Lab Objective

To get more practice using JMP commands, and to illustrate the benefits of random sampling in surveys and causal studies.

Lab Procedures

In a survey, the sampled data should be representative of the target population. The simplest way to guarantee representative data is to collect data from randomly selected units in the population. We'll illustrate this using real data.

Open the file agpop from the course directory. This file is taken from the 1992 U.S. Census of Agriculture. It contains data on agricultural characteristics of all 3,078 counties in the United States. Variables include acres92 (number of acres devoted to farming in 1992), farms92 (number of farms in 1992), largef92(the number of farms with more than 1,000 acres), smallf92 (the number of farms with fewer than 9 acres), and similar variables for the 1987 and 1982 censuses. Also included are county and state names, and a variable indicating the county's region of the country (West, Northeast, North Central, South). For more information on the Census of Agriculture, including data from the 1997 census, you can visit the web site of the National Agricultural Statistics Service.

Data analysis tip: When looking at a data set for the first time, it is always a good idea to play around with it to get a feel for what it contains. For example, I saw some -99 values in the data. Obviously, it is not possible to have negative numbers of farms or negative acres of land. The conclusion I can reach is that the -99s identify missing data. Missing data require special care, and you should seek out a professional statistician when you have lots of missing data. For this lab, we'll be stupid and treat -99s as genuine values.

Questions: Exploring the data

Hints for questions 1 - 3: With smart sorts and summaries, you can answer these questions very quickly.

1) What is the trend in total acres devoted to farmland in Durham County, NC, from 1982 to 1992? That is, did Durham become more or less agriculturally based over those 10 years? Report numbers to back up your claims.

2) What is the trend in total acres devoted to farmland in the state of North Carolina over the same period? Hint: In Tables-Summary, you can get summaries of more than one variable simultaneously by holding the "Shift" button while highlighting the variables.

3) Which state had the smallest number of farms in 1992?

The Census of Agriculture is a census, so the data set can be used to obtain quantities for the entire population. For example, we can calculate the total amount of acres devoted to farming in the whole United States, the total number of farms in the whole United States, etc. Let's use JMP to get some of these quantities.

Select the Analyze menu option in JMP, then click on Distribution. You'll see a box with the names of the variables. Highlight farms92, then hit Y-columns. Do this with all the 1992 variables. Now click Okay to get summaries of the variables, such as the means, medians, and many other statistics we'll use later in the semester. You'll also see histograms and possibly other graphical displays. We'll use those later in the semester as well.

Write down the population means on scrap paper for use in a later question.

Since we have the actual population means, there's no need to take random samples. There's no point in estimating numbers when you can know them exactly! However, our objective for lab is to see if random sampling works in a real data set. So, here's what we'll do. We'll use JMP to take a random sample of 500 counties. If random selection truly gives a representative sample, the averages of the variables in the sample should be close to the averages of the variables in the whole population of 3,078 counties.

At first glance, it may seem preposterous to claim that 500 counties can represent 3,078 counties. Look at the ranges of some of the variables: the acres92 has a smallest value of -99 and a largest value of 7,229,985 acres, and the number of large farms in a county stretches from 0 to 579. How are we possibly going to get a sample that reflects the characteristics of all these wide-ranging variables with only 500 out of 3078 counties?!? Let's see what happens....

Question:

4) Take a random sample. Based on comparisons between the sample means and population means, does it seem that picking counties at random provides a representative sample? Talk to the TA or instructor about your conclusions, and any questions that you may have. After you talk to the TA or instructor, they will give you credit for answering this question.

It's easy to take a simple random sample in JMP from a data file. First, make sure that no columns are highlighted. Then, select Tables from the menu options, then select Subset. Choose the option for Random Sample. Enter 500 as the sample size, i.e. the number of counties to be sampled. Hit OK and you get a new data table with 500 randomly sampled counties. If you want to take another random sample to check if the results from the first sample were just dumb luck, close this new data table and repeat the previous instructions.

The sample size 500 was chosen arbitrarily. Later in the semester, we'll learn a principled method of choosing sample sizes.

To me, what's amazing about this is that you usually get pretty close by just throwing darts. In fact, you would be hard pressed to get closer on all variables by any non-random method of selecting data. I dare you to try at home.

Data analysis tip: Here's a generic method for taking a random sample from a population. First, give each unit on the sampling frame a distinct number in the range 1 to N, where N is the total number of units on your sampling frame. Second, open a new data file in JMP and create a single column with numbers from 1 to N. Third, pick a random sample of these numbers from this file using the Subset - Random Sample method. Finally, collect data for those units whose numbers were picked in the sample.

To generate a column of numbers in JMP that go from 1 to N, go to Cols - Column Info. Select New Property - Formula. Then, select Edit Formula. Next, select Numeric - Count. Enter 1 in the from box; enter the number N in the to box and the steps box. Click Okay until you get back to the data sheet.