Learn Statistics Fast: A Simplified Detailed Version for Students

Learn Statistics Fast

This is an excellent overview of the fundamentals of statistics for those who have forgotten some of what they previously learned, those whose instructors left them dazed and confused, or those who just need a quick reference.

Introduction    

I. Terminology

A. Population:  A collection of subjects, events, or scores with a common characteristic.  Large, infinite, theoretical

B. Parameter:  A numerical characteristic of a population.  Greek letter: μ, σ²,σ

C. Sample:  A subgroup of a population.  Small, finite, empirical.

D. Statistic:  A numerical characteristic of a sample. 

Roman letter:  , s², s.

II. Definition of Statistics

Statistics is an area of science concerned with the extraction of information from sample data and its use in making inferences about a population from which the sample data are obtained.

III. Areas of Statistics

A. Descriptive vs. Inferential Statistics

1. Descriptive statistics:  procedures to summarize given data.

2. Inferential statistics:  procedures to estimate parameters in the population from given statistics in the sample.

B. Parametric vs. Nonparametric Statistics

C. Traditional (objective) vs. Bayesian (subjective) Statistics

D. Exploratory vs. Confirmatory Data Analysis

E. Univariate vs. Multivariate Data Analysis

IV. Structure of Statistics (Bridge Illustration)

V. Steps of Psychological Research

A. Structure a hypothesis or hypotheses.

B. Design an experiment.  (Experimental Design)

C. Sample subjects.  (Sampling Theory)

D. Collect data.  (Measurement Theory)

E. Analyze the data.  (Statistics)

Write up and present.  (Publish)

VI. Experimental Design

A. Terminology

1. Variable:  The characteristic of a set of objects or events whose members may be measured and are free to vary  (X, Y, Z).

2. Independent Variable (IV):  The variable manipulated by the experimenter independently of other variables.

3. Dependent Variable (DV):  The outcome variable whose value depends on the manipulation of IV.

4. Confounding, Extraneous, or Nuisance Variable:  The variable which the experimenter wants to control, which may affect the result of an experiment.

B. Types of Experiment

1. True Experiment.  (Controlled Lab Style)

a. Observation of DV

b. Manipulation of IV

c. Control of Extraneous Variable (EV) (randomization)

d. The only design to identify a casual relationship

2. Natural Observation.  (Survey)

a. Observation of DV

b. No manipulation of IV

c. No control of EV

d. Devoted to either uncovering relationship or estimating populations general characteristics.

3. Quasi-Experiment

a. Observation of DV

b. Manipulation of IV

c. No control of EV

d. Mid-way between True Experiment and Natural Observation

VII. Measurement

A. Definition: Systematic assignment of numbers to the characteristic of objects or events.

B. Three Properties of Measurement

1. Absolute Zero:  the number zero means the absence of the characteristic being measured.

2. Equal Intervals:  a unit of measurement scale is the same no matter where on the scale it occurs.

3. Magnitude:  one value on the scale can be judged as greater than, equal to, or less than some other value in terms of the characteristic being measured.

C. Stevens' (1951) Level of Measurement

1. Ratio Scale: has all three properties (e.g., speed, weight, height, reaction time, # of people).

2. Interval Scale: has two properties; equal interval and magnitude (e.g. temperature).

3. Ordinal Scale: has the magnitude property (e.g., order of racing, beauty contest).

4. Nominal Scale: absence of all properties (e.g., jersey number). Just a classification.

D. Measurement Process (theoretical only).

1. Discrete Variable: assume only a finite number of values between two points.

2. Continuous Variable: potentially takes an infinity of values between two points.

3. But, in fact, all measurement is discreet, due to either its discrete nature or limits in the precision of measurement.

4. Qualitative (frequency, categorical) vs Quantitative (numerical, measurement data).

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VIII. Summation Rule

A. Notation

n

ΣXi = X1 + X2 + . . . + Xn

i=1

i:  Subscript: