EXAMPLE: Suppose you are interested in studying the current Sampling Unit: an individual fishPopulation: the values of the variables under study for all Sampling in Observational vs Experimental StudiesIn general, sampling strategies for observational studies muCluster = rock = “primary sampling unit”Response Variable: ____Math test score____________Factors: _______A) Hours of Sleep_______________1) Does any kind of sleep deprivation affect test scores?Compare no deprivation to each of other typesTopic (2) – Sampling and Experimental Design 2-1 Topic (2) – Sampling and Experimental Design Some Definitions Experimental (or Sampling) Unit is the object or event from which the measurements are taken e.g. tree where the number of leaves is measured leaf where the weight is measured acre of land where the number of trees is measured hurricane where maximum inches of rain/hour is recorded year where the number of hurricanes of class 4 is recorded A Variable is the information recorded on an experimental unit e.g. Y = number leaves/tree Y = weight of leaf Y = number of trees/acre Y = max inches of rain/hour for a hurricane Y = number of hurricanes of class 4/ year NOTE: There can be several variables measured at once on the same experimental unitTopic (2) – Sampling and Experimental Design 2-2 e.g. number of leaves on the tree, the diameter at breast height of the tree, the species, etc. Categorical Variables are variables that can only take on values that are non-numeric categories or groups. The set of possible values should be mutually exclusive and exhaustive. Mathematical operations cannot be performed on categorical variables even if coded with numbers. e.g. color of a rose make of a car ethnic group species of tree name Quantitative Variables are numeric in value and hence have meaning as a measurement or quantity. Further, arithmetic operations can be performed on quantitative variables. e.g. number of car accidents on campus in July length of an antenna weight of a book kilowatts used in an hour number of segments in the abdomen of a arthropodTopic (2) – Sampling and Experimental Design 2-3 1) Discrete Variable – quantitative variable which can take on only certain values number of car accidents on campus in July number of segments in the abdomen of a arthropod size class of a fish when recorded to the nearest 5 cm 2) Continuous Variable – quantitative variable which can take on any value in one or more intervals length of an antenna weight of a book kilowatts used in an hour Population: the complete set of values of one or more variables that could be measured on the entire set of experimental units under study. The definition of population depends on the particular research problem under study and on the method of sampling from that population. Sample: the set of values of one or more variables that were measured on a subset of the population of interest.Topic (2) – Sampling and Experimental Design 2-4 EXAMPLE Research problem: effect of a drug on blood plasma cholesterol level in people who present at the doctor’s office with high levels Population: the cholesterol levels before and after drug treatment of individuals who 1) have high cholesterol levels and 2) could be picked for the study Sample: the before and after blood plasma cholesterol levels of the 100 people selected to participate in he study EXAMPLE Research problem: effect of a herbicide on corn yields in 100 m2 plots Population: set of corn yields for all 100 m2 plots that could have been selected for herbicide treatment Sample: set of corn yields for the 100 m2 plots that were selected for herbicide treatmentTopic (2) – Sampling and Experimental Design 2-5 RESEARCH STUDIES An important part of statistics is the data collection effort. It is done in order to draw some conclusions or make some inferences about the population being sampled. To do this one develops and carries out a RESEARCH STUDY. The study describes the methods for collecting and analyzing the data in order to test the hypotheses of interest. Two kinds of research studies: OBSERVATIONAL STUDIES are those in which data are observed on a sample of the population. Here the usual interest is either describing the population or comparing two or more populations. A problem with observational studies is the inability to assign causality. Effects of environmental conditions on lung cancer rates.Topic (2) – Sampling and Experimental Design 2-6 EXPERIMENTAL STUDIES are planned and are studies in which units are manipulated or treated in order to observe the responses to the treatment. Comparing damage by the corn earworm on corn treated with one of three levels of pesticide. EXAMPLE: Suppose you are interested in studying the current diet of wild striped bass in the Chesapeake Bay and whether diet varies by region. So, you identify five sites at which you will collect fish and determine their stomach contents. Data will be collected in summer only. You will record the length, weight, body condition index, stomach weight, stomach contents by weight within categories, and you intend to age the fish using otoliths. Type of Research Project: observational Variables: Length, weight, body condition index, stomach weight, stomach content by species, weight of each species found in the stomach, age, location of the capture of the fish, date of capture, any variables describing the location where the fish was caught such as water temperature, etc.Topic (2) – Sampling and Experimental Design 2-7 Sampling Unit: an individual fish Population: the values of the variables under study for all fish that could have been caught at these 5 locations at the time of the study NOTE: please note the explicitness of this description. It does not extend to other fish at other locations and times since we did not randomly select these 5 sites or the times of collection (summer). The sites and times were chosen specifically for their physico-chemical characteristics and so all we can really determine is estimation of the characteristics of fish at those locations at that time. Sample: The fish caught during the study. The Population Size is the number of individuals, objects or events in your population. When the population is countable, the size is denoted with
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