Chapter 1

I. Definitions

A.Statistics - set of methods and rules for organizing, summarizing, and interpreting information

B. Statistic - a specific type of statistical method

C.Population - a set of all things (individuals in psychology) that have at least one characteristic in common

D.Sample - a subset of individuals selected from the population

E. Sampling - the process by which the sample members are selected

F. Parameter - a value that describes a population (Greek letters)

G.Statistic - a value that describes a sample (Latin letters)

H.Data, data set, datum -

I.Descriptive Statistics - procedures used to summarize, organize, and simplify data

J.Inferential Statistics - procedures used to study samples and make generalizations about the populations from which they were selected

K.Sampling error - discrepancy, or error, between a sample statistic and a population parameter.

L.Random selection or random sampling - a process for obtaining a sample that requires that every member of the population have an equal chance of being selected for the sample. A sample obtained by random selection is called a random sample.

II. Scientific Methods

A.Science is the process of discovery of relations between variables.
1.variables - characteristics that have different values for different individuals
2.constants - characteristics that have the same value for all individuals

B.Correlational method - two variables are observed to see if they are related (weak inferences)

C.Experimental method - one variable is manipulated to assess its effect upon a second variable.
1.independent variable - the variable that the experimenter manipulates, must have more than one level, and any individual must be able to be assigned to any of the levels
2.dependent variable - the variable that the experimenter measures to see whether the IV has produced an effect
3.control - the researcher attempts to control all extraneous variables when assessing the IV-DV relation.
4.experimental group - receives IV
5. control group - doesn't receive IV
6.random assignment - a process of control that insures that there is no bias in the way that individuals are assigned to the experimental or to the control groups

D.Quasi-experimental method - same as the experimental method except that the IV is not manipulated. Individuals are selected for their group membership (e.g., male vs female, etc.)

E. Theories and hypotheses
1.Theory - statement of relation among variables. Theories organize and unify data and specify the mechanisms the account for the relation among variables. Theories permit predictions.
2.Hypothesis - a specific prediction about how an independent variable will effect a dependent variable

F.Constructs and operational definitions - variables that psychologists are often interested in are not directly observable because they are hypothetical. Therefore, we must be able to provide definitions that are observable to study these variables.
1.Construct - hypothetical concepts used in theory to organize data in terms of the underlying mechanisms.
2.Operational definitions - defines construct in terms of specific operations used to manipulate or measure the construct.

III. Scales of Measurement

A.Definition - assignment of numbers to according to rules.

B.Scales - levels of measurement.

1. Qualitative

i.Nominal

Properties - 1) categories are mutually exclusive, no object can belong to more than one category; 2) categories can't be ordered.

E.G., gender (0, 1), race, etc.

Transformations - any numeric substitution that preserves categories

ii.Ordinal

Properties - 1) categories are mutually exclusive, no object can belong to more than one category; 2) categories have a logical order; 3) categories are ordered according to amount of what is being measured, BUT the differences in amount between categories is NOT the same.

E.G., grades (A, B, C), winners in a race (1st, 2nd, 3rd), etc.

Transformations - any numeric substitution that preserves the order among categories

2. Quantitative

iii.Interval

Properties - 1) categories are mutually exclusive, no object can belong to more than one category; 2) categories have a logical order; 3) categories are ordered according to amount of what is being measured; 4) the differences between categories is the same, BUT the zero point on the scale is arbitrary.

E.G., temperature in degrees F or C, IQ, etc.

Transformations - addition of a constant or multiplication by a positive constant

iv.Ratio

Properties - 1) categories are mutually exclusive, no object can belong to more than one category; 2) categories have a logical order; 3) categories are ordered according to amount of what is being measured; 4) the differences between categories is the same; 5) a true zero point on the scale indicating the absence of the thing being measured.
E.G., temperature in degrees K, time, etc.

Transformations - multiplication by a positive constant

F. Discrete vs continuous variables
1.Discrete - a variable that consists of separate, indivisible categories. No values can exist between adjacent categories.
2.Continuous - a variable that has an infinite number of possible values can exist between adjacent values. Limited by the resolution of the measurement scale.

IV. Summation Notation

A. Summation operator, sigma

B. Order of operations

1. Any calculation in parentheses

2. Exponents (squaring, square root, etc.)

3. Multiplication and division (*, /)

4. Summation (S)

5. Addition and subtraction (+, -)


C. Define N