In this section we deal with the fifth step in the research process, the design. Chapter Three explains some of the basics regarding populations, samples and validity. We explore how to draw samples from populations, how to assign samples to groups, the influence of the sample on the external validity of the study, and the effect of other events and actions on the internal validity of the study.
Populations and Samples
Population  Any set of people or events from which the sample is selected and to which the study results will generalize.
Sample  A group of people or events drawn from a population. A research study is carried out on a sample from a population. The goal is to be able to find out true facts about the sample that will also be true of the population. In order for the sample to truly reflect the population, you need to have a sample that is representative of the population. The best method to use to obtain a representative sample is to randomly select your sample from the population. A study that has a large, randomly selected sample or a carefully matched sample is said to have external validity.
A nonrandom sample reduces the external validity of the study. Much medical research is done on the patients one sees in the clinic, this is a nonrandom sample that is not representative of a larger population and will not generalize. Because it will not generalize is not a fatal flaw in the study. A study with a nonrandom sample still identifies true facts about the sample and perhaps those findings will be true for others as well. It is best to define your population first, and then obtain a random sample.
The sample size required depends on the requirements of the study and size of the population. As a rule the bigger the better. If the sample is too small then the performance of a few individuals can have a big effect on the data, and render the data less representative of the population.
Sample Selection Methods  There are several methods for drawing random samples. All methods produce good random samples.
Sample Assignment Methods  If you have more than one group then subjects need to be assigned to groups. It is important that groups be equal at the beginning of a study. If the groups are not equal then you cannot know if the independent variable caused changes in the subjects or if the inequality did. There are two good methods for assigning your sample to experimental groups and a third way, not so good, that often occurs:
Summary of Sample Selection and Assignment. Figure 4 summarizes the preceding discussion in terms of sample selection and assignment. The diagram also points out the consequences of how the sample is selected and assigned on the external and internal validity of the study. The next section discusses these two aspects of validity in more detail.
Samples and the Validity of a Study
A valid research study is one that finds the truth. We hope to discover facts and principles that explain or predict. There are two components of validity that have been identified. These components are external and internal validity. We can use these components of validity as criteria to see if a particular study is valid.
External validity is dependent on the adequacy of the sample. If the sample is representative of the desired population then our results will generalize. This is called generalizability. Thus, if we study patients in a free clinic can we generalize to patients of a private physician? The answer is no, to be able to generalize to both groups we must include subjects from both care sources.
To have a generalizable sample, first define your population, then randomly select a large sample. With a random sample of sufficient size research findings can generalize to the larger population. As a rule of thumb random sample sizes of twenty subjects per group are minimally sufficient.
Internal validity refers to the adequacy of our study design and the degree of control we have exercised in our data gathering. Good internal validity is insured by application of the concept of control. This concept is very important in research. By control we mean that all variables except the dependent variable are controlled by the experimenter. In this way if the dependent variable changes during the study then that change is due to the changes the experimenter made in the independent variable(s). The concept of control has six major parts:
In evaluating the internal validity of a study we ask this question: Was the experimental manipulation the only possible cause of a change in the dependent variable? In general, if a study adequately responds to the six factors above, then it will have controlled for many extraneous influences, will allow the researcher a good chance of detecting any change in the dependent variable, and will have internal validity. Note that a study can have good internal validity and NOT find any changes in the dependent variable due to the independent variable. Also, a study can have good internal validity, but without a generalizable sample, it may have no external validity. Finally, remember that a study with no external validity still found true relationships for the sample that was studied. If I study Mongolian fishermen in Cleveland, I cannot generalize to Vietnamese shrimpers in the Gulf, but I still know more about Mongolian fishermen.
Do not confuse internal validity with the validity of the method by which the dependent variable is measured, called test validity. Internal validity refers to the overall degree of control exercised. Test validity refers to the suitability of the measuring instrument used.
Over the years a number of terms have been introduced that describe various factors that can adversely influence the internal validity. We have already discussed most of these factors, but we have not necessarily used these common terms before. The list below will familiarize you with these names and their definitions.
Summary of Internal and External Validity
Samples and Probability
Probability is the science of figuring how often something will happen. Probabilities are based on past events. If I toss a coin, there are two outcomes, heads or tails. If I toss a coin a lot of times, I will find that half of the time I get a head. Thus, the probability of getting a head on the next coin toss is 1 outcome divided by 2 possible outcomes or .5.
Why is it that the probability of getting a head is .5 and not .6 or .4? This has to do with the concept of "random events". When I toss a coin there are two outcomes, heads or tails. The result of my coin toss is a random event; each outcome has an equal chance of occurring. Since there are two possible outcomes, and the outcome is a random event, then the probability of a head is .5 (or 50 times out of 100 I will get a head). If I roll a die, which has six sides (six outcomes), the probability of my getting "three spots" is one divided by six or .17 (17 times out of 100 I will get "three spots" when I roll a die). The probability of any random event is the number of events (tosses or rolls) divided by the number of possible outcomes.
When we take a random sample from a population, each subject we select is a random event. Thus, if our population was 60% women and 40% men, the probability of our drawing a woman each time would be .6 and of drawing a man would be .4. If we draw a big sample, the final proportion of men and women in our sample would be the same as in the population. Each event has an equal chance of occurring and thus will occur in the proportion with which it exists. This is why a random sample is the easiest and best way to draw a sample.
Random samples are only the best way if the sample can be large. With a small sample, you may not get the proportions to "average out". If we only drew five people from a population that was 60% women and 40% men we could very well draw five women, just by chance. Only with a large sample (say 20 to 100) will the random events produce samples that are proportional to the population.
Use of the Random Number Table  A random number table is often used for subject assignment and sample selection. While subjects can be selected or assigned by drawing their name out of a hat, a more elegant method is to use a random number table. The steps below illustrate the use of a random number table.
To use the table:
Table of Random Numbers

COLUMN 

1 
2 
3 
4 

1 
10480 
91646 
16308 
51259 
2 
22368 
89198 
19885 
60268 
3 
24130 
64809 
04146 
64904 
4 
42167 
16376 
14413 
58586 
5 
37570 
91782 
06691 
09998 
6 
88321 
53498 
30168 
29119 
7 
48235 
31016 
25306 
63553 
8 
52636 
20922 
38005 
09429 
9 
87529 
18103 
00256 
42751 
10 
71048 
59533 
92420 
19734 