Patrick Barlow and Tiffany Smith
Descriptive Statistics
Parametric Statistics
Non-Parametric Statistics
 Null
Hypothesis
 Alternative Hypothesis
 Mean
 Standard Deviation
 Correlation
 Confidence Interval
the statistics to the research question, not the
other way around!
 First, ask yourself, “Am I interested in….
 Fit
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Describing a sample or outcome?”
Looking at how groups differ?”
Looking at how outcomes are related?”
Looking at changes over time?”
Creating a new scale or instrument?
Assessing reliability and/or validity of an instrument?
 Second,
“How am I measuring my outcomes?”


Descriptive Statistics
Parametric Statistics

Common tests of relationships

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
Common tests of group differences

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
Independent t-test
Between subjects analysis of variance (ANOVA)
Common tests of repeated measures



Pearson r
Linear/multiple regression
Dependent t-test
Within subjects ANOVA
Tests of categorical data
Odds Ratio / Chi Square
 Logistic Regression


Common Psychometric tests
Cronbach’s Alpha
 Principal Components and Factor Analysis

Numbers used to describe the sample
 They do not actually test any hypotheses (or yield any
p-values)
 Types:
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Measures of Center 
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Measures of Spread 

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Mean
Median
Mode
Quartiles
Standard Deviation
Range
Variance
Frequencies
 Most
powerful type of statistics we use
 Researchers must make sure their data meets a
number of assumptions (or parameters) before
these tests can be used properly.

Some key assumptions


 In
Normality
Independence of observations
research, you always want to use parametric
statistics if possible.
Pearson r correlation
Linear/Multiple Regression
 What

is it?
A statistical analysis that tests the relationship
between two continuous variables.
 Commonly

Associated Terms:
Bivariate correlation, relationship, r-value, scatterplot,
association, direction, magnitude.
Moderate
Strong
Weak
Relationship:r > .50
No Relationship:
Relationship:
Relationship:
r ≈ |.10|
|.00|
r ≈ |.30|
10
Each has a Pearson
Correlation of r=.82, is & is
statistically
significant
11
Anscombe, F.J., Graphs in Statistical Analysis, American Statistican, 27, 17-21
 What

Study found a relationship between GPA and sense of
belonging, r=.35, p = .03.
 What

to interpret:
Results show r = .35, p = .03, R2=.12
 How

you read:
to interpret:
There is a weak, significant positive relationship
between college GPA and students’ sense of
belonging to the university. As sense of belonging
increases, GPA also increases.
 What is it?
 A statistical
analysis that tests the relationship
between multiple predictor variables and one
continuous outcome variable.
Predictors: Any number of continuous or
dichotomous variables, e.g. age, anxiety, SES
 Outcome: 1 Continuous variable, e.g. ER visits per
Month

 Commonly Associated Terms:
 Multivariate, beta weight, r2-value,
forward/backward regression,
sequential/hierarchical regression,
standard/simultaneous regression,
statistical/stepwise regression.
model,
13
Independent t-test
Between Subjects Analysis of Variance (ANOVA)
 What

is it?
Tests the difference between two groups on a single,
continuous dependent variable.
 Commonly

associated terms:
Two sample t-test, student’s t-test, means, group
means, standard deviations, mean differences, group
difference, confidence interval, group comparison.
 What



p-values (<.05)
Mean differences and standard deviations
Confidence intervals
 How

to interpret?
to interpret?
There is a significant difference between the two
groups where one group has a significantly
higher/lower score on the dependent variable than the
other.

What you read:


Students who were put on academic probation (M=1.50,
SD=.40) had lower sense of belonging than students who
were not put on academic probation (M=3.50, SD=.75), p =
.02.
What to interpret:
p-value: .02
Mean sense of belonging for both groups: academic
probation = 1.50 & non-academic=3.50.
 Standard deviations for both groups: on academic probation
=.40 & not on academic probation=.75.



