Textbook Notes (368,986)
Biology (363)
BIOL 300 (1)
Chapter 1

Bio 300 Ch. 1.docx

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Department
Biology
Course
BIOL 300
Professor
Michael Whitlock
Semester
Fall

Description
Chapter 1: Statistics and Samples 1.1- What is Statistics? - Biologists study properties of living things - Measuring properties of living things is a challenge because: o No two individuals of a population are exactly alike o Can’t measure everyone in a population due to time constraint and limited funding - Measuring properties of living things are done through a sample of individuals drawn from the population - Sampling brings uncertainty to the measurements because properties of the sample are not the same as the true values in the population - Statistics- technology that describes and measures aspects of nature from samples; makes it possible to quantify the uncertainty in measures - Estimation- process of inferring an unknown quantity of a target population using only sample data o Estimation allows us to assess differences between groups and relationship between variables - Parameter- quantity describing a population; “the truth”; ex. averages, proportions, measures of variation, measures of relationship…etc - Estimate- related quantity calculated from a sample; “approximation of the truth, subject to error” - Statistics tells us how best to estimate these parameters using our measurements of a sample - By measuring every possible member of the population, we could know the parameter without error, but that is rarely possible - Instead, we use estimates based on incomplete data to approximate the true value - Hypothesis testing- process of determining how well a “null” hypothesis about a population quantity fits a sample of data o Null hypothesis- specific claim regarding the population quantity; made for the purposes of argument and often embodies the skeptical point of view 1.2- Sampling Populations - Our ability to obtain reliable measures of population characteristics and to assess the uncertainty of these measures depends on how we sample populations  Populations and Samples - Population- entire collection of individuals or units of interest; composed of large number of individuals; ex. all cats that have fallen from buildings in NYC - Sample- subset of individuals or units taken from the population; smaller set of individuals; used to draw conclusions that apply to whole population; ex. fall cats brought to one veterinary in NYC o Sometimes a basic unit of sampling is literally a single individual or a group of individuals o Scientists use several terms to indicate the sampling unit, such as “unit”, “individual”, “subject”, or “replicate”  Properties of Good Samples - Estimates based on samples typically depart somewhat from the true population characteristic - Sampling error- chance different between an estimate and the population parameter being estimated o Larger samples are less affected by chance than smaller samples therefore will have lower sampling error and higher precision - Precision- indicated by spread of estimates resulting from sampling error - Accuracy (Unbiased)- indicated by distance from the true mean value - Bias- systematic discrepancy between estimates and the true population characteristics - Major goal of sampling is to minimize sampling error and bias in estimates - Ideally, all the estimates are tightly grouped, indicating low sampling error, and they are centered on the bull’s-eye, indicating low bias o Estimates are precise if they are tightly grouped and highly repeatable o Estimates are imprecise if they are spread out and not repeatable o Estimates are accurate (unbiased) if they are centered on the bull’s- eye o Estimates are inaccurate (biased) if they are displaced systematically to one side of the bull’s-eye - Both precision and accuracy are important because lack of either means that an estimate is likely to differ greatly from the truth - Final goal of sampling is to allow the precision of an estimate to be quantified  Random Sampling - Random sample- sample in which each member of the population has an equal and independent chance of being selected - For a random sample, every unit in the population must have an equal chance of being included in the sample o Hard-to-sample individuals must be included in the sample, otherwise it would lead to bias due to their differences in characteristics from the rest of the population - For a random sample, the selection of units must be independent – the selection of any one member of the population must in no way influence the selection of any other member o Individuals from the same household cannot be included in the sample because it makes the sample effectively smaller and causes the data to be skewed - Random sampling minimizes bias and makes it possible to measure the amount of sampling error - How to take a random sample (Method 1): o Create a list of every unit in the population of interest and give each unit a number between 1 and the total population size o Decide on the number of units to be sampled (call this number n) o Using a random-number generator, generate n random integers between 1 and the total number of units in the population o Sample the units who numbers match those produced by the random number generator - How to take a random sample (Method 2): o Make the basic unit of sampling a group instead of a single individual o Take the average of the measurements of all the individuals within a unit (group) as the single independent observation for that unit (group) o Create a list of every unit (group) in the population of interest and give each unit (group) a number between 1 and the total population size o Decide on the number of units (groups) to be sampled (call this number n) o Using a random-number generator, generate n random integers between 1 and the total number of units (groups) in the population o Sample the units (groups) who numbers match those produced by the random number generator  Sample of Convenience - Sample of convenience- collection of individuals that are easily available to the researcher - Researcher must assume that a sample of convenience is unbiased and independent like a random sample, but there is no way to guarantee it - Sample of convenience may be biased because it doesn’t accurately represent that entire population of interest due to leaving out specific groups of individuals - Sample of convenience might also violate the assumption of independence if individuals in the sample are more similar to one another than individuals chosen randomly from the population  Volunteer Bias - Volunteer bias- bias resulting from a systematic difference between the pool of volunteer (the volunteer sample) and the population to which they belong - Volunteer bias arises
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