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```Descriptive Statistics

Used to describe or summarize sets
of data to make them more
understandable
– measures of central tendency

mean, median, mode
– measures of variability

range, standard deviation
– measures of association

correlation coefficient
Measures of Central
Tendency
 What
is the average family
income above?

Mean - the arithmetic average
– Total sum of all scores divided by the number
of scores

Median - the center score
– 50th percentile score, half of the scores are
above and half are below

Mode - the score that occurs the most
Measures of Variability
(amount of variation in the data – how
similar or diverse the scores are)

Range - the difference between the
highest and lowest score in a set of
data
– Not always reliable – extreme scores
(outliers) can create a deceptively large
range.
Measures of Variability

Standard deviation - reflects the
average distance between every
score and the mean
– Better gauge of whether scores are
packed together or dispersed
– Large std. deviations signify that
scores are more scattered, therefore
the mean is not terribly typical
Normal Distribution


Normally distributed variables produce
the familiar symmetric, bell-shaped
curves obtained when large numbers of
observations are made on a single
variable
Curves can be skewed in a positive or
negative direction depending on the
position of the long tail (outliers), not
the position of the bulge
Normal Distribution
Skewed Distribution
Measures of Association
Correlation Coefficient 
Often we measure more than one
variable
– Grade point and SAT score
Are they related?
 Correlation statistic is a way to find
out

Inferential Statistics
Descriptive statistics summarize a data
set
 We often want to go beyond the data
 Is the world at large like my sample?
 Are my descriptive statistics
misleading?
 Inferential statistics give probability
that the sample is like the world at
large

Statistics and Probability


Probability means how likely
something is
How likely are results like mine to
occur by chance?
Statistical Significance

How likely it is that a study’s results
occurred by chance
(t-test or chi-square test)
– Statistically significant – reflects the real
world rather than chance – p≤.05

A result would be considered significant if it
would be expected to occur by chance 5 or
fewer times in 100 repetitions of the study.
– Not significant – results reflect chance –
p≥.05
Inferential Statistics
When is an observed difference reliable?
 Representative samples are better than
biased samples.
 Less-variable observations are more
reliable then those that are more
variable.
 More cases are better than fewer.
Sources of Bias


Biased sample - when the members of
a sample differ in a systematic way
from the larger population the
researcher is interested in
Example
– interested in all voters
– contact by telephone
– biased sample - lower economic groups may not
own telephones
Ethical Issues in
Psychological Research
Right to privacy
 Informed consent

– use of deception

Animal rights
– Is there justification for discomfort or harm a
research procedure may produce?

APA publishes ethical guidelines
```
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