Methods Introduction: Statistics with Lions – Part 1
The following blog and its continuations cover a fictional project based on constructed data and accompany it from the initial descriptive examination (Part 1) to the evaluation using various analytical methods and graphical representations. Understanding the data is the focus of the first part, because without knowing your own data, no good analysis can take place. Moreover, far too often we see that calculations are simply done in a "rush." No simple look at descriptive statistics, which, especially with a certain experience, already holds some significance for the later analyses, no consideration of outliers, etc. For all parts of this blog, it is true that especially in graphics, the detailed description of commands in Stata is omitted, as this would go too far for a blog. Blog entries on the topic of graphics will follow in the future. As in any good statistical analysis, a brief introduction to the data stands at the beginning.
Introduction to the Data
The circus games (ludi circenses) in ancient Rome were an extraordinarily popular attraction for the city population at the time. At the same time, the games were a way to get rid of political troublemakers and prisoners. This method was not only foolproof and extremely popular but also had an unfortunate side effect: fat lions. During an archaeological excavation at the Colosseum in Rome, tally marks and entries about the lions kept there for the games were found on clay tablets. These included information on the sex, age, weight, and type of the lions, as well as details on how long the lions had been used for the games. After painstakingly piecing together the shards, the data were transferred to an Excel file and are thus ready for evaluation.
Descriptive Evaluation
The executing archaeologists of the project began to evaluate the surprising find descriptively.
tab sex
tab art
su weight months
Overall, there are N=517 records about lions, of which 53.19% (N=275) are male and 46.81% (N=242) are female. Apparently, it was irrelevant for entertainment which gender a lion had. Regarding the types, at the time of counting, there were 156 Barbary lions (30.17%), 167 Maasai lions (32.30%), and 194 Senegal lions (37.52%). The average weight of all lions is M=150.57 with a standard deviation of SD=32.709, with weight ranging from 75kg to 209kg. On average, the lions had been in use for 12.74 months (almost 1 year) (SD=6.948), at least one month and at most 33 months, almost 3 years.
Graphical Consideration
To quickly grasp how age, weight, and gender relate to each other without deeper statistics, the researchers created a scatter plot (see below). Not surprisingly, the weight of the lions increases with age, with no apparent difference in gender visually. Two striking outliers were also marked in the data, which may still be of interest later.
A research question arises
A Research Question EmergesRegarding the data, the following note must be made: The weight of the lions upon their arrival in Rome was apparently not recorded. Thus, from the above graphic, we only know that lions with a higher age also weigh more, but not what weight gain a single lion had during its stay in the circus. The local researchers hope to find additional clay tablets with more data through new excavations (we will report here), but currently, the existing data situation must be accepted as sufficient. Thus, it cannot be said with certainty that the lions became fatter due to their time in the circus, but looking at the circumstances, it is assumed. We simply assume this at this point. The researchers' first obvious question was subsequently whether the lions – now not living in their natural environment and well-fed – became heavier due to their time in the circus.
Graphically, it is shown that lions that are new to the circus still weigh around 100kg, and the weight increases up to a duration of 16 or 17 months, only to maintain their weight for a certain time (18-24 months). Only from the 25th month do they seem to lose weight again.
Even though the initial weight of the animals was not available, it was at least intended to determine whether there were possibly older animals that were only in the circus for a short time, and vice versa. The above graphic clearly shows that lions under 9 years old are only in the circus for up to about 13 months and that lions of middle and older age spread more broadly. However, it was not intended to become more specific without deeper statistical analyses at this point. Nevertheless, the graphic suggests that the lions were caught exclusively at a young age, possibly because they were more trainable at this age. The consideration is rounded off by a table listing the means, standard deviations, medians, and minimum and maximum values, which give the researchers a purely descriptive confirmation of their assumption.
tabstat weight, statistics(count mean sd median min max) by(months_kat)
Outlook
Whether the archaeologists are also right from a statistical point of view and the lions really became heavier the longer they were in the circus will be shown in Part 2 of the blog.
