relatively accurate reflection of the relationship between Grade Point Average and handedness at my high school, because the data is limited to such, there is no information regarding its accuracy for students in other places in the world.
Continuing, because I am currently in 11th grade (junior), more of my friends on Facebook are juniors as well, and thus, more of the data collected is from juniors than 12th grade seniors.
Another limiting factor is that of the handedness itself. As stated in the introduction, left-handedness is far less common than right-handedness, and because of that, approximately 78% () of my data was from students who identify themselves as right-handed, whereas only 22% () of the students identified as left-handed. Because of this, there is a comparatively insufficient amount of data about left-handed students. Ideally, there would be an equal or nearly equal amount of left and right-handed participants.
Conclusion
Despite the limitations, the determined value, 8.04, is still a valid result. The value decisively rejects the null hypothesis that handedness and GPA are independent and accepts the alternative hypothesis that students’ GPA is dependent on their dominant hand when writing, despite the above limitations. To apply this to my introduction and the purpose of my project, this value entails that despite the claims that left-handed people are more intelligent, based on IB students’ grade point averages, there is no statistical evidence that can conclusively prove that there is a difference in the intelligence level of left-handed students in comparison to their right-handed counterparts.
Works Cited
"Left Handed Facts." Left Handed Facts. PJC Associates, 2012. Web. 15 Dec. 2011. <http://lefthandedfacts.net/>.
