Gettysburg Address

Perhaps the most vital concept in statistics is the use of a sample to discover things about a population.

Consider the population of 268 words below:

Four score and seven years ago, our fathers brought forth upon this continent a new nation: conceived in liberty, and dedicated to the proposition that all men are created equal.

Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battlefield of that war.

We have come to dedicate a portion of that field as a final resting place for those who gave their lives that that nation might live. It is altogether fitting and proper that we should do this.

But in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow this ground. The brave men, living and dead, who struggled here have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember, what we say here, but it can never forget what they did here.

It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us, that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion, that we here highly resolve that these dead shall not have died in vain, that this nation, under God, shall have a new birth of freedom, and that government of the people, by the people, for the people, shall not perish from the earth.

(a) Select a sample of ten representative words from this population by circling them in the passage above.

The passage above is Lincoln's Gettysburg Address. For our purposes, we are considering this to be a population of words from which you obtained a sample of ten words. In most situations, the entire population is not observable, and we must consider only a sample from the population of interest. The practice of statistics is to utilize information from the sample (eg, an opinion poll, a market research study, testing of a limited amount of product) to learn something about the corresponding population (eg, all registered voters, all potential buyers, all shipped production). To do this effectively, it is important that the sample is reasonably representative of (eg, has the same characteristics as) the larger population.

(b) Record the words and the number of letters in each word for the 10 words in your sample

	1	2	3	4	5	6	7	8	9	10
Word
# letters

(c) Determine the average (mean) number of words in your sample of ten words:

Average = Sum of all letters / 10 =

(d) The average number of letters per word in the population of all 268 words is 4.29. Was the average for your sample larger than this?

(e) Do you believe the ten words in your sample are representative of the lengths of the 268 words in the population? Briefly explain your response.

When sampling methods produce characteristics in the samples that systematically differ from the characteristics of the population, these sampling methods are considered biased.

(f) Would you say that the sampling method used here - simply asking people to circle ten words - is biased? If so, in which direction? Why might this be the case?

(g) What if you closed your eyes and just pointed at a location in the passage using the word most clearly identified? Might this method of sampling also be biased? Explain.

In general, human judgment is not the best approach to acquire representative samples from populations. A simple random samplegives every element in the population the same chance of being selected for the sample. While clear in principle, implementation of simple random sampling is often not so simple.

The first step is to generate a sampling frame where each member of the population is given a number. Then it is best to utilize a computer to generate random numbers to be selected (using the sampling frame) for the sample itself.

To really examine the nature of a sampling method, it would be desirable to take many repeated samples. In real situations, this likely is not going to be possible, and we will have the one sample that was obtained with which to work.