PSYC2317, Dr. Hsu, Chap 1 (8th ed.)
1.1
Statistics and science
(A) Statistics: (a) facts and figures, (b) a set of mathematical procedures for
organizing, summarizing, and interpreting information.
(B) Science: methods for making observations.
Statistics: tools for science.
1.2
Population and samples
(A) Population: the entire set of the individuals of interest for a
particular research question.
Sample: a set of individuals selected from a population, usually intended
to represent the population in a research study.
Random Sampling: every individual in the population has the
same chance of being selected. The sample thus selected is called
a ramdom sample.
(B) Variables and Data:
Variable: a characteristic or condition that changes or has different
values for different individuals.
Data: measurements or observations.
(C) Parameter: a numeric value describes a characteristic of a
population (ex. mean, median, etc.)
Statistic: a numeric value describes a characteristic of a
sample.
Sampling Error: the discrepancy (or error) exists between a sample statistic
and the corresponding population parameter.
(D) Descriptive Statistical Methods: to summarize, organize, and
simplify data. (Raw data --> mean (average), tables, graphs.)
Inferential Statistical Methods: to make inferences about
population based on sample data (generalization).
(see p. 10, Example 1.1, Fig. 1.3)
1.3
I.
Data Structures, Research Methods, and Statistics
Measuring two variables for each individual:
Correlational Method: to identify relationships between
variables. Can not be used to identify cause-effect. (p. 13, Fig. 1.4)
II.
Measuring two (or more) groups of scores:
Experimental Method: can identify cause-effect.
(p. 14, Fig. 1.5, p. 15, Fig. 1.6)
a. manipulation: creating systematic change in one variable.
b. control: 1. random assignment of subjects, 2. uniform
procedure and condition, 3. experimenter bias ("doubleblind" procedure).
Non-experimental(or Quasi-experimental) Methods: (p. 17, Fig. 1.7)
examines differences between pre-existing groups of subjects (men vs.
women, college graduates vs. high-school graduates, etc.) <nonequivalent
groups> or before-after or pre-post studies.
PSYC2317, Dr. Hsu, Chap 1 (8th ed.)
1.4.
Variables and Measurements
Discrete and Continuous Variables
(A) Discrete variable: separate, indivisible categories, typically
restricted to whole, countable numbers, ex. dice value, # of
people, # of visits to doctor’s office. etc.
(B) Continuous variable: infinite number of possible values that
fall between any two observed values, divisible into an infinite
number of fractional parts, ex. time, height, weight, age, etc.
*Real limits: For a continuous variable, each score actually
corresponds to an interval on the scale. The boundaries that
separate these intervals are called real limits - located exactly
half way between the scores.
Scales of Measurement
*Data collection involves measurements of our observations.
(A) The nominal scale: Observations are labeled and categorized,
examples: sex, occupation, type of personality, SS#.
Does not make any quantitative distinctions between
Observations (Does not indicate size and order of events).
(B) The ordinal scale: Observations are ranked in terms of size
magnitude, ex. order of preference,1st, 2nd, 3rd, etc. Does not
reveal how much of the difference.
(C) The interval scale: Equal intervals between numbers on the
scale reflect equal differences, ex. temperature, IQ scores, etc.
No absolute zero point (Zero point is arbitrary). Ratios are not meaningful.
(D) The ratio scale: There exists an absolute zero point (zero means
absence of something.) Ratio of numbers reflects the ratio of
magnitude, ex. height, weight, volume, income.
1.5 Statistical notation and summation
***(p.27 Order of Math Operations)
(A) Notation: scores for variables - X, Y, Z.
number of scores - N (for population), n (for sample)
summation - adding up a set of scores
(B) Summation:
sum of the squared scores
squared total
(C) use summation notation to express calculation:
a. Add 5 points to each score and then sum the resulting values.
b. Sum the scores, then add 15 points to the total.
c. Square each score and subtract 5 points from each squared value,
then sum the resulting value.
d. Subtract 2 points from each score, then square the resulting
value, then sum the squared values up.
** [ Answers:
a.
(X +5)
b.
X + 15
c.
( X – 5)
d.
(X-2)
]