How to interpret:

Participants on academic probation had significantly lower
sense of belonging than students who were not put on
academic probation.
 What

is it?
Tests the difference among more than two groups on a
single, continuous variable.

Post-Hoc tests are required to examine where the differences
are.
 Commonly

associated terms:
F-test, interactions, post-hoc tests (tukey HSD,
bonferroni, scheffe, dunnett).
 What

p-values (<.05)



Main effect: Shows overall significance
Post-hoc tests: shows specific group differences
Mean differences, standard deviations
 How


to interpret?
to interpret?
Main Effect: There was an overall significant
difference among the groups of the independent
variable on the dependent variable.
Post-Hoc: Same interpretation as an independent ttest

What you read:

A researcher looks at differences in average satisfaction on
three different reading interventions (A, B, and C).



What to interpret:



Main effect: Overall F=20.10, p=.01
Post-hoc: Comparison of Intervention “A” to Intervention “B” shows
average satisfaction to be 4.32 (SD=.50) and 3.56 (SD=1.2),
respectively, p=.04.
Main effect: p-value=.01
Post-hoc: p-value=.04, group means show Intervention “A” has
higher satisfaction ratings than Intervention “B”.
How to interpret:


Main effect: There is a significant overall difference among the
three interventions on satisfaction.
Post-hoc: Students who received Intervention “A” have
significantly higher satisfaction than those who received
Intervention “B”
Dependent t-test
Within Subjects Analysis of Variance (ANOVA)

What is it?


Commonly Associated Terms:


Tests the differences for one group between two time-points
or matched pairs
Pre and posttest, matched pairs, paired samples, time.
What to interpret?
p-values (<.05)
 Mean change between measurements (i.e. over time or
between pairs)


How to interpret:?

There is a significant difference between the pretest and
posttest where the score on the posttest was significantly
higher/lower on the dependent variable than the pretest.
 What

An article shows a difference in average test score
before (M=79.50, SD=8.00) and after (M=85.25,
SD=7.90) an educational intervention, p=.08.
 What


to interpret:
p-value=.08
Mean change=7.75 more points after the educational
intervention.
 How

you read:
to interpret:
Average test score did not significantly change from
before the intervention to after the intervention;
however, there may be a practically relevant difference.

What is it?


Commonly Associated Terms:


Multiple time-points/matched pairs, repeated measures, posthoc.
What to interpret?



A statistical analysis that tests differences of one group
between two or more time-points or matched pairs (e.g.
pretest, posttest, & follow-up or treatment “A” patient,
treatment “B” matched patient, & placebo matched patient).
Main effect: p-values
Post-hoc: p-values, mean change, direction of change.
How to interpret:


Main Effect – There was an overall significant difference
among the time points/matched pairs on the dependent
variable.
Post-Hoc: Same as a dependent t-test.

What you read:

An article shows a difference in average classroom comfort
before (M=1.5, SD=2.0), after (M=3.30, SD=.90), and six
months following a cohort-building intervention (M=4.20,
SD=3.0).


What to interpret:



Main effect: Overall F=3.59, p=.02.
p-value=.02, statistically significant
Mean change=1.8 higher classroom comfort at postintervention
How to interpret:

Classroom comfort significantly increased from baseline to
six-months following a cohort-building intervention;
however, post-hoc tests will be needed to show where that
differences lies.

Mixed ANOVA: Used when comparing more than one group over
more than one time-point on a measure


Factorial ANOVA: Comparing two or more separate
independent variables on one dependent variable.


Example – Males vs. female students, before and after a foreign
language course – Average score on an assessment
Example – Who taught the course (Ms. Lang, Mr. Beard, or Ms.
Brinkley), AND which teaching method was used (online, face to
face) – Average post-test assessment score
Analysis of covariance (ANCOVA): Examining the differences
among groups while controlling for an additional variable

Example – Online or face to face course, controlling for baseline
knowledge – Average post-test assessment score
All of these methods are used to test interaction effects
Odds Ratio / Relative Risk (Chi-square test of independence)
Logistic Regression

What is it?


