4/24/13
Amanda Cardenas

Amanda Cardenas
My research question was, “is the circumference of a cranium related to cumulative GPA?” The purpose of this study was to gather data, as randomly as possible, that would aide in determining if any type of linear correlation exists between a person’s cumulative grade point average and the size of their cranium. With that being said, I would like to present my numerical variables, as well as what units of measurement were used in collecting data. My first numerical variable (x) was the circumference of a cranium, with the unit of measurement being centimeters. My second numerical variable (y) was cumulative GPA, with the unit of measurement being a GPA scale of 0.0 – 4.0.
Given the variables chosen and prior to completing the data collection, my expectation would be that there would be very little, if any, positive linear correlation between the two variables. The rationale behind my expectation being that I myself have a relatively small cranium circumference; however, my cumulative grade point average could be considered above average. In addition, I don’t predict that a larger cranium circumference would yield a relationship with a lower GPA. All things considered, I believe cumulative grade point average to be independent from cranium circumference.
The population of interest involved in this study was students attending Salt Lake Community
College – Redwood Campus. I chose this population due to the fact that I needed to select a population that would be able to provide a cumulative grade point average, and given that I am a SLCC student myself, the thought of involving my fellow peers was an attractive idea. Furthermore, I tend to believe that there are different kinds and/or categories of intelligence, and I felt that SLCC would provide a variety of subjects majoring in differing fields. In other words, I would feel confident that grade point averages would be representative of diverse forms of intelligence.
In order to ensure that data was collected as randomly as possible, I conducted several separate drawings in order to determine when, where, and who I would be collecting data from; thus any typical college day, time, building, and individual had as close to an equal chance of being selected as possible. I made the decision to draw out three options so that I would have the opportunity to gather data on three separate occasions, thus broadening the variety of students I could utilize in gathering information from.
The following options were available in the drawings I conducted: o Day of the week (Monday – Friday) o Time (8:00 a.m. – 8:00 p.m.) o Location within the Redwood Campus (Administration Building, Technology Building, Student
Center, etc.) o Selection of every “kth” individual (every 1 st – 5 th individual)
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Amanda Cardenas
As I mentioned above, I conducted three separate drawings that yielded the following results: o Friday, 12:00 p.m., Library, every 2 nd individual o Monday, 4:00 p.m., Applied Technology Center, every 2 nd individual o Thursday, 10:00 a.m., Construction Trades Building, every 3 rd individual
In addition to complying with the above results, I also used the same measuring tape, and was vigilant in making sure that the placement of the measuring tape, and tautness, was consistent with all the subjects to ensure accurate data was recorded. In an attempt to protect the privacy of the subjects, I designed an individual data sheet for each of the subjects. After recording cranium circumference measurements on the data sheet, I asked the subject themselves to enclose their cumulative GPA on the data sheet, fold it in half, and place it in the “collection box.” I hoped that this would aide in making the subjects feel more comfortable in disclosing their true grade point averages.
X
(Cranium
Circumference in
Centimeters)
56.65 2.735432 51.3 53.9 56.85 59 62.1 10.8 59
None
Lower Fence: 46.25
Upper Fence:66.25
When outliers exist it can drastically affect the mean, and therefore make it a less effective measure of center. In those cases, the median would be a better measure of center due to the fact that it is not as influenced by outliers. However, in this case my first quantitative variable presented no outliers, making the appropriate measure of center the mean.
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Amanda Cardenas
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Amanda Cardenas
Y
(Cumulative GPA)
3.416667 0.47422 2.4 3 3.5 3.9 4 1.6 3.9, 4.0
None
Lower Fence:1.65
Upper Fence:5.25
As explained previously, because the second quantitative variable presented no outliers, the appropriate measure of center was the mean.
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Amanda Cardenas
Dependent Variable: Cumulative GPA
Independent Variable: Cranium Circumference
Cumulative GPA = 4.2507725 - 0.014723841 Cranium Circumference
Sample size: 30
R (correlation coefficient) = -0.0849
Estimate of error standard deviation: 0.48087063
Intercept 4.250773 1.851366 ≠ 0
Slope -0.01472 0.032644 ≠ 0
28 2.29602 0.0294
28
-
0.45104
0.6554
Model
1 0.047043 0.047043 0.20344 0.6554
Error 28 6.474624 0.231237
Total 29 6.521667
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Amanda Cardenas
“Cumulative GPA =4.2507725 - 0.014723841 Cranium Circumference” or ŷ = 4.2507725 - 0.014723841x
The mean (56.65) and standard deviation (2.74) can be used together to convey the center and the spread of the set of data for my first quantitative variable. Likewise, the 5 number summary proves to be a great tool in uncovering the distribution of each variable. Cranium circumference had a minimum value of 51.3 and a maximum value of 62.1. The lower quartile (53.9) represented the median of the bottom half, while the upper quartile (59) represented the median of the top half. I utilized the lower and upper fences in identifying possible outliers (lower fence: 53.9
– 1.5(5.1); upper fence: 59 + 1.5(5.1)). Completion of these calculations concluded there were no outliers in my first quantitative variable.
The mean (3.42) and standard deviation (0.47) can be used together to convey the center and the spread of the set of data for my second quantitative variable. Likewise, the 5 number summary proves to be a great tool in uncovering the distribution of each variable. Cumulative GPA had a minimum value of
2.4 and a maximum value of 4.0. The lower quartile (3.0) represented the median of the bottom half, while the upper quartile (3.9) represented the median of the top half. I utilized the lower and upper fences in identifying possible outliers (lower fence: 3.0
– 1.5(0.9); upper fence: 3.9
+ 1.5(0.9)). Completion of these calculations concluded there were no outliers in my second quantitative variable.
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Amanda Cardenas
With an R (correlation coefficient) of -0.0849, it is fair to say that there is no linear correlation, or an extremely weak negative linear correlation, between the two variables. This implies that there is a lack of linear correlation between cranial circumference and cumulative GPA.
Although my original hypothesis was correct in that there would be a very weak, if any, linear relationship between the two variables, the statistics differed from my original hypothesis in that instead of there being a weak positive linear correlation, the data showed that there was actually a very weak negative linear correlation between the two variables. After analyzing the data, and with the R value being so close to zero, I can conclude that no linear correlation, or an extremely weak negative linear correlation, exists between cranium circumference and cumulative grade point average.
Some of the major difficulties I encountered while collecting the data were finding enough subjects that were willing to take the time in having their information recorded, and arranging my schedule so that I could be at the proper building, on the right day, at the right time. Believe it or not, being as short as I am presented a surprising complication. The taller subjects were difficult to obtain measurements from due to the fact that my arms were not able to reach up high enough to get a proper measurement. One individual was beyond accommodating when he offered to kneel down, in the dirt mind you, so that I could get the measuring tape around his head. Needless to say, I was beyond humiliated, but I was able to obtain the information I needed, and he was a complete gentlemen about the whole situation.
If I had to complete a similar study in the future, I think I would come prepared with a step stool in order to provide better access in measuring taller individuals. I believe this would ease uncomfortable situations, and eliminate any possibility of a subject having to kneel. In addition, I would modify my expectations for how people might react to study, given that some individuals may be reluctant to participate. Another thing I could do differently is to adjust my appearance. Perhaps if I wear something more professional, students would have more trust the validity of the study I am conducting. If we are being honest, in the future I would attempt to avoid any type of research question that would require surveying people, particularly because people were hesitant, and in some instances discourteous, in allowing physical contact in order to obtain needed measurements.
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