Statistics

Statistics

1. Overview of Statistics

   • Data
     • Consist of information coming from observations, counts, measurements, or responses 
   • Statistics
     • The science of collecting, organizing, analyzing, and interpreting data in order to make decisions
     • Descriptive Statistics
       • The branch of statistics that involves the organization, summarization, and display of data
     • Inferential Statistics
       • The branch of statistics that involves using a sample to draw conclusions about a population.  A basic tool in the study of inferential statistics is probability
   • Population
     • The collection of all outcomes, responses, measurements, or counts that are of interest
   • Sample
     • A subset or part of a population
   • Parameter
     • A numerical description of a population characteristic
   • Statistic
     • A numerical description of a sample characteristic

2. Data Classification

   • Qualitative Data
     • Consists of attributes, labels, or nonnumerical entries.
     • Ordinal Level
     • Nominal Level
   • Quantitative Data
     • Consists of numerical measurements or counts
     • Interval Level
     • Ratio Level
   • Nominal Level of Measurment
     • Data at this level are categorized using names, labels, or qualities.  No mathematical computations can be made at this level.
   • Ordinal Level of Measurement
     • Data at this level can be arranged in order, or ranked but differences between data entries are not meaningful.
   • Interval Level of Measurement
     • At the interval level, a zero entry simply represents a position on a scale; the entry is not an inherent zero.
   • Ratio Level of Measurement
     • A ration of two values can be formed so that one data value can be meaningfully expressed as a multiple of another.

3. Data Collection and Experimental Design

   • Data Collection
     • Observational Study
       • A researcher observes and measures characteristics of interest of part of a population but does not change existing conditions
     • Experiment
     • Treatment
       • Applied to part of a population and responses are observed.
     • Control Group
       • In which no treatment is applied.
     • Experimental Units
     • Placebo
       • harmless, unmedicated treatment that is made to look like the real treatment.
     • Simulation
       • The use of a mathematical or physical model to reproduce the conditions of a situation or process.
     • Survey
       • An investigation of one or more characteristics of a population.
   • Experimental Design
     • Confounding Variable
       • Occurs when an experimenter cannot tell the difference between the effects of different factors on a variable.
     • Placebo Effect
       • Occurs when a subject reacts favorably to a placebo when in fact the subject has been given no medicated treatment at all.
     • Blinding
       • A technique where the subjects do not know whether they are receiving a treatment or a placebo.
     • Double-Blind Experiment
       • Neither the experiment nor the subjects are receiving a treatment or a placebo.
     • Randomization
       • The process of randomly assigning subjects to different treatment groups.
     • Completely Randomized Design
       • Subjects are assigned to different treatment groups through random selection.
     • Blocks
       • Groups of subjects with similar characterstics.
     • Randomized Block Design
       • Subjects are divided with similar characteristics into blocks and then within each block , randomly assign subjects to treatment groups.
     • Matched-Pairs Design
       • Where subjects are paired up according to a similarity.
     • Sample Size
       • The number of subjects
     • Replication
       • The repetition of an experiment under the same or similar conditions.
   • Sampling Techniques
     • Census
       • Count or measure of an entire population.
     • Sampling
       • A count or measure of part of a population.
     • Sampling Error
       • The difference between the results of a sample and those of the population.
     • Random Sample
       • One in which every member of the population has equal chance of being selected.
     • Simple Random Sample
       • Sample in which every possible sample of the same size has the same chance of being selected.
     • Stratified Sample
       • A sample that is drawn from a number of separate strata of the population, rather than at random from the whole population, in order that it should be representative.
     • Cluster Sample
       • Cluster sampling is a sampling plan used when mutually homogeneous yet internally heterogeneous groupings are evident in a statistical population. It is often used in marketing research.
     • Systematic Sample
       • a type of probability sampling method in which sample members from a larger population are selected according to a random starting point and a fixed, periodic interval. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.