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Introduction to The Practice of Statistics Cheat Sheet (DRAFT) by

1.1 Intro to Statistics contains important topics as well as formulas and central ideas.

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Defini­tion(s)

Statistics
Statistics is the science of collec­ting, organi­zing, summar­izing, and analyzing inform­ation to draw conclu­sions or answer questions. In addition, statistics is about providing a measure of confidence in any conclu­sions.
Data
(1) A fact or propos­ition used to draw a conclusion or make a decision. Data can be numerical, or non-nu­mer­ical. A key aspect of data is that they vary. (2) The list of observed values for a variable.
Population
The entire group of interest to be studied.
Individual
A person or object that is a member of the population of interest being studied.
A statistic
A numerical summary of a sample.
Descri­ptive Statistics
Consist of organizing and summar­izing data. Descri­ptive statistics describe data through numerical summaries, tables, and graphs.
Infere­ntial Statistics
Uses methods that take a result from a sample, extend it to the popula­tion, and measure the reliab­ility of the result.
Parameter
A numerical summary of a popula­tion.
Variables
The charac­ter­istics of the indivi­duals within the popula­tion.
Qualit­ative (categ­orical) Variables
Allow for classi­fic­ation of indivi­duals based on some attribute or charac­ter­istic.
Quanti­tative (numer­ical) Variables
Provide numerical measures of indivi­duals. The values of a quanti­tative variable can be added or subtracted and provide meaningful results.
Approach
A way to look at and organize a problem so that it may be solved. Remember that many problems have more than one approach leading to a correct solution.
Discrete (count­able) Variable
A discrete variable is a quanti­tative variable that has either a finite number of possible values or a countable number of possible values. The term countable means that the values result from counting, such as 0, 1, 2, 3, and so on. A discrete variable cannot take on every possible value between any two possible values.
Continuous (measu­rable) Variable
A continuous variable is a quanti­tative variable that has an infinite number of possible values that are not countable. A continuous variable may take on every possible value between any two values.
Qualit­ative Data
Observ­ations corres­ponding to a qualit­ative variable.
Quanti­tative Data
Observ­ations corres­ponding to a quanti­tative variable. These can be broken down into two catego­ries: 1) Discrete Data - observ­ations corres­ponding to a discrete (count­able) variable. 2) Continuous Data - Observ­ations corres­ponding to a continuous (measu­rable) variable.
Nominal Level of Measur­ement
A variable is at the nominal level of measur­ement if the values of the variable 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
Ordinal Level of Measur­ement
A variable is at the ordinal 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 a ranked or specific order.
Interval Level of Measur­ement
A variable is at the interval 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. A value of zero does not mean the absence of the quantity. Arithmetic operations such as addition and subtra­ction can be performed on values of the variable.
Ratio Level of Measur­ement
A variable is at the ratio 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. A value of zero means the absence of the quantity. Arithmetic operations such as multip­lic­ation and division can be performed on the values of the variable.
 

The Process of Statistics

1. Identify the research objective. A researcher must determine the questi­on(s) he or she wants answered. The questi­on(s) must clearly identify the population that is to be studied. 2. Collect the data needed to answer the questi­on(s) posed in (1). Conducting research on an entire population is often difficult and expensive, so we typically look at a sample. This step is vital to the statis­tical process, because if the data are not collected correctly, the conclu­sions drawn are meanin­gless. Do not overlook the importance of approp­riate data collec­tion. We discuss this step in detail in Sections 1.2 through 1.6. 3. Describe the data. Descri­ptive statistics allow the researcher to obtain an overview of the data and can help determine the type of statis­tical methods the researcher should use. We discuss this step in detail in Chapters 2 through 4. 4. Perform inference. Apply the approp­riate techniques to extend the results obtained from the sample to the population and report a level of reliab­ility of the results. We discuss techniques for measuring reliab­ility in Chapters 5 through 8 and infere­ntial techniques in Chapters 9 through 15.