December 12, 2014
Height vs. Shoe Size
I chose two quantitate variables in this study in order to see if they had any linear relationship. The dependent (response) variable was a person’s shoe size in united states meaurements and the independent (explanatory) variable was person’s height in inches. I chose these two variables because I assume before the study that there would be appositive linear relationship between height and shoe size. In other words, the taller the individuals are, the larger their foot size will be.
I collected the data from twenty males all from the Montclair State University. The results for this study could be beneficial for homeless shelters and clothe drives; for example men could come in give their height and receive a care package of goods including a pair of shoes that suit their height and size perfectly. Individuals were asked to write down (roughly) their height, along with their shoe size. The reason I say rough is because all information is subject to biased because most heights were rough estimates, along with shoe size, which truly doesn’t measure the size of ones, foot. Because with shoe size you have to consider variables such as the different shapes of the human foot; so in order to make my data as accurate as I could make it I restricted my study to males, because males and females have different shoe scales. For future studies the sources of error mentioned above should be addressed, but when taking all this information into consideration my data still resulted in a positive linear trend.
Right off the bat I could see a strong positive linear trend. Proving my hypothesis that an individual a taller individual has a larger shoe size. I came to this conclusion by plugging my data into a scatter plot. Where height in inches was represented on the x-axis, and shoe size was on the y-axis.
Chart 1 below displays the height in inches with the corresponding shoe size from each participant in my study, the data is in ore detail displayed as a scatter plot graph titled Graph 1.
Graph 1 – Scatterplot
Correlation between Height (in) and Shoe Size (us) is:
r = 0.98546412
The data Graph 1 represents a distinct pattern that is a straight-line pattern with a positive slope. The variable (r) represents the linear coefficient for these variable, as computed by Stat Crunch is 0.98546412; this indicates an extremely strong correlation between someone’s height and shoe size. Since there were no outliers in graph 1, no values needed to be taken away. The critical correlation coefficient values were n = 20 and α = .05, are +/- 0.396 (Table A-6). Since the critical correlation coefficient value is less than linear correlation coefficient “r” (0.396 < 0.985), due to this information we are able to confirm the positive linear relationship between men heights and shoe size. In statistical terms since 0.985 or “r” is a value that is found in the right tail beyond the rightmost critical value, once again we are able to confirm the positive linear relationship between men heights and shoe size. The positive linear relationship was further proved through analyzing if my linear correlation coefficient fell between -0.396 and +0.396 and because it didn’t you can conclude that there is a linear conclusion, if my value fell between that range, you can conclude that there is not a linear correlation. Similar conclusions could be made based of the calculations of the P-value, and whether or not it’s greater or less than the significance level. Since the significance level in this case is 0.05, the P-value is significantly less, so this further proves there is a linear relationship between my two variables. Conversely if the P-value was greater than 0.5, one would conclude that there is no linear relationship. While reviewing this information, a important concept to always remember is that just because a linear...
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