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CHAPTER 7:
SUMMARIZING AND
INTERPRETING DATA
Descriptive Statistics
 Descriptive statistics: measures that help us summarize
data sets.
 Inferential statistics: a set of statistical procedures used
by researchers to test hypotheses about populations.
 Distribution: a set of scores.
 Central tendency: representation of a typical score in a
distribution.
 Variability: the spread of scores in a distribution.
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Central Tendency
 Mean
 the calculated average of the scores in
a distribution.
 Median
 the middle score in a distribution,
such that half of the scores are above and half
are below that value.
 Mode
 the most common score in a
distribution.
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Central Tendency
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Variability
Range
 The
range is the most basic measure and is simply the
difference between the highest and lowest scores in a
distribution.
 However,
the range ignores all the scores between the
most extreme scores and therefore is a crude measure of
variability.
 The
standard deviation and variance are much more
precise measures of variability.
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Variability
Standard deviation
 The
standard deviation is a measure representing the
average difference between the scores and the mean of
the distribution.
 However, if you were to simply calculate the differences
between the scores and the mean and add them up, you
would find that the value is always 0.
 Thus, the standard deviation is determined by calculating
the difference between each score and the mean,
squaring those values, adding them up, and dividing by n 1 (where n is the number of scores).
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Variability
Variance
 The
variance is simply the standard deviation
squared.
 Standard
deviation and variance measures are
important for inferential statistical tests.
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Graphs/Tables
 Graphs (also called figures) and tables of data are
useful tools for quickly summarizing data in a visual
way.
 They
can represent a frequency distribution for a data set,
which indicates how often each score or category appears
in a distribution.
 In
a frequency distribution, the different responses are
graphed on the x-axis (the horizontal axis) and the
frequency of each response in the distribution is graphed
on the y-axis (the vertical axis).
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Graphs/Tables
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Graphs/Tables
 Bar graph  a graph of the means for different
conditions in a study where the bar height
represents the size of the mean.
 Line graph  a graph of the means for different
conditions in a study where each mean is
graphed as a point and the points are connected
in a line to show differences between mean
scores.
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Graphs/Tables
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Graphs/Tables
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Graphs/Tables
 Scatterplot: a graph showing the relationship
between two dependent variables for a group of
individuals.
 Predictor
variable: the dependent variable in a
correlational study that is used to predict the score
on another variable.
 Outcome variable: the dependent variable in a
correlational study that is being predicted by the
predictor variable.
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Inferential Statistics
 Hypotheses
 Null
hypothesis
 Predicts no effect
or relationship in the population.
 Scientific/alternative
 Predicts an
hypothesis
effect or relationship in the population.
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Inferential Statistics
 Significance testing  the p value is less than or equal
to alpha in an inferential test, and the null hypothesis
can be rejected.
Alpha level: the probability level used by researchers to
indicate the cutoff probability level (highest value) that allows
them to reject the null hypothesis.
 p Value: the probability value associated with an inferential
test that indicates the likelihood of obtaining the data in a
study when the null hypothesis is true.
 Critical region: the most extreme portion of a distribution of
statistical values for the null hypothesis determined by the
alpha level (typically 5%).

McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Inferential Statistics
 Errors
 Type
I error: error made in a significance test when
the researcher rejects the null hypothesis when it is
actually true.
 Type II error: error made in a significance test when
the researcher fails to reject the null hypothesis when
it is actually false.
 Power: ability of a significance test to detect an
effect or relationship when one exists (equal to
1—the probability of a Type II error).
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Inferential Statistics
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.
Predicting a Null Hypothesis
 In many cases, the alternative hypothesis is also
the researcher’s hypothesis.
 Many would argue that it is not appropriate for
a researcher to predict the null hypothesis
because significance tests do not provide
evidence for the null hypothesis.
 If
researchers want to predict the null hypothesis,
they must be prepared to conduct several studies in
order to obtain some support for their hypothesis.
McBride, The Process of Research in Psychology. Third Edition © 2016 SAGE Publications, Inc.