We used our data to examine two different trends.
1. Temperature Dependence
How does the day's temperature affect the numbers of people sitting on the steps? Is one gender more sensitive to temperature changes than the other?
Our first graph presents all our data. For each day of data collection, we plotted the number of people, males, and females (y axis) against that day's temperature (x axis). It's would be hard to extrapolate beyond our data points. The linear trend won't continue forever -- as the temperature gets uncomfortably hot, fewer people will sit on the steps. Also, The graph assumes no rain.
This below graph shows the same data with October 31's modal outlier omitted. As expected, removing the outlier increases the R2 value. To be thorough, we have plotted scatterplots of the residuals: Data Analysis: Residuals
Because our data points are groups of people, we can creatively interpret mathematical features revealing behavioral differences between males and females:
● The slope of the regression model might be interpreted as an indicator of temperature sensitivity. The greater slope of the female model suggests that females are more sensitive to differences in temperature. The slope of the female model (0.522) means that one extra female will appear on the steps for every increase of 1.92°F. The slope for men (0.284) means that an increase of 3.52°F is required to bring one extra male to the steps.
● The R2 scores might be interpreted as a degree of predictability. The female R2 (0.4465) is higher than the male R2 (0.1568) indicating that the female model better captures the variability of the data. Females' respond to temperature in a more predictable manner than males.
2. Gender-linked Seating Preference
Left vs. Right differences
Does one gender have an obvious left-right preference?
Our null hypothesis is that sides are picked randomly, which would result in 50% of sitters on each half. Our data, however, showed that males prefer the right side, 56% to 44%, so we set our alternate hypothesis as p(right)>50%. Our measured data point is 1.71 standard deviations above the null hypothesis, yielding a p value of 4.3% We can subtract 4.3% from 100% and conclude with 95.7% confidence, that our results are statistically significant, and not just the result of random variation in sampling. It's therefore reasonable to conclude that men do in fact show a right side preference according to our data.
Although we did perform these calculations for women, it's easy to see that our data does not demonstrate a significant left/right preference among women.
We also examined Right/Left variations is subsections of the steps. As shown below, men's preference for the right side intensifies when we consider only the lower outside sections. We did not calculate p values for this data:
Additionally, by comparing the top, middle, and bottom sections of the steps, we find that males prefer to sit higher up on the steps (or perhaps women prefer to sit lower on the steps):
In the final part of our analysis, we subjected the two counts (male and female) to a chi-square comparison test to quantify the degree of preference shown by each group for a section of the steps.
The chi-square result of 0.0479, calculated from X2 = 17.055 with 9 degree of freedom, is sufficient proof that the two counts do in fact differ in their distribution on the stairs. There is merely a 5% chance that the disparate distribution of the two counts is the result of random variation from the null hypothesis: that the two counts are homogenously distributed across the steps. Thus, we can confidently say that men and women exhibit preference when sitting on the steps.
The details of this preference can be viewed with the standardized residuals of the chi-square test: c=(obs-exp)/sqrt(exp).
The z-scores in each of these cells show the male preference for higher steps on the right hand side of the staircase. The residuals in cells 1,2,4,5,6, and 10 are positive, meaning larger than expected numbers of men are sitting in those areas. The opposite is true of cells 3,7,8,9; the negative residuals show a smaller than expected turnout.
The residuals of the female distribution are similarly illuminating. The cells corresponding to male preference, cells 1,2,4,5,6,10, have negative residuals while the cells neglected by male sitters, cells 2,7,8,9, are positive in the female sitters.
It should be noted that none of the residuals scores are particularly large. This is expected due to the statistically significant, though overall rather modest degree of prejudice exhibited by the two genders.
