Quantitative approaches Quantitative approaches Plan Lesson 3: Sampling 1. Introduction to quantitative sampling 2. Sampling error and sampling bias 3. Response rate 4. Types of "probability samples" 5. The size of the sample 6. Types of "non-probability samples" 1 2 Quantitative approaches Quantitative approaches 1. Introduction to quantitative sampling Sampling: Definition Sampling = choosing the unities (e.g. individuals, famililies, countries, texts, activities) to be investigated 3 4 Quantitative approaches Quantitative approaches Sampling: quantitative and qualitative Population and Sample "First, the term "sampling" is problematic for qualitative research, because it implies the purpose of "representing" the population sampled. Population Quantitative methods texts typically recognize only two main types of sampling: probability sampling (such as random sampling) and Sample convenience sampling." (...) any nonprobability sampling strategy is seen as "convenience sampling" and is strongly discouraged." IIIIIIIIIIIIIIII Sampling This view ignores the fact that, in qualitative research, the typical way of IIIIIIIIIIIIIIII IIIII selecting settings and individuals is neither probability sampling nor IIIII convenience sampling." IIIIIIIIIIIIIIII IIIIIIIIIIIIIIII It falls into a third category, which I will call purposeful selection; other (= «!Miniature population!») terms are purposeful sampling and criterion-based selection." IIIIIIIIIIIIIIII This is a strategy in which particular settings, persons, or activieties are selected deliberately in order to provide information that can't be gotten as well from other choices." Maxwell , Joseph A. , Qualitative research design..., 2005 , 88 5 6 Quantitative approaches Quantitative approaches Population, Sample, Sampling frame Representative sample, probability sample Population = ensemble of unities from which the sample is Representative sample = Sample that reflects the population taken in a reliable way: the sample is a «!miniature population!» Sample = part of the population that is chosen for investigation. The choice may be based on Probability sample = Sample that has been randomly randomness or not. chosen. Therefore, every unity has a known probability to be chosen. Sampling frame = list of all the unities from which the choice is made. 7 8 Quantitative approaches Quantitative approaches Representativity: an empirical question 2. Sampling error, sampling bias The representativity of the sample cannot be assured by following a given method. If we use the correct methods (random choice, stratification etc.) we can only maximize the probability of producing a representative sample. It is an empirical question (and should be tested) if the sample is really representative of the population. For example: we would investigate if the percentage of women in the sample are not significantly different from those of the population (==> the sample is representative concerning gender). 9 10 Quantitative approaches Quantitative approaches Errors: different types Sampling error, sampling bias 1. Sampling error due to chance, size of sample Sampling error = Differences between the sample and the 2. Sampling bias not due to chance or size of population that are due to the sampling sample. E.g. non-response linked (the randomness). Sampling error can be to the specific theme of the diminished by increasing the size of the research sample 3. Data collection error e.g. bad question wording; bad interviewing Sampling bias = Differences between the sample and the 4. Data processing error e.g. wrong coding population that are not due to sampling 5. Data analysis error e.g. wrong statistical model; (the randomness); the sampling bias erroneous data analysis does not diminish with increased sample size. 6. Data interpretation error e.g. wrong interpretation of results 11 12 Quantitative approaches Quantitative approaches Sampling error/bias: example (I) Sampling error/bias: example (II) smokers non-smokers smokers non-smokers smokers non-smokers smokers non-smokers O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O Population : N = 200 Population : N = 200 Population : N = 200 Population : N = 200 Sample : N = 32 Sample : N = 32 Sample : N = 32 no error/bias a bit of error/bias a lot of error/bias P(s) = 0.5; p(s) = 0.5 P(s) = 0.5; p(s) = 0.47 P(s) = 0.5; p(s) = 0.33 13 14 Quantitative approaches Quantitative approaches Sampling error: decreases Possible reasons for sampling bias with increasing sample size Experiment with a coin • The sampling frame does not include all the elements of the Probability of throwing «!heads!»? population (example: telephone directory) • The choice is not really random (example: open telephone P «!in reality!» = 0.5 directory at a random page and choose the next 600 names) We do 5 tries with N =1,2,5,20 • Certain groups of respondents have a higher (lower) response rate (example: the very poor, the very rich, ther very active, With growing N, the p is approaching the P the people with an active interest in the question, the people critical of surveys) N = 1 -> p = 0, 1, 0, 1, 1 N = 2 -> p = 0, 0.5, 0.5, 1, 0 N = 5 -> p = 0.6, 0.2, 0.4, 0.8, 0.1 N = 20 -> p = 0.4, 0.35, 0.45, 0.35, 0.55 15 16 Quantitative approaches Quantitative approaches Sampling error vs.