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POPULATIONS AND SAMPLING |
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Populations |
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Definition - a complete set of elements (persons or objects) that possess some common characteristic defined by the sampling criteria established by the researcher |
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Composed of two groups - target population & accessible population |
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Target population (universe) |
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The entire group of people or objects to which the researcher wishes to generalize the study findings |
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Meet set of criteria of interest to researcher |
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Examples |
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All institutionalized elderly with Alzheimer's |
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All people with AIDS |
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All low birth weight infants |
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All school-age children with asthma |
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All pregnant teens |
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Accessible population |
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the portion of the population to which the researcher has reasonable access; may be a subset of the target population |
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May be limited to region, state, city, county, or institution |
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Examples |
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All institutionalized elderly with Alzheimer's in St. Louis county nursing homes |
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All people with AIDS in the metropolitan St. Louis area |
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All low birth weight infants admitted to the neonatal ICUs in St. Louis city & county |
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All school-age children with asthma treated in pediatric asthma clinics in university-affiliated medical centers in the Midwest |
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All pregnant teens in the state of Missouri |
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Samples |
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Terminology used to describe samples and sampling methods |
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Sample = the selected elements (people or objects) chosen for participation in a study; people are referred to as subjects or participants |
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Sampling = the process of selecting a group of people, events, behaviors, or other elements with which to conduct a study |
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Sampling frame = a list of all the elements in the population from which the sample is drawn |
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Could be extremely large if population is national or international in nature |
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Frame is needed so that everyone in the population is identified so they will have an equal opportunity for selection as a subject (element) |
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Examples |
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A list of all institutionalized elderly with Alzheimer's in St. Louis county nursing homes affiliated with BJC |
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A list of all people with AIDS in the metropolitan St. Louis area who are members of the St. Louis Effort for AIDS |
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A list of all low birth weight infants admitted to the neonatal ICUs in St. Louis city & county in 1998 |
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A list of all school-age children with asthma treated in pediatric asthma clinics in university-affiliated medical centers in the Midwest |
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A list of all pregnant teens in the Henderson school district |
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Randomization = each individual in the population has an equal opportunity to be selected for the sample |
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Representativeness = sample must be as much like the population in as many ways as possible |
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Sample reflects the characteristics of the population, so those sample findings can be generalized to the population |
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Most effective way to achieve representativeness is through randomization; random selection or random assignment |
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Parameter = a numerical value or measure of a characteristic of the population; remember P for parameter & population |
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Statistic = numerical value or measure of a characteristic of the sample; remember S for sample & statistic |
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Precision = the accuracy with which the population parameters have been estimated; remember that population parameters often are based on the sample statistics |
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Types of Sampling Methods - probability & non-probability |
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Probability Sampling Methods |
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Also called random sampling |
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Types of probability sampling - see table in course materials for details |
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Simple random |
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A table displaying hundreds of digits from 0 to 9 set up in such a way that each number is equally likely to follow any other |
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See text for random sampling details & table of random numbers |
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Stratified random |
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Population is divided into subgroups, called strata, according to some variable or variables in importance to the study |
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Variables often used include: age, gender, ethnic origin, SES, diagnosis, geographic region, institution, or type of care |
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Two approaches to stratification - proportional & disproportional |
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Proportional |
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Subgroup sample sizes equal the proportions of the subgroup in the population |
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Example: A high school population has |
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15% seniors |
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25% juniors |
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25% sophomores |
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35% freshmen |
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With proportional sample the sample has the same proportions as the population |
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Disproportional |
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Subgroup sample sizes are not equal to the proportion of the subgroup in the population |
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Example |
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Class |
Population |
Sample |
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Seniors |
15% |
25% |
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Juniors |
25% |
25% |
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Sophomores |
25% |
25% |
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Freshmen |
35% |
25% |
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With disproportional sample the sample does not have the same proportions as the population |
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Cluster random sampling |
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A random sampling process that involves stages of sampling |
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The population is first listed by clusters or categories |
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Procedure |
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Randomly select 1 or more clusters and take all of their elements (single stage cluster sampling); e.g. Midwest region of the US |
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Or, in a second stage randomly select clusters from the first stage of clusters; eg 3 states within the Midwest region |
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In a third stage, randomly select elements from the second stage of clusters; e.g. 30 county health dept. nursing administrators from each state |
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Systematic |
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A random sampling process in which every kth (e.g. every 5th element) or member of the population is selected for the sample after a random start is determined |
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Example |
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Population (N) = 2000, sample size (n) = 50, k=N/n, so k = 2000 ) 50 = 40 |
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Use a table of random numbers to determine the starting point for selecting every 40th subject |
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With list of the 2000 subjects in the sampling frame, go to the starting point, and select every 40th name on the list until the sample size is reached. Probably will have to return to the beginning of the list to complete the selection of the sample. |
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Non-probability sampling methods |
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Characteristics |
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Not every element of the population has the opportunity for selection in the sample |
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No sampling frame |
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Population parameters may be unknown |
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Non-random selection |
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More likely to produce a biased sample |
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Restricts generalization |
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Historically, used in most nursing studies |
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Types of non-probability sampling methods |
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Convenience - aka chunk, accidental & incidental sampling |
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Selection of the most readily available people or objects for a study |
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No way to determine representativeness |
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Saves time and money |
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Quota |
