Unformatted text preview: Probability (Random) Sampling Probability Sampling Utilizes some form of random selection All units in the population have equal probability of being chosen Nomenclature: N = number of cases in the sampling frame n = number of cases in the sample NCn = number of combinations of n (cases) from N (sampling frame) f (sampling fraction) = n/N Random Selection vs. Random Assignment Random selection individuals are randomly selected as representing a population Random assignment individuals are randomly assigned to different groups or treatments Sampling Simple Random Sampling (SRS) the selection of sampling elements or units whereby each possible unit from a population has an equal chance of being selected. It also assumes that chances of selection are independent. SRS usually entails selection without replacement of elements or units previously selected Fairly easily to conduct and are the basic statistical sampling technique in social sciences and public health. With large samples, SRS can be expensive and time consuming. Sampling frame refers to the population list from which the SRS will be selected. Sampling ratio/interval the ratio of the sample to the size of the population (ex. Pop.=1250, Sample = 75) Sampling Ratio is 75/1250 = .06 or 6%. Key SRS Concepts Sampling or standard error is the disparity between the SRS estimate and the true/actual results based on the population. It is a statistical concept based on probability theory (central limits theorem). Sampling distribution is the statistical likelihood that an infinite number of sample results will represent the true population or the normal curve (bell shape distribution). In practice only one sample is selected. Key Concepts of SRS Central limit theorem represents the mathematical distribution of an infinite number of SRS where the results form a normal curve. Confidence interval is the statistical range (e.g., + 3) based on the central limit theorem and represented by the pvalues 95% (p < 0.05), 99% (p = 0.1) or 99.9 ( p < 0.001). That is, the researcher expresses "confidence" that their results (95 out of 100 times) are likely to be within 3 or +3 of the results for the true population. Central limit theorem Central http://www.ruf.rice.edu/~lane/stat_sim/sampling_d http://www.ruf.rice.edu/~lane/stat_sim/sampling_di Stratified Sampling Stratified sampling refers to the subdivision of the population of interests into separate strata or groups and the selection of a random sample from each stratum. Each stratum would comprise the entire sample. It differs from SRS or systematic sampling because it allows the researcher greater control over who will be selected. The size of each stratum can be determined by the research question (e.g., hypertension) and the distribution of strata (e.g., young Asian males) within the population of interest (Asian men). Stratified Sampling Stratified sampling reduces the sampling error because it is more likely to representative of the true population. Accurate information (e.g., U.S. Census data) is needed about the population prior to the selection of a stratified sample. Substantial cost is often associated with stratified sampling compared to SRS. Stratified sampling is used most often in surveys of large, geographically dispersed, and diverse populations (e.g., national samples). Stratified Sampling Disproportionate to size stratified sampling refers to the selection of strata (e.g., Asian Americans) either above the proportion (i.e., oversampling) in the population of interest (South) or under their proportion (i.e.,undersampling) in the population (e.g., native born residents of PA). Disproportion to size sample requires the use of statistical weights in the analysis to adjust for the unequal probability of selection. A major advantage is that it allows the researcher to have a larger sample size for a specific population group. Stratified Sampling Proportionate to size stratified sampling means that the sample strata are selected relative to their proportion in the population. For example with the Asian American male population, the young Asian male population may be defined as between 1830 years old. If they represent 32% of the Asian male population in the U.S., then this would be the proportion of young Asian Americans in the total stratified sample. Systematic Random Sampling
1. 2. 3. 4. 5. 6. Randomly order your sampling frame Determine the total number of individuals in your sampling frame (N) Determine a needed sample size (n) Get an interval size (K) Select a random number between 1 and k Select every kth unit in your sampling frame
k = N/n Systematic Sampling Example Take a page from the phone book: Randomize the listing (N= 150) You need 50 people (n = 50) Interval size (k) = 3 Select a number from 13...(2) Sample every 2nd person on your list Cluster (Area) Random Sampling Divide your population into clusters Geographic boundaries work well Randomly select clusters within your population to sample Measure ALL units within the selected clusters Random Sampling Summary Non-Probability (NonRandom) Sampling Nonrandom sampling
In reality, often difficult to get truly random sampling in humans
1. 2. 3. 4. 5. 6. Convenience Purposive Expert Proportional Quota Nonproportional Quota Snowball Convenience sampling Most often "public opinion" poll type measures Just getting information from those available at the moment "Snapshot" research Not representative Purposive sampling Sampling with a purpose Most often things like "Market Research" Looking for particular sections of a population to get information from Based on categorization or the ability to do so Expert Sampling Sampling a group of "Experts" Individuals with demonstrable knowledge and expertise in an area Can be used to demonstrate or approve the use of other types of sampling in a particular situation Proportional Quota Sampling Nonrandom sampling with the purpose of getting specific numbers of individuals that is proportionate to the number of individuals in the population of interest 60% men 40% women in the population Sample 60 men and 40 women in a 100 person sample Non-Proportional Quota Sampling Only identify the minimum number of individuals with a particular characteristic to sample So you are concerned that you have at least enough people to talk about effects within the population of interest Males in Nursing Black Women in Aerospace Engineering Snowball Sampling AKA "Word of Mouth" sampling Identify people who meet a criteria and then ask them to refer you to other individuals and so on... Non-Random Sampling Summary ...
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- Spring '07
- ) Sampling