Transcript Slide 1

Chapter 7
Summarizing and
Interpreting Data:
Using Statistics
Dawn M. McBride
The Process of Research in Psychology
Second Edition
Steps in the Research Process
2
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Statistics: Descriptive vs. Inferential

Descriptive Statistics


Inferential Statistics

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techniques for summarizing and understanding
data without examining every score
techniques that use descriptive statistics to test
hypotheses about the population (make
inferences)
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Measures of Central Tendency

Values that represents typical score in a
distribution

Mean-average of the scores in a distribution.

Median-middle score in a distribution, half of
the scores are above and half are below the
median
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Mode-most common score in a distribution.
.
Central Tendency
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Outliers
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Normal Distribution
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
The distributions of many natural
phenomena are at least approximately
normally distributed

Quetelet: Flemish scientist, 1800’s
human characteristics such as height,
weight, and strength are normally
distributed
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Normal Distribution of Scores
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Variability

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How much scores differ from each other
across the response scale (options)

In a 1 to 5 rating scale, if most participants
respond with 2 to 4 -- low variability

If participants use all values 1 to 5– higher
variability
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Variability: Range
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The difference between the highest and
lowest scores in a distribution

Highest score = 75

Lowest Score = 25

Range
= ?
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Variability: Standard Deviation (SD)


Standard deviation (SD)

How different scores are from the sample’s Mean

The higher the SD value, the higher the variability
of the scores around the mean
Variance
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The SD2
---- SD squared
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Variability: Standard Deviation (SD)

Average difference between the scores and the
mean of the distribution.
 The
sum of the differences between each score and
the distribution mean = 0, therefore
 the standard deviation= square root of
M-Sc1 2 + M-Sc2 2 + M-Sc32 = SD
N-1

N-1= Degrees of Freedom- number of scores that can vary in the
calculation of a statistic
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Variability: Variance
 The
standard deviation squared
Variance = SD2
Standard deviation and variance
measures are important for inferential
statistical tests.
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Descriptive Statistics
Lab
15
#20
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Graphs/Tables

Display frequency distribution of
scores for a data set

how often each score or category
appears in a distribution.

x-axis (the horizontal axis) –
Response Options
y-axis (the vertical axis) --frequency of
each response in the distribution is

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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Frequency Distribution
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Graphs – Experimental Study
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Bar Graph
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Line Graph
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Height of bar shows value of the mean for
different conditions in a study
Mean for each condition is graphed as a point
and the points are connected in a line
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Bar Graph
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Line Graph
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Displays of Data: Graphs
Lab
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#21
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Percentage of men and women who sought counseling for
anxiety and depression (Lab 21 – Bar graph)
60
50
40
Men
Women
30
20
10
0
Anxiety
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Depression
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Percentage of men and women who sought counseling for
anxiety and depression (Line Graph Lab 21)
60
50
40
Men
Women
30
20
10
0
Anxiety
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Depression
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Inferential Statistics
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
Hypotheses

Significance Testing

Errors
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Hypotheses

Null hypothesis

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Scientific/Alternative hypothesis
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predicts no effect or relationship in the
population or effect in the opposite
direction as the scientific hypotheses
predicts an effect (cause) or relationship
in the population (with or without specific
direction)
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Types of Research Questions:
Correlation

Is there a relation between two constructs?
 Pearson Correlation coefficient r

Ranges form 0 to 1 -- (r =1 identical distributions)

Value of r can be
or
positive
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negative
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Hypotheses:
No direction specified
Variables
Direction
• Depression and self esteem
• GPA and Hours Watching TV
• Math-self efficacy and math test score
• Marital stress and relationship
satisfaction
• Size of students’ ears and IQ
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Correlations: Hypothesis
Variables
Direction
• Depression and self esteem
• GPA and Hours Watching TV
• Math-self efficacy and math test score
• Marital stress and relationship
satisfaction
• Size of students’ ears and IQ
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
+
+
?
Scatter Plot: Correlations
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Types of Research Questions:
Means (1/2)

Is there a difference in the mean of a
construct between two or more groups

Quasi-independent variable – age

In a memory test, Mean scores were:
 Test #1 Adults
= 90 ----- Children = 62
When is a difference in means large enough to be
meaningful?
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Line Graph
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Types of Research Questions:
Means (2/2)

True Independent Variable

Is there a difference in the Mean # of aggressive
behaviors in children who played Violent versus Non
Violent Videogames?
Study 1
Study 2
Mean Aggressive Mean Aggressive
Play Behs.
Play Behs.
Violent VG
Non-Violent VG
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4.3
2.5
significant?
2.9
2.7
significant?
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Bar Graph-
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Group Means Study #1 & #2
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
When is a difference between groups large
enough to be “significant” ?