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Selection of sample to reflect certain characteristics of the population |
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Similar to stratified but does not involve random selection |
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Quotas for subgroups (proportions) are established |
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E.g. 50 males & 50 females; recruit the first 50 men and first 50 women that meet inclusion criteria |
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Purposive - aka judgmental or expert's choice sampling |
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Researcher uses personal judgement to select subjects that are considered to be representative of the population |
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Handpicked subjects |
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Typical subjects experiencing problem being studied |
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Snowball |
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Also known as network sampling |
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Subjects refer the researcher to others who might be recruited as subjects |
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Time Frame for Studying the Sample |
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See design notes on longitudinal & cross-sectional studies |
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Longitudinal |
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Cross-sectional |
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Sample Size |
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General rule - as large as possible to increase the representativeness of the sample |
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Increased size decreases sampling error |
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Relatively small samples in qualitative, exploratory, case studies, experimental and quasi-experimental studies |
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Descriptive studies need large samples; e.g. 10 subjects for each item on the questionnaire or interview guide |
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As the number of variables studied increases, the sample size also needs to increase in order to detect significant relationships or differences |
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A minimum of 30 subjects is needed for use of the central limit theorem (statistics based on the mean) |
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Large samples are needed if: |
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There are many uncontrolled variables |
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Small differences are expected in the sample/population on variables of interest |
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The sample is divided into subgroups |
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Dropout rate (mortality) is expected to be high |
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Statistical tests used require minimum sample or subgroup size |
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Power Analysis |
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Power analysis = a procedure for estimating either the likelihood of committing a Type II error or a procedure for estimating sample size requirements |
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Background Information for Understanding Power Analysis: Type I and Type II errors |
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Type I error |
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Based on the statistical analysis of data, the researcher wrongly rejects a true null hypothesis; and therefore, accepts a false alternative hypothesis |
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Probability of committing a type I error is controlled by the researcher with the level of significance, alpha. |
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Alpha a is the probability that a Type I error will occur |
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Alpha a is established by researcher; usually a = .05 or .01 |
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A lpha a = .05 means there is a 5% chance of rejecting a true null hypothesis; OR out of 100 samples, a true null hypothesis would be rejected 5 times out of 100 and accepted 95 times out of 100. |
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Alpha a = .01 means there is a 1% chance of rejecting a true null hypothesis; OR out of 100 samples, a true null hypothesis would be rejected 1 time out of 100 and accepted 99 times out of 100 |
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Type II error |
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Based on the statistical analysis of data, the researcher wrongly accepts a false null hypothesis; and therefore, rejects a true alternate hypothesis |
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Probability of committing a Type II error is reduced by a power analysis |
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Probability of a Type II error is called beta b |
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Power, or 1- b is the probability of rejecting the null hypothesis and obtaining a statistically significant result |
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Type I & Type II Errors
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In the real world, the actual situations is that the null hypothesis is : True |
In the real world, the actual situations is that the null hypothesis is : False |
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Based on statistical analysis, the researcher concludes that: Null true: Null hypothesis is accepted |
Correct decision: the actual true null is accepted |
Type II error: the actual false null is accepted |
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Based on statistical analysis, the researcher concludes that: Null false: Null hypothesis is rejected & alternate is accepted |
Type I error: the actual true null hypothesis is rejected |
Correct decision: the actual false null is rejected & alternate is accepted |
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Background Information for Understanding Power Analysis: Population Effect Size - Gamma g |
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Gamma g measures how wrong the null hypothesis is; it measures how strong the effect of the IV is on the DV; and it is used in performing a power analysis |
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Gamma g is calculated based on population data from prior research studies, or determined several different ways depending on the nature of the data and the statistical tests to be performed |
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The textbook discusses 4 ways to estimate gamma (population effect size) based upon: |
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Testing the difference between 2 means (t-test) |
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Testing the difference between 3> means (ANOVA) |
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Testing bivariate correlation (relationship) between 2 variables (Pearson's r) |
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Testing the difference in proportions between 2 groups (chi-square) |
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If there is no relevant research on topic to estimate the population effect size (gamma), then use guidelines for gamma g or its equivalent |
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Testing the difference between 2 means (t-test) - gamma g for small effects g = .20; medium effects g = .50; large effects g = .80 |
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Testing the difference between 3> means (ANOVA) - eta squared h2 for small effects h2 = .01; medium effects h2 = .06; large effects h2 = .14 |
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Testing bivariate correlation (relationship) between 2 variables (Pearson's r) gamma g for small effects g = .10; medium effects g = .30; large effects g = .50 |
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Testing the difference in proportions between 2 groups (chi-square - no conventions for unknown populations |
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Determining Sample Size through Power Analysis |
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Need to have the following data: |
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Level of significance criterion = alpha a, use .05 for most nursing studies and your calculations |
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Power = 1 - b (beta); if beta is not known standard power is .80, so use this when you are determining sample size |
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Population size effect = gamma g or its equivalent, e.g. eta squared h2; use recommended values for small, medium, or large effect for the statistical test you plan to use to answer research questions or test hypothesis |
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Use tables on pages 455-459 of Polit & Hungler or other reference |
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Mathematical formulas and computer programs can also be used for calculation of sample size |
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Sampling Error and Sampling Bias |
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Sampling error = The difference between the sample statistic (e.g. sample mean) and the population parameter (e.g. population mean) that is due to the random fluctuations in data that occur when the sample is selected |
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Sampling bias |
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Also called systematic bias or systematic variance |
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The difference between sample data and population data that can be attributed to faulty sampling of the population |
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Consequence of selecting subjects whose characteristics (scores) are different in some way from the population they are suppose to represent |
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This usually occurs when randomization is not used |
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Randomization Procedures in Research |
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Randomization = each individual in the population has an equal opportunity to be selected for the sample |
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Random selection = from all people who meet the inclusion criteria, a sample is randomly chosen |
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Random assignment |
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The assignment of subjects to treatment conditions in a random manner. |
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It has no bearing on how the subjects participating in an experiment are initially selected. |
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See Polit & Hungler, pg. 160-162 for random assignment to groups and group random assignment to tx. using a random numbers table |
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