Chapter 1

Steps for Systematic Sampling

1) Approximate the population size N, if possible. 2)Determine the sample size desired n. 3) Compute N/n and round down to the nearest. 4) integer to get the value of k. 5) Randomly select a number between 1 and k to get the value of p. 6)The sample now consists of p, p + k, p + 2k, p + 3k,... p + (n - 1)k

Steps in Conducting an Experiment

1) I.D. the problem to be solved. 2) Determine the factors that affect the response variable. 3) Determine the no. of experimental units. 4) Determine the level of each factor; control or random. 5) Conduct the experiment. 6) Test the claim

The Process of Statistics

1) Identify the research objective. 2) Collect the data needed to answer the question(s) posed in (1). 3) Describe the data. 4) Perform inference

Steps for Simple Random Sampling

1) Obtain a frame that lists all individuals in the population of interest. 2)Number the individuals from 1 - N. 3) Use a random number device to select the sample

Experiment

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

Census

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

Parameter

A numerical summary of a population

Statistic

A numerical summary of a sample which can be descriptive or inferential

Individual

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

Experimental Unit

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

Discrete Variables

A quantitative variable that either has a finite or a countable number of possible values, such as 0, 1, 2, 3...

Continuous Variables

A quantitative variable that has an infinite number of possible variables that are not countable, such as any possible value between any two values

Designed Experiment

A researcher assigns individuals to a certain group, intentionally changes the value of an explanatory variable, and then records the value of the response variable

Simple Random Sampling

A sample size n from population N is obtained using random sampling

Sample

A subset of the population that is being studied

Data

Also called information, describes characteristics of an individual and are used to draw conclusions or make a decision

Qualitative Variables

Also known as Categorical variables, are a classification of individuals based on some attribute or characteristics

Lurking Variable

An explanatory variable that was not considered in a study, but affects the value of the response variable, and is typically related to explanatory variables considered in the study

Placebo

An innocuous medication that looks, tastes, and smells like the experimental medication

Treatment

Any combination of the values of the factors/explanatory variables

Case-control Studies

Are retrospective requiring individuals to look back in time or require the researcher to look at existing records. Individuals who have certain characteristics may be matched with those who do not

Variables

Characteristics of the individuals within the population, can be qualitative or quantitative

Cross-section Studies

Collect information about individuals at a specific point in time or over a very short period of time.

Descriptive Statistic

Consists of organizing and summarizing data, based on the sample, and describing it through numerical summaries, tables, and graphs

Three Types of Observational Studies

Cross-section, Case-controlled, and Cohort studies

Completely Randomized Design Experiment

Each experimental unit is randomly assigned to a Treatment

Non-response Bias

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

Randomized Block Design Experiment

Experimental units are divided into homogenous groups called blocks, and within each block the experimental units are randomly assigned to treatments

Cohort Studies

First identifies a group of individuals to participate in the study (cohort), then they are observed over a long period of time, during which characteristics about the individuals are recorded and some individuals will be unintentionally exposed to certain factors while others are not. At the end of the study the value of the response variable is recorded for the individuals

Ratio Level

Has the properties of the interval level, and the ratios of the values of the variables have meaning such that multiplication and division can be performed on the values of the variable, and a value of zero does mean the absence of the quantity

Ordinal Level

Has the properties of the nominal level, however the naming scheme allows for ranking in a specific order

Interval Level

Has the properties of the ordinal level, and the differences in the values of the variable have meaning such that addition and subtraction can be performed on values of the variables, and a value of zero does not mean the absence of the quantity

Observational Study

Measures the value of the response variable without attempting to influence the value of either response or explanatory variables, and does not allow a researcher to claim causation, only association

Double-blind Experiment

Neither the experimental unit nor the researcher in contact with the experimental knows which treatment the experimental unit is receiving

Levels of Measurement of a Variable

Nominal, Ordinal, Interval, and Ratio Levels

Quantitative Variable

Provide numerical measures of individuals, which can be added or subtracted to provide meaningful results; can be discrete or continuous variables.

Non-sampling Errors

Results from under-coverage, non-response bias, response bias, or data entry error

Sampling Error

Results from using a sample to estimate information about a population because the sample gives incomplete information about the population

Bias & 3 Sources of Bias in Sampling

Results of sample are not representative of the population: Sampling bias; Non-response bias; Response bias

Cluster Sample

Selecting all individuals within a randomly selected collection, or group, of individuals

Systematic Sample

Selecting every kth individual from the population, and the first individual selected is a random number between 1 and k

Stratified Sample

Separating the population into non-overlapping homogenous groups called strata and then obtaining a simple random sample from each strata

Control Group

Sevres as a baseline treatment that can be used to compare to other treatments

4 Basic Sampling Techniques

Simple random, stratified, systematic, and cluster

Response Bias

The answers on a survey do not reflect the true feelings of the respondent (due to: misrepresented answers; wording of questions; type of question, open or closed; data entry error

Confounding

The effect of two or more factors (explanatory variables) on the response variable cannot be distinguished

Population

The entire group to be studied

Single-blind Experiment

The experimental unit (or subject) does not know which treatment he or she is receiving

Matched-pairs Design Experiment

The experimental units are paired up, so that they are related in some way, and there are only two levels of treatment assigned to the pairs

Convenience Sample

The individuals of a sample are easily obtained and not based on randomness, which yields results that are meaningless

Random Sampling

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

Under-coverage

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

Statistics

The science of collecting, organizing, summarizing, and analyzing information (data) to draw conclusions or answer questions, in which it provides a measure of confidence in any conclusions

Sampling Bias

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

Inferential Statistics

Uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result

Nominal Level

Values of the variable name, label, or categorize, but the naming scheme does not allow for arrangement or ranking

Explanatory vs. Response Variable

Varying the amount of an explanatory variable affects the value of the response variable

Replication

When each treatment is applied to more than one experimental unit