Snow Ears nibbled on his pencil as he pondered his problem. His boss Dr. Scales had asked him to find out the average ear length of rabbits and hares in the forest because he believed that different ear lengths affects a hare's or a rabbit's counting skills. Well: How in the world was he going to prove or disprove his boss's hypothesis!
There were both European Hares and Rabbits, a whole bunch of Cottontails, and even Jackrabbits. There had also been quite a few immigrants from China, Yunnan, Burma and Alaska. This was going to be a tough one, Snow Ears thought to himself and at the same time wondered if the differences in Hare or Rabbit habit will affect the result but then he pushed it out of his mind. His boss was only interested in the length of their ears anyway. Hence he shall collect data only on the length of ears.
Since there were adult rabbits as tiny as 14 cm and jackrabbits that stretched to over 70 cm, it would not be fair to calculate the length of the ears in centimetre alone because that would skew the data. Instead, after some discussion with Dr. Scales, Snow Ears decided to use the ratio of ears to length of face, which was defined as being from the tip of the nose to the crown of each rabbit-hare that answered the questions. To make sure that there would be no mistake in that data, Snow Ears or those trained by him would have to do the measurements with a standard measuring tape. He listed out the data points.
Length of face : ______ cm
Length of ears : ______ cm
Ratio : ______
After some nibbling, scratching, sniffing and paw chewing, he came up with 5 questions to test a respondents counting skill. A respondent who got all answers correct would get a mark of '6', while a respondent who got all the answers wrong would be given a '1'. He was told not to use '0' because this might nullify some data. For example if 10 respondents were to score '0' then their response might be accidentally omitted from the final Mean Value because 10 × 0 = 0.
1 + 0 = _____
1 + 1 = _____
1 + 3 = _____
1 - 1 = _____
2 - 1 = _____
Next, he decided on what kind of background data he had to collect. Respondents would only be allowed to choose from a fixed category of answers. This was to reduce his volume of work later, as well as to reduce any confusion.
The final design of the questionnaire came out as per the following.
Gender : Male Female
Type : Hare Rabbit Jackrabbit Cottontail
Length of face : ______ cm
Length of ears : ______ cm
Ratio : ______
1 + 0 = _____
1 + 1 = _____
1 + 3 = _____
1 − 1 = _____
2 − 1 = _____
Since the whole project was generously financed by Goose, Snow Ears hired 8 other rodents to help him go around nests and burrows in the forest in their quest for willing participants. It took them two stressful weeks to collect the data, especially since their subjects had a habit of bolting on being approached by strangers. Finally they managed to get 400 respondents.
Scales eyed the table Snow Ears prepared.
Each group appeared to be equally represented. "Well done, Snow Ears." Scales then proceeded to plot out a graph from the data in the table.
The graph showed that the sample's test scores conformed to almost a normal bell-shape. The snake's tail twitched: Though a little spread out, the data has the appearance of how a normal population was suppose to look like. He drew a table of the data to help him calculate the central tendency.
From the Total column he established that the score which occurs the most frequently was "3". Hence he wrote down MODE = 3 in his notes.
Next he studied the accumulated number and calculated out the median position by dividing the number of respondents (400) in half. The Median score was also "3" since 200 was inside the accumulated total of 232. Again his notes showed MEDIAN = 3.
Trembling with excitement, he summed up the all the scores and divided them by the number of respondents to get the Mean Average. He wrote down MEAN = 3.3
Finally he split the data according to ear-to-face ratio and drafted out four graphs. He decided to use MODE to find the average for each Ratio Class since he was only interested in the most frequent occurrence of each test score.
Scales was elated with the result because it showed that the average intelligence was higher amongst the long-eared group. Now he has proof. However, Snow Ears wondered if the difference in counting skill was based on evolutionary needs because he did notice that hares and jackrabbits had longer ears than rabbits and cottontails, and these species have better counting skill. He drew up another table showing test scores to category.
True enough, the scores tally exactly to the snake’s graph for the length of ear-to-face ratio. Snow Ears decided to say nothing. After all, Dr. Scales should know best.
Central tendencies are used to show what an average person is like in a situation or what he will do in a given circumstance. That is the reason why if you draw out a graph showing a relationship between the number of respondents (y-axis) to the value being measured (x-axis) the graph will look like a bell. In the case where you are trying to study one particular group against an established hypothesis, and if the graph is skewed or almost flat, then it may mean that there is a deviation in the community you are studying. In the ear-to-face ratio graphs above Scales made the assumption that rabbit-hares with longer ears are smarter because their graph skewed to the right side of the graph where all rabbit-hares were plotted.
If the results don’t make sense, then the hypothesis used may not apply for the sample. However, as the story above illustrates, sometimes a relationship may appear to exist but the actual reason may be something else. It’s a pity that Snow Ears was too timid to follow up on his intuition because in effect he has more experience than Scales in dealing with the above subject since he himself is a rabbit. If he pursues the data further, they both may learn that Rabbits do badly in Math compared to Hares because burrowing and hiding is better valued than speed and punches. Hence the cause of the difference may be cultural and not physical.
