Sampling

Sampling A sample is a small number of individuals representing a larger group. Samples and Populations  A sample in a research study is a relatively small number of individuals about whom information is obtained. The larger group to whom the information is then generalized is the population. Why use samples?  Although the best data comes from studying an entire population, samples are used because they are smaller and less unwieldy. It can be too time consuming and expensive to study an entire population. Defining the population Whether a researcher is drawing a sample or is studying an entire population, the population needs to be defined. This helps focus the research. Target vs. accessible populations  The target population is the population a researcher would like to generalize to. Often this isn’t possible, so the accessible population is used. For example, a researcher might want to target all male elementary teachers in the United States, but actually collects data from the male elementary teachers in Hawaii. Random vs. nonrandom sampling  Random sampling is completely based on chance. For example, one might identify all members of a population, (n=250) write their names on separate pieces of paper, and then draw 25 names out of a hat to determine who is actually to be included in the study. Nonrandom sampling  In a nonrandom sample, members are selected on the basis of a particular set of characteristics, rather than a random chance of being included. Simple random sample  In a simple random sample, each and every member of a population has an equal and independent chance of being selected. Table of random numbers  A table of random numbers is used to identify the people to be included in a sample. These are usually found in statistics books, or can be generated by some calculators and computers. Stratified random sample  In stratified random sampling, subgroups within a target population are identified to be included in proportion to the numbers in which they exist in the population. For example, a researcher studying aggressive behavior in dog breeds found in Hawaii would want to include a sample of registered breeds in the proportion they are found in the state. Cluster sampling  In situations where simple random sampling isn’t possible, as is often the case in schools, groups or clusters are identified for inclusion in research. For example, a researcher might choose to study all of the students in some specific classes. Two stage random sampling  This technique combines random sampling with cluster sampling. It allows a bigger group to be targeted for generalization. Systematic sampling with a random start  In this procedure, a random number is generated to identify the first member selected for a sample, and then every nth member of the population is selected for inclusion. For example, the first member selected in a population of 500 might be # 412, and then every 7th person is chosen: 419, 426, 433, 440, 447, and so on. When you pass 500, you loop back to the beginning. Sampling ratio  This is the proportion of individuals selected for a study. For example, you might select to study ten percent of the population. The ratio is defined as the sample size divided by the population size. Convenience sample  When it isn’t possible to draw a random or systematic nonrandom sample, a researcher might choose to study the individuals who are available. This is known as a convenience sample. Purposive sampling  A purposive sample is one identified on the basis of specific characteristics identified by the researcher. For example, if a researcher wanted to study all of the foreign-born teachers in a school district, he or she would try to identify all of those individuals and include only them. External validity  Since the entire point of sampling is to generalize the results to a larger population, researchers need to be sure their work actually does represent the population. The extent to which information can be generalized to a larger population is known as external validity. Representative samples  A representative sample provides the most accurate portrayal of the population being studied. Replication studies  A replication study follows the format of a previous study, but uses a new group of subjects or a new set of conditions or both. Ecological generalizability  This term refers to the degree to which a study can be generalized to a different set of conditions. For example, researchers studying rural schools might have difficulty generalizing their results to urban schools. Data  Data is a plural word that refers to the kinds of information researchers collect. Data should be followed by a plural verb, such as “Data are” or “Data were”. Instrumentation  The process of preparing to collect data is called instrumentation. It involves the selection of the method by which data will be collected, as well as the procedures and conditions for collecting them. Validity  This term refers to the defensibility of the inferences a researcher can make from a study using an instrument. Reliability  Reliability refers to consistency of results. If a study is repeated, will it yield similar findings? A good example of reliability might be having three different people grading students’ essays. Will all three of them agree on what constitutes an A, B, C, etc? Or will their scoring vary widely? If there is a large variety, the grades would not be reliable. Objectivity  This characteristic refers to the absence of subjective bias on the part of the researcher. For example, political analyst with a particular ideological bent might conduct a poll differently from one who has no affiliation. Different types of instruments  Researcher instruments are used by the researcher to collect data; a tally sheet or rubric are examples.  Subject instruments are completed by the subject. A survey questionnaire is an example.  Informant instruments are completed by knowledgeable participants providing information in addition to that collected by researchers and given by subjects. Selecting instruments  Instruments may be selected in one of two ways. Either a researcher locates one that has been developed by another person, or he/she designs a new one. The advantage of selecting existing ones is that they have often been field tested for reliability and validity. Collecting data  Data may be collected in a variety of ways. Respondents might give written responses, or they might perform a task. Doing a miscue analysis on a student is an example of a performance analysis. Rating scales  The difference between observation and rating is that when a researcher rates a subject, he or she is making a judgment of some type. On the other hand, when a researcher makes an observation, he or she is merely recording behavior and not judging it. For example, a rating might be that a girl made 3 baskets in 20 attempts, thus scored 2 on a scale of poor to good on free throws, while an observation would just note the number of baskets/attempts. Researcher instruments  Interview schedules  Tally sheets  Performance checklists  Anecdotal records  Time-and-motion logs Subject instruments          Questionnaires Self-checklists Attitude scales Personality inventories Achievement tests Aptitude tests Performance tests Projective devices Sociometric devices Scores  Raw scores are the initial scores obtained on a test. The number right out of a total number of questions is an example.  Derived scores have been scaled to show their relative position with respect to other raw scores. Derived scores  Percentile ranks  Age/grade equivalence  Standard scores Norm-referenced vs. Criterion referenced  A norm-referenced test is developed to provide scores that replicate a normal curve among the population tested. Thus, among a population taking the test, half of the people should score above average and half below.  A criterion referenced test is based on a goal and an identified percentage is targeted to reach that goal. Measurement scales  A nominal scale, the simplest scale, identifies groups by a number, e.g. “1” for male and “2” for female.  An ordinal scale provides an rating from most to least. A Likert scale is an ordinal scale.  An interval scale is an ordinal scale that has the addition of equal distances between the points. IQ is measured using an interval scale.  A ratio scale is an interval with a true zero and is rarely used in educational measurement.