Statistics

The study of how to collect, organize, analyze, and interpret numerical and categorical information.

Scientific Method

A series of steps followed to solve problems including collecting data, formulating a hypothesis, testing the hypothesis, and stating conclusions (choose, perform, develop, design, gather, analyze, formulate)

descriptive statistics

Numeric values(graphs) calculated from a dataset with the purpose of characterizing the behavior of the variables

inferential statistics

involves methods of using information from a sample to draw conclusions regarding the population

Population

set of all the individuals of interest in a particular study

Finite population

A population in which each individual member can be given a number

infinte population

collection of objects or individuals that are no boundaries or we can not measure about the total number of individuals in the occupied territories

sample

subset of the population. individuals selected from a population, usually intended to represent the population in a research study

Parameter

value that describes a population

Statistic

Value that describes a sample

Variable

A characteristic about each individual element of a population or sample

Data (singular)

value of the variable associated with one element of a population or sample. This value may be a number, or a symbol

Data (plural)

the set of values collected for the variable from each of the elements belonging to the sample

Experiment

a planned activity whose results yeild a set of data

Sampling error

naturally occuring discrepency between a sample statistic and the cooresponding population parameter

Individual

the objects described by a set of data: person (animal), place, and thing. In a medicinal trial, the people in the study referred to as called subjects

Valid Measure

one that is relevant or appropriate asa representation of that property.

Reliable Measure

measurement such that the random error is small

Census

In Population data, the variable is measured for EVERY individual of interest

Sample Survey

in sample data, the variable is measured from ONLY SOME of the individuals of interest

Quantitative (Numerical) variable

variable that quantifies an element of the population. has a numerical measurment for which operations such as addition or averaging make sense.

Ex: Ag, GPA, Tuition, Fees

Ex: Ag, GPA, Tuition, Fees

Qualitative (attribute) variable

A variable that categorizes or describes an element of a population. has a nominal measurement that descibes an individual by placing them in a category or group.

Ex: Phone number, college year, addresses.

Ex: Phone number, college year, addresses.

Discrete variable

characterized by gaps or interruptions in the values we assume. gaps implies absence between those values. ALl values are whole numbers

Ex: number of cars in garge, count of males in a group

Ex: number of cars in garge, count of males in a group

Continuous variable

does not possess the gaps or interruptions characteristic of a discrete variable. decismals are allowed between any two values.

Ex: length of pole, height of basketball player, age of tree

Ex: length of pole, height of basketball player, age of tree

Nominal scale

an unordered set of categories only by name. only permit you to determine whether two individuals are the same or different

Ordinal Scale

an ordered set of categories. Ordinal measurements tell you the direction of difference between two individuals

Interval Scale

ordered series of equal size categories. Identify direction and magnitude of a difference. The zero point is located arbituarily on an interval scale

Ratio scale

an interval scale where a value of zero indicates none of the variable. ratio identifies the direction and magnitude of difference and allows ratio comparisons of measurement.

Designing a Statistical Study

1. Identify the variable(s) of interest (the focus) and the population of the study.

2. Develop a detailed plan for collecting data. If you use a sample, make sure the sample is representative of the population.

3. Collect the data.

4. Describe the data, using descriptive statistics techniques.

5. Interpret the data and make decisions about the population using inferential statistics.

6. Identify any possible errors.

2. Develop a detailed plan for collecting data. If you use a sample, make sure the sample is representative of the population.

3. Collect the data.

4. Describe the data, using descriptive statistics techniques.

5. Interpret the data and make decisions about the population using inferential statistics.

6. Identify any possible errors.

Variability

the degree of dispersion (spread) of data points in a distribution

Lurking Variable

A variable that has an important effect on the response variable and the relationship amoung the variables in a study but is not one of the explanatory variables studied either because it is unknown or not measured.

Confounded variables

two variables such that their effects on the respose variable cannot be distingushed from eachother

treatment

any specific experimental condition applied to the subjects

Observational study

a researcher observees and collects data but does not change existing conditions

Experimental study

a researcher applies a treatment to a part of a population and observes the responses to the treatment. another part of the population is given a placebo called the control group

placebo effect

occurs when a subject recieves no treatment, but believes he or she is in fact recieveing treatment and responds favorably

Complete random experiment

a random process is used to assign each individual to one of the treatments

Randomized block experiment

individuals are first sorted into blocks, and then a random process is used to assign each individual in the block to one of the treatments

(single) blind

an experiment in which the subjects alone do not know which treatment they are recieving

Double blind

an experiment in which neither the subjects or the people working know which treatment each is recieving

Information

reduced margin of error

Simulation

numerical facsimile or representation of a real world phenomenon

randomization

used to assign individuals to the treatment groups. this helps prevent bias in the selected members for each group. this includes using an appropriate sampling technique

Data Collection Methods

Experiment, survey, census, sampling frame, sample design

random sample

no bias introduces by the sampling technique employed. the process by which the sample data is selected progreses without definite aim, reason, or pattern

random error

measurement mistake caused by the factors that vary from one measurement to another; statistical error due to chance

Simple random sampling

each element of the pop has an equal probability of being selected. a random number table is utilized to select the individual elements of the pop for the sample

Stratified Sampling

assign each element of the population to a group (stratum). perform simple random sampling from each stratum

Cluster Sampling

assign each element of the population a group or cluster. randomly select the desired number of clusters. every element within the selected cluster is used for the sample

Systematic sampling

list every member of the target population and uniquely assign a number to each member. randomly select a number. this number will be the starting point of the sample selection. Select member for the sample at equivalent intervals.

Convenience Sampling

a statistical method of drawing representative databy selecting people bc of the ease of their volunteering or selecting units because of their availability or easy access

Multi-stage sampling

a sampling method where the pop is divided into a number of primary groups from which samples are drawn. these are then divided into secondary groups from which samples are drawn, and so on

Biased sampling method

a sampling method that produces data which systematically differs from the sampled population. An unbiased sampling method is not biased.

volunteer sample

sample collected from those elements of the pop which chose to contribute the needed information on their own initiative

Statistics

The science of data.

Individuals

Objects described by a set of data, they do not necessarily have to be people.

Observation

A piece of data about the individual.

Population

The entire group of individuals we want information about.

Sample

A group in the population.

Parameter

A number that describes a characteristic of the population

Statistic

A number that describes a characteristic of the sample.

Variable

A characteristic of an individual.

Categorical Variable

Separates individuals into categories.

Quantatative Variable

Separates individuals based on numeric values.

Distribution

Tells us possible values for the variable and how often certain variables occur.

Observational Study

Study where researcher observs but does nothing to influence outcome or responses.

Experimental Study

Researcher experiments to influence outcomes and responses.

Sampling Design

The way to select samples.

Bias

When responses are slanted toward certain outcomes.

Voluntary Response Sample

Respondeds choose to be included in surveys. Ex: Comment cards at hotels.

Convenience Sample

Researcher samples those who are willing/available.

Undercoverage

Not sampling from the entire population.

Non-response

Those who don’t respond to surveys, equal to the number surveyed minus the number responded, all divided by the number surveyed.

Response Bias

A form of innacurate responses.

Wording Effects

How a question is worded: may have some affect on answers.

Simple Random Sample

A random sample that allows every possible sample of size n the same chance of being selected.

Systematic Random Sample

Select a starting point at random and then choose every kth individual, where k = (Population Size)/(Sample Size) rounded DOWN to nearest whole number

Stratified Random Sample

Divide the population into groups and take a SRS of each group.

Cluster Random Sample

Divide the population into groups, but this time take a SRS of groups