Intro To Statistics - Chapter 1

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The science of Collecting, Organizing, Summarizing, and Analyzing information to draw conclusions or answer questions. Additionally, provides a measure of confidence in any conclusions.

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"Statistics"

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The entire group to be studied.

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Population

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

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Individual

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A subset of the population that is being studied.

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Sample

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A numerical summary of a sample.

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A Statistic

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This type of statistics consists of organizing and summarizing data. Describes data through numerical summaries, tables, and graphs.

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Descriptive Statistics

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This type of statistics uses methods that take a result from a sample, extends it to the population, and measures the reliability of the result.

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Inferential Statistics

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A numerical summary of a population.

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Parameter

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1.) Identify the research objective. What is the question you want answered, what is the population to be studied?

2.) Collect the data (needed to answer the questions posed in 1). Usually with samples.

3.) Describe the Data.

4.) Perform Inference. Apply the appropriate techniques to extend the sample to the population and report a level of reliability of the results.

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The Process of Statistics

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Variables that allow for classification of individuals based on same attribute or characteristic.

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Qualitative or Categorical Variables

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Variables that provide numerical measures of individuals. These variables can be added or subtracted and provide meaningful results.

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Quantitative Variables

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A quantitative variable that has either a finite number of possible values or a countable number of possible values. You count to get the value of this variable.

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Discrete Variable

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A quantitative variable that has an infinite number of possible values that are not countable. You measure to get the value of this variable.

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Continuous Variable

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The variable is at this level of measurement if the values 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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Nominal Level of Measurement

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A variable is at this level of measurement if it has the properties of the nominal level of measurement, however the naming scheme allows for the values of the variable to be arranged in ranked or specific order.

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Ordinal Level of Measurement

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A variable is at this level of measurement if it has the properties of the ordinal level of measurement and the differences in the values of the variable have meaning. Arithmetic operations such as addition and subtraction can be performed on the values of the variable.

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Interval Level of Measurement

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A variable is at this level of measurement if it has the properties of the interval level of measurement and the ratios of the values of the variable have meaning. Arithmetic operations such as multiplication and division can be performed on the values of the variables.

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Ratio Level of Measurement

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This type of study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables.

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Observational Study

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This type of study occurs when 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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Designed Experiment

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This occurs in a study 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 or variables not accounted for in the study.

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Confounding

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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.

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Lurking Variable.

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1.) Cross-Sectional Studies

2.) Case-Control Studies

3.) Cohort Studies

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3 Types of Observational Studies

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These observational studies collect information about individuals at a specific point in time or over a very short period of time.

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Cross-Sectional Studies

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These studies are retrospective, meaning that they require the researcher to look at existing records. In these studies, individuals who have a certain characteristic may be matched with those who do not.

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Case-Control Studies

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This type of study first identifes a group of individuals to participate in the study. The group is then observed over a period of time. During this period, characteristics of the individuals are recorded and some individuals will be exposed to certain factors (not intentionally) and others will not. At the end of the study the value of the response variable is recorded for the individuals.

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Cohort Studies

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A list of all individuals in a population along with certain characteritics of each individual.

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Census

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

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Random Sampling

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A sample of size n from a population of size N is obtained from this type of sample if every possible sample of size n has an equally likely chance of occurring.

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Simple Random Sample

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A sample of this type is type is obtained by separating the population into non-overlapping groups and then obtaining a Simple Random Sample from each group. The individuals within each group should be homogeneous (or similar) in some way.

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Stratified Sample

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A sample of this type is obtained by selecting every kth individual from the population. The first individual selected corresponds to a random number between 1 and k.

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Systematic Sample

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A sample of this type is obtained by selecting all individuals within a randomly selected collection or group of individuals.

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Cluster Sample

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A sample of this type is one in which the individuals are easily obtained and not based on randomness.

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Convenience Sample

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This occurs when the results of the sample are not representative of the population.

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Bias

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This occurs when the technique used to obtain the sample's individuals tends to favor one part of the population over another.

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Sampling Bias

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

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Nonresponse Bias

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This occurs when the answers on a survey do not reflect the true feelings of the respondent.

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Response Bias

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1.) Interviewer Error

2.) Misrepresented Answers

3.) Wording of Questions

4.) Ordering of Questions or Words

5.) Type of Question

6.) Data-Entry Error

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Types of Response Bias

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This kind of error results from undercoverage, nonresponse bias, or data-entry error.

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Nonsampling Errors

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This kind of error results from using a sample to estimate information about a population.

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Sampling Error

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A controlled study conducted to determine the effect that varying one of more explanatory variables or factors has on a response variable.

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Experiment

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Any combination of the values of the explanatory variables (or factors) in an experiment.

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A Treatment

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A person, object, or some other well defined item upon which a treatment is applied.

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Experimental Unit

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In this type of experiment, the experimental unit (or subject) does not know which treatment he or she is receiving.

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Single-Blind Experiment

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In this type of experiment, neither the experimental unit nor the researcher in contact with the experimental unit knows which treatment the experimental unit is receiving.

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Double-Blind Experiment

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1.) Identify the problem to be solved.

2.) Determine the factors that affect the response variable.

3.) Determine the number of experimental units.

4.) Determine the level of each factor.

5.) Conduct the experiment.

6.) Test the claim.

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Steps in Designing an Experiment

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This occurs when each treatment is applied to more than one experimental unit, this ensures the effect of a treatment is not due to some characteristic of a single experimental unit.

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Replication

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This type of experimental design is one in which each experimental unit is randomly assigned to a treatment.

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Completely Randomized Design

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This type of experimental design is one in which the experimental units are paired up. The pairs are selected so that they are related in some way (that is, the same person before and after a treatment, twins, husband and wife, same geographical location, and so on). There are only two levels of treatment in this design.

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Matched-Pairs Design

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A sample of size n from a population of size N is obtained through this method if every possible sample of size n has an equally likely chance of occuring.

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Simple Random Sample

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

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Random Sampling

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A list of all the individuals within the population.

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A Frame