Introduction to Basic Statistics - Basic Statistics for Behavioral Sciences - Lecture Notes, Study notes of Statistics for Psychologists

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Basic Statistics for

The Behavioral Sciences

LECTURE NOTES

Ch. 1. Introduction

I. Four Basic Terms A. Population; a collection of subjects, events, or scores with a common characteristic (often infinite). B. Parameter; a numerical characteristic of a population. μ, σ², σ. C. Sample; a subgroup of a population. D. Statistic; a numerical characteristic of a sample. M, s², s.

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

III. Area of statistics A. Descriptive statistics; procedures to summarize given data. B. Inferential statistics; procedures to estimate parameter(s) in the population from given statistic(s) in the sample.

IV. Structure of statistics

────────────┐ draw samples ┌────────────┐ population │ (sampling theory) │ sample │ │parameter │ ──────────────> │ statistic │ │(finite │ <────────────── │ │ │infinite) │ draw inferences │measurement │ └───────────┘ (probability └────────────┘ theory)

V. Steps in 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 (statistical analysis). F. Write up and present the results of the research.

2. Cluster Sampling (multi-stage sample) a) Useful if we have some information about hierarchical stages (units) of the population. b) In the first stage, sample the first largest units. In the second stage, sample the second largest units within each largest unit sampled, and go on until you get the last unit. c) e.g., 1st - states 2nd - counties 3rd - school 4th - classes
3. Stratified Random Sampling a) Divide the population according to given information, then apply SRS inside each subgroup (stratum). b) We can get more precise estimation of parameters. B. Measurement
4. Definition; systematic assignment of numbers to characteristics of objects or events.
5. Three properties of measurement. a) Absolute zero; the number zero corresponds to the absence of the characteristic being measured. b) Equal intervals; a unit of measurement is the same no matter where on the measurement scale it occurs. c) Magnitude; one value on the scale can be judged greater than, equal to, or less than some other value.
6. Stevens' level of measurement. a) Ratio scale; has all three characteristics (speed, weight, RT). b) Interval scale; has two properties, equal intervals and magnitude (temperature). c) Ordinal scale; has the magnitude property (order in finishing race, ranking). d) Nominal scale; absence of all the properties (football jersey number).

4. Measurement process (theoretical only) a) Discrete variable; assume only a finite number of values between two points (# of people). b) Continuous variable; potentially takes an infinity of values between any two points on the scale (weight, height). c) But, in fact, all measurement is discrete, due to either its discrete nature or its limits in the precision of measurement. d) Quantitative, numerical, or measurement variable. e) Qualitative, non-numerical, or categorical variable.

VIII. Summation Rules A. Summation notation n ΣXi = X 1 + X 2 + X 3 + ⋅⋅⋅⋅⋅⋅ + Xn i= i = subscript, starting point of the summation. n = sample size, ending point of the summation. X = random variable. B. Summation rules (assume X, Y = random variable, c = constant)

1. Σc = nc
2. ΣcX = cΣX
3. Σ(X+c) = ΣX + Σc = ΣX + nc
4. Σ(X+Y) = ΣX + ΣY
5. ΣXY = X 1 Y 1 + X 2 Y 2 + ⋅ ⋅ ⋅ + XnYn ≠ (ΣX)*(ΣY)
6. ΣX² = X² 1 + X² 2 + ⋅ ⋅ ⋅ + X²n ≠ (ΣX)²