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Statistics, Data, and Statistical Thinking
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1.1 The Science of Statistics 1.2 Types of Statistical Applications 1.3 Fundamental Elements of Statistics 1.4 Types of Data 1.5 Collecting Data 1.6 The Role of Statistics in Critical Thinking
Terms in this set (52)
Statistics
The science of data. This involves collecting, classifying, summarizing, organizing, analyzing, and interpreting numerical information.
Descriptive statistics
Utilizes numerical and graphical methods to look for patterns in a data set, to summarize the information revealed in a data set, and to present that information in a convenient form.
Inferential statistics
Utilizes sample data to make estimates, decisions, predictions, or other generalizations about a larger set of data.
Population
A set of units (usually people, objects, transactions, or events) that we are interested in studying.
Variable
A characteristic or property of an individual population unit.
Measurement
The process we use to assign numbers to variables of individual population units.
Census
Used to measure a variable for every unit of a population.
Sample
A sample is a subset of the units of a population.
Statistical inference
An estimate, prediction, or some other generalization about a population based on information contained in a sample. That is, we use the information contained in the smaller sample to learn about the larger population.
Reliability
How good the inference is.
Resource constraints
Constraining factors (insufficient time and / or money) that affect a statistical method of data collection.
Uncertainty (Degree of)
The element introduced when a measure of reliability is not used.
Bound on the estimation error
A number that our estimation error is not likely to exceed
Measure of reliability
A statement (usually quantified) about the degree of uncertainty associated with a statistical inference.
Four Elements of Descriptive Statistical Problems
1. The population or sample of interest; 2. One or more variables (characteristics of the population or sample units) that are to be investigated; 3. Tables, graphs, or numerical summary tools; 4. Identification of patterns in the data.
Five Elements of Inferential Statistical Problems
1. The population of interest; 2. One or more variables that are to be investigated; 3. The sample of population units; 4. The inference about the population based on information contained in the sample; 5. A measure of reliability for the inference.
Quantitative data
Measurements that are recorded on a naturally occurring numerical scale.
Qualitative data
Measurements that cannot be measured on a natural numerical scale; they can only be classified into one of a group of categories.
Published source
The data set of interest has already been collected for you and is available.
Designed experiment
A method of collecting data that involves a ______ in which the researcher exerts strict control over the units in the study.
Survey
The researcher samples a group of people, asks one or more questions, and records the responses. _____ can be conducted through the mail, with telepone interviews, or with in-person interviews. Although in-person _____ are more expensive than mail or telephone surveys, they may be necessary when complex information is to be collected.
Observational study
The researcher observes the experimental units in their natural setting and records the variable(s) of interest. The researcher makes no attempt to control any aspect of the experimental units.
Representative sample
Exhibits characteristics typical of those possessed by the target population.
Random sample
Ensures that every subset of fixed size in the population has the same chance of being included in the sample.
Parameters
Statistical measures that are computed regarding the characteristics of a population.
Sample design
Refers to the technique employed to select a subset of participants from the population and gather the data from the population.
Voluntary response
A very common design employed particularly in opinion surveys. In this design, a general appeal is made for responses to one or more questions. Members of the population decide for themselves whether or not to respond. It is likely that only very motivated listeners will respond.
Convenience sampling
In this design, members of the population are chosen based on the convenience of including them.
Quota sampling
In this procedure, interviewers are assigned to interview a fixed amount of members of the population. These amounts are organized around categories such as race, gender, residence, or economic status; in many cases, the amounts are set to match known or assumed demographic information about the population.
Simple random sampling (SRS)
Several important features: 1. Involves selecting individuals at random from the population without replacement; 2. a sample of size n is to be chosen from the population, where every population subset of size n has an equal chance of being selected; 3. every member of the population has an equal chance of being included in the sample.
Bias
A systematic error that favors a particular segment of the population or that tends to encourage only certain outcomes in the data.
Stratified random sample
If a population has distinct groups, it is possible to divide the population into these groups and draw SRS's from each of the groups. The groups are called strata. Strata are designed so that members in each strata are more homogeneous, that is, more similar to each other. The results of all of the SRS's are then grouped together to form the sample. This technique is particularly useful in populations that can be stratified into groups by gender, race, or geography (such as urban, rural, and suburban) when the researcher wants to ensure representation from each group.
Multi-stage cluster sample
The process involves taking stages and SRS's within a cluster. While this multi-stage technique sounds very complicated, it is atually quite efficient and cost-effective.
Systematic sample
This method of sampling begins with the listing of the population. Then, a decision is made as to a systematic way of choosing members. For example, if it is decided to sample 1 of every 50, the investigator would randomly select one of the first 50 and then continue selecting every 50th member from that point on. In this way, if member 12 was selected first, then members 62, 112, 162, and so on would be selected. For systematic sampling to be valid, the investigator must make sure that the ordering principle is not connected to the nature of the population.
Valid probability methods of sampling
1. The interviewers and subjects themselves are not choosing the subject who is interviewed; 2. There is a definite procedure for selecting participants in the sample and that procedure involves the use of probability.
Sampling frame
The list of possible subjects who could be selected in a sample.
Response bias
1. The wording of the questions; 2. The order of choices; 3. The deamenor and / or appearance of the interviewer; 4. Honesty
Non-response bias
When members of the population are chosen but cannot be contqacted to participate, non-response bias may occur. This is true since non-respondents tend to to differ from those who are readily available. Efforts are made to reduce this as much as possible.
Household bias
Another type of bias involving the power of smaller households in relation to larger ones
Random sampling error
Error that occurs because of chance variation
Sampling method error
Error that occurs because of the choice of sampling method.
Non-sampling method error
Error that occurs in the responses by members in the sample.
Comparative experiment
A type of experimental design that involves two or more groups.
Independent (explanation) variables
Explanation
Dependent (response) variables
Response
Control group
Consists of the units who are not to receive the treatment that is the focus of the experiment
Treatment group
Units in this group receive the treatment.
Confounded variables
Two variables are _______ if the investigator cannot separately identify their effects on the response variable.
Lurking variables
A variable that has an effect on the response variable but is not measured as part of the study of interest.
Factors
Another name for explanatory variables.
Levels
A treatment is a combination of specific values of each of the factors; these values are called _______.
Statistical thinking
Involves applying rational thought to assess data and the inferences made from them critically.
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