Evolutionary biologists are often interested in “form-function relationships” to help explain evolution history of say an animal species. Harris and Steudel (2002) investigated factors that are related to the jumping ability of domestic cats.
Because jump ability and height are largely dependent on takeoff velocity, several traits were recorded for 18 healthy adult cats such as relative limb length, relative extensor muscle mass, body mass, fat mass relative to lean body mass, and the percentage of fast-twitch muscle fibers to see which might best explain maximum takeoff velocity (based on high-speed videos).
Open the CatJumping.txt data file and produce numerical and graphical summaries of the takeoff velocity variable. Describe the distribution of takeoff velocities in this sample (shape, center, variability, unusual observations).
JMP output for velocity: boxplot and histogram of takeoff velocity from 280 to 420 cm/sec, with Quantiles (median 339.55, quartiles 316.175 and 369.625, maximum 410.8, minimum 286.3) and Summary Statistics (mean 343.28, standard deviation 33.08, n = 18).
R iscamsummary output for cats velocity: n = 18, minimum 286.3, Q1 317.25, median 339.55, Q3 368.4, maximum 410.8, mean 343.28, SD 33.077, skewness 0.222.
R histogram of takeoff velocity with bins from 280 to 420 cm/sec; tallest bar between 300 and 320, roughly mound-shaped with single observations in the 280, 380, and 400 bins.
The distribution is pretty symmetric or slightly skewed to the right (though depending on bin choices might see a visual outlier in the 420 bin). Most cats had a velocity around 320-380 cm/sec but one was as small as 286.30 cm/sec and the high outlier was at 410.80 cm/sec.
Do you think there will be a relationship between a cat’s takeoff velocity and its body mass? If so, do you think heavier cats will tend to have larger or smaller takeoff velocities than lighter cats?
Describe the relationship between a cat’s takeoff velocity and its body mass, as displayed in this scatterplot. Does this pattern confirm your earlier expectation?
Do any of these cats appear to be outliers in the sense that its pair of values (body mass, takeoff velocity) does not fit the pattern of the majority of cats? If so, identify the ID for that cat and describe what’s different about this cat (in context).
Scatterplots are useful for displaying the relationship between two quantitative variables. If one variable has been defined as the response variable and the other as the explanatory variable, we will put the response variable on the vertical axis and the explanatory variable along the horizontal axis.
In describing scatterplots you will describe the overall pattern between the two variables focusing primarily on three things:
Direction: Is there a positive association (small values of y tend to occur with small values of x and large values of y tend to occur with large values of x) or a negative association (small values of y tend to occur at large values of x and vice versa)?
The above scatterplot reveals a fairly strong, negative association between body mass and takeoff velocity, meaning that heavier cats tend to have a smaller takeoff velocity than larger cats. The relationship is somewhat linear but has a bit of a curved pattern. There is one outlier cat (cat C) with a very high takeoff velocity despite having a very large body mass.
Now produce a scatterplot of takeoff velocity vs. percentage of body fat. Describe the association. Would you say that the association with velocity is stronger than with body mass? More or less linear?
For the other two variables (hind limb length and muscle mass), would you expect to see a positive or negative association with takeoff velocity? Explain. Then look at scatterplots, and comment on whether the association is as you expected.
There are only 5 males but they tend to be heavier than the females. When the body mass is similar the velocities are similar though a little higher for males. The larger outlier is a male and there is also a very large male in terms of body mass.
The researchers found significant relationships of takeoff velocity with hind limb length and fat-mass ratio, but not with all measured muscle variables. Later in this chapter you will study inferential tools for assessing these relationships.
The dataset KYDerby25.txt contains information on each running of the Kentucky Derby since 1875. The speeds of the winning horses have been calculated (taking into account the change in track length in 1896).