Inferential Statistics
 Used to determine what can be learned
about the population of interest based on
the data obtained from the sample.

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Based on probability theory: what are the
chances that we are correct to reject the
null hypothesis (and by default accept the
alternative hypothesis)?
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
DELETE
Scientific/Alternative hypothesis

One-tailed Hypothesis – In the population,


Two-Tailed Hypothesis – In the population,

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Children who watch aggressive VG will differ
in the number of aggressive play behaviors
than children who play non-aggressive VG
Children who watch aggressive VG will display
a higher number of aggressive play
behaviors than children who play nonaggressive VG
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Scientific/Alternative hypothesis
 Two-Tailed

Predicts a hypothesis in either
direction (a difference; a correlation)

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Hypothesis
Children who watch aggressive Vs will
differ in the number of aggressive
play behaviors compared to children
who watch non-aggressive Vs
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Null Hypotheses
(two-tailed hypotheses)

Null hypothesis

Predicts no effect:
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Children who watch aggressive Vs will
not differ in the number of aggressive
play behaviors than children who watch
non-aggressive Vs
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
How likely it is that we will obtain the observed
mean when the null hypotheses is true
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Scientific/Alternative hypothesis
 One-tailed

Predicts an effect in one direction
(higher vs. lower; + vs. -)

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Hypothesis
Children who watch aggressive Vs will
display a higher number of aggressive
play behaviors than children who
watch non-aggressive Vs
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Null Hypotheses
(one-tailed hypotheses)

Null hypothesis

Predicts an effect in the opposite
direction or no effect:

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children who watch aggressive Vs will
display a lower number or similar
number of aggressive behaviors than
children who watch non- aggressive Vs.
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Significance Testing
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Significance Testing
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
Is there enough evidence in the data to
reject the null hypothesis and accept the
alternative (or scientific) hypotheses?

What are the chances of obtaining the
means observed in the sample when the
null hypothesis is correct (or true)?
90%, 50% 10% 5% ????
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Assumptions
We assume that
• If we took a large number of samples (subgroups) from the
population of interest
• Calculated the mean for each sample (e.g.in the memory
test)
• Made a plot of these values,
• The distribution of means would be normal.
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Distribution of Sample Means
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
Distribution of all possible sample means of all
possible samples from a population will
resemble a normal distribution

Most sample means will be close to the mean
of the population
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Significance Testing

Alpha level


P Value

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highest probably value acceptable as evidence
that sample value is too extreme for null
hypothesis to be true (level of risk willing to take)
Actual probability given by the inferential test
(Pearson correlation; T-Test) of obtaining the
correlation/mean observed in study sample, when
the null hypothesis is true
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Significance Testing

Alpha Level



P Value



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Chosen by researcher: .10; .05; .01; 001
p<.05 -- null hypothesis is rejected
Actual probability with one’s sample
Obtained from inferential test
Compared to Alpha level
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Significance Testing

Critical region
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portion of distribution of sample means in
the normal curve containing extreme (high
and low) scores

Size is equal to alpha level

Location- in one tail; or both tails
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Errors
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Errors

Type I error: reject the null hypothesis when
it is true (an effect is claimed, but it does not
really exist)


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Alpha = .05 --- 5% of making a Type I error
Type II error: retain the null hypothesis when
it is false (an effect is not claimed, but it does
really exist)
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Type I and Type II Error
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Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Power


Ability of a significance test to detect and
effect (difference in means, significant
correlation) when one exists (optimal--80%)
The following increase power




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Larger alpha level
Larger sample size
Larger size of the effect
Higher internal reliability of measurements
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Confidence Interval

Gives an estimated range of values that will
include the mean of a population (or %,
correlations) with specific probability level
99% or 95%)

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Estimate of the mean ± Margin of Error

Opinion poll 82% agree smoking is harmful ± 3%
 Confidence interval 79% - 85%

Mean Beck Depression score women 14 ± 5
 Confidence interval 9 --- 19
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Predicting Null Hypotheses
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
Significant statistical tests provide evidence against
he null hypotheses but not for it

Not possible to draw strong conclusions in the
absence of a significant result

A series of studies with high levels of power (80%)
that consistently support null hypotheses, would
provide support for the lack of the hypothesized
effect.
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.
Common Pitfalls



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Problem: Supporting the null hypothesis—students
often make the error of stating that the null hypothesis is
supported with a nonsignificant result.
Problem: Stating that results “prove” the hypothesis
is true—students sometimes make the mistake of
stating that statistical results prove that an effect exists .
Problem: Ignoring the power of the test—researchers
sometimes do not consider the power of their tests
carefully enough, concluding that a nonsignificant result
can be relied on with the same certainty as a significant
result.
Dawn M. McBride - The Process of Research in Psychology, 2nd Edition © 2013 SAGE Publications, Inc.