Chapter One

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Statistics

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Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. In addition, statistics is about providing a measure of confidence in any conclusions.

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Population

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The entire group of individuals to be studied

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Individual

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A person or object that is a member of the population being studied

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Sample

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A subset of the population that is being studied

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Statistic

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A numerical summary of a sample

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Descriptive statistics

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Descriptive statistics consists of organizing and summarizing data. Descriptive statistics describe data through numerical summaries, tables, and graphs.

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Inferential statistics

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Inferential statistics uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result.

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parameter

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is a numerical summary of a population

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Variables

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are the characteristics of the individuals within the population.

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Qualitative, or categorical, variables

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allow for classification of individuals based on some attribute or characteristic.

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Quantitative variables

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provide numerical measures of individuals. The values of a quantitative variable can be added or subtracted, and provide meaningful results.

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discrete variable

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a quantitative variable that has either a finite number of possible values or a countable number of possible values. The term countable means that the values result from counting, such as 0, 1, 2, 3, and so on. A discrete variable cannot take on every possible value between any two possible values.

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continuous variable

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a quantitative variable that has an infinite number of possible values that are not countable. A continuous variable may take on every possible value between any two values.

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Data

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The list of observed values for a variable.

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Qualitative data

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are observations corresponding to a qualitative variable.

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Quantitative data

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are observations corresponding to a quantitative variable.

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Discrete data

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are observations corresponding to a discrete variable.

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Continuous data

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are observations corresponding to a continuous variable.

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nominal level of measurement

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the values of the variable name, label, or categorize. In addition, the naming scheme does not allow for the values of the variable to be arranged in a ranked or specific order.

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ordinal level of measurement

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it has the properties of the nominal level of measurement, however, the naming scheme allows for the values of the variable to be arranged into a ranked or specific order.

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interval level of measurement

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it has the properties of the ordinal level of measurement and the differences in the values of the variable have meaning. A value of zero does not mean the absences of the quantity. Arithmetic operations such as addition and subtraction can be performed on the values of the variable.

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ratio level of measurement

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it has the properties of the interval level of measurement and the ratios of the values of the variable have meaning. A value of zero means the absence of the quantity. Arithmetic operations such as multiplication and division can be performed on the values of the variable.

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explanatory variable

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a variable whose value is thought to impact the value of a response variable.

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response variable

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the variable of interest in the outcome of a study

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observational study

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measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. That is, in an observational study, the researcher observes the behavior of individuals without trying to influence the outcome of the study.

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designed experiment

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If a researcher assigns the individuals in a study to a certain group, intentionally changes the value of an explanatory variable, and then records the value of the response variable for each group

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Confounding

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in a study occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable not accounted for in the study.

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lurking variable

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an explanatory variable that was not considered in a study, but that affects the value of the response variable in the study. In addition, lurking variables are typically related to explanatory variables considered in the study.

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retrospective study

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requires individuals to look back in time or require the researcher to look at existing records.

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prospective study

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is one in which the data are collected over time.

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census

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a list of individuals in a population along with certain characteristics of each individual

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Random sampling

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is the process of using chance to select individuals from a population to be included in the sample.

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simple random sampling

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sample of size n from a population of size N is obtained through if every possible sample of size n has an equally chance of occuring

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simple random sample

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sample of size n from a population of size N

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frame

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a list of all the individuals within the population

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sample without replacement

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an individual who is selected is removed from the population and cannot be chosen again.

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sample with replacement

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a selected individual is placed back into the population and could be chosen a second time

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seed

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an initial point for a random number generator to start creating numbers.

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stratified sample

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obtained by dividing the population into nonoverlapping groups called strata and then obtaining a simple random sample from each stratum. The individuals within each stratum should be homogenous (similar) in some way.

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systematic sample

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obtained by selecting every kth individual from the population. The first individual selected corresponds to a number between 1 and k.

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cluster sample

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obtained by selecting all individuals within a randomly selected collection or group of individuals

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convenience sample

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a sample in which the individuals are easily obtained and not based on randomness

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self-selected

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survey is one in which the individuals themselves decide to participate in the survey.

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Voluntary response

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another phrase used to describe self-selected surveys.

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bias

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the results of the sample are not representative of the population

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Sampling bias

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means that the technique used to obtain the sample's individuals tends to favor one part of the population over another

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Undercoverage

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occurs in a sample when the proportion of one segment of the population is lower in a sample than it is in the population

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Nonresponse bias

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exists when individuals selected to be in the sample who do not respond to the survey have different opinions from those who do.