Business Law

Module 2: Comparing Two Categorical Variables In Module 1, we looked at describing a single variable, and in Module 2, we will start to compare variables to one another and look for a relationship between them. Before we start to make such a comparison, it is important to make a note of the importance of random sampling and say a few words about a good hypothesis. Random Sampling Most of thedata used by political scientists is a sample of the population they are trying to measure. A population is every single case of what the researcher wants to study. Usually it is not possible to obtain data on every single member of a population, so a researcher uses a sample instead. A sample is a smaller set of cases of the population. In order for a sample to be accepted for use in statisticaltesting, the sample must be representative of the population as a whole. To assure that a sample is representative of the population, researchers use a technique known as random sampling. The idea behind random sampling is to arrange all the members of the population in a list, randomly select a number of them, and obtain data from them. The key is that every member of a population must have anequal chance of being selected; if this weren’t true, then the sample wouldn’t be truly random, and therefore not representative of the population. Most statistical tests, and all of them discussed in this guide, assume that the data you are testing is truly representative of the population and uses random sampling. Suppose that a researcher wants to do a study on the American public. He obtains alist of telephone numbers of every person in Alabama, Colorado, Indiana, Maine, and Oregon. He then randomly selects 1000 numbers and obtains the data from them that he needs. Is this sample representative of his target population? No, of course not. Only people in those five states have a chance to be surveyed, whereas someone in Michigan has no chance of being surveyed. Therefore, the populationfor his sample is only the public in those five states and not the entire American public. Now suppose that same researcher is able to get a list of all the phone numbers of everyone in America. To obtain his sample, he selects every 10,000th person on the list and surveys him or her. Is this an acceptable method for the researcher to use? Again, the answer is no. The method the researcher usedis not random. Everyone on the list does not have an equal chance to be selected because only every 10,000th person is selected. This is calculated rather than random. The most popular way of getting a random sample is by using a table of random numbers (available in most statistics textbooks). Other methods of making selections random could involve rolling dice or computer randomness programs.The data used in this guide can be assumed to be a random sample. GSS1998.dta and NES2000.dta are prime examples of random samples obtained by professional organizations. STATES.dta and WORLD.dta are examples of times when it is possible to collect data on an entire population. Thus, we don’t have to concern ourselves with whether these samples are representative. Keep in mind that evenrepresentative samples contain some sampling error. The statistical tests that we will be exploring will explain how to account for this error and make a conclusion about a relationship with some certainty.

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A Good Hypothesis Every empirical study starts with a good hypothesis. A hypothesis explains the results that a researcher thinks he will obtain from his testing. Usually a hypothesis hasbeen well researched and involves a theory that the researcher hopes to support with data. A good hypothesis provides three important pieces of information about the study: the population, the variables involved, and the expected direction of the relationship. A good rough skeleton of a hypothesis is: In comparing (insert population), those (cases) with a higher (independent variable) will have a...