Commonly Associated Terms:


A statistical analysis that tests the odds or risk of an event occurring or not
occurring based on one or more predictor variables (independent).
Unadjusted odds ratio (OR), relative risk (RR), 2x2, chi-square, absolute risk
reduction, absolute risk, relative risk reduction, odds, confidence intervals,
protective effect, likelihood, forest plot.
What to interpret?
If a 2x2 table: interpret the OR or RR and confidence intervals rather than
the p-value.
 If more than a 2x2 table, then the p-value and frequencies may be more useful.


How to interpret:
Odds Ratio < 1: For every unit increase in the independent variable, the odds
of having the outcome decrease by (OR) times.
 Odds Ratio > 1: For every unit increase in the independent variable, the odds
of having the outcome increase by (OR) times.
 Odds Ratio = 1 or CI crosses 1.0 or p > .05: You are no more or less likely to
have the outcome as a result of the predictor variable. (this would be nonsignificant)


What are the odds of leaving college if a student
has been placed on academic probation?



What you read:


IV: Academic probation (Y/N)
DV: Completion (Y/N)
The odds ratio (95% CI) for college completion and
academic probation showed OR=2.00 (95% CI=1.44 - 2.88),
p <.05.
What you interpret:
OR > 1 (2.00)
95% CI is small, and does not cross 1.0 (1.44 to 2.88)
 p-value is below .05



How you interpret:

Students are two times more likely to leave college if they
were placed on academic probation.

What is it?



Commonly Associated Terms:
 Adjusted odds ratio (AOR), multivariate adjusted odds ratio, likelihood,
protective effect, risk, odds, 95% confidence interval, classification table,
dichotomous DV.
What to interpret?


A statistical analysis that tests the odds or risk of an event occurring or not occurring
based on one or more predictor variables (independent) after controlling for a number of
other confounding variables.
OR (these are your measures for risk of the outcome occurring given the predictor
variable), p-value for OR, confidence intervals for OR (should not cross over 1.0, should
not be overly large e.g. 1.2 – 45.5), classification table (if it is provided).
How to interpret:



Odds Ratio < 1: For every unit increase in the independent variable, the odds of having
the outcome decrease by (OR) times after controlling for the other predictor variables.
Odds Ratio > 1: For every unit increase in the independent variable, the odds of having
the outcome increase by (OR) times after controlling for the other predictor variables.
Odds Ratio = 1 or CI crosses 1.0 or p > .05: You are no more or less likely to have the
outcome as a result of the predictor variable after controlling for the other predictor variables.
(this would be non-significant)

Does age, male sex, and time spent playing video games,
increase the odds of being on academic probation?
Predictor Variables: age (scale), sex (M/F), Gaming (ordinal, 0hrs, 13hrs, 4-6hrs, etc.)
 DV: Probation (Y/N)


What you read:

The ORs (95% CI) for each predictor variable are:




What you interpret:


Age: OR=1.40 (95% CI=0.88 to 6.90), ns
Sexmale: OR=3.00 (95% CI=2.22 to 5.20), p <.001
Gaming: OR=6.75 (95% CI=4.69 to 8.80), p <.001
The OR, CI, and p-value for each predictor.
How you interpret:

Both sex and time spent gaming increase the odds of being on
academic probation. Specifically, men are 3.00 times more likely to be
on academic probation than females, and for every unit increase in
gaming time, the odds of being on probation increases by 6.75 times.
Questions?

Work together (in groups of 3-4) to create survey
research scenarios / questions that could be
addressed using the analyses you have learned about
in class.
Use your “Commonly Used Statistics” handout as a
resource!
Be prepared to share your answers 
Cronbach’s Alpha
Principal Component Analysis / Factor Analysis
Other psychometric tests
 Psychometric
tests are used to examine the
characteristics and performance of a survey or
assessment instrument.
 Reasons to use these tests




Reliability
Validity
Dimension reduction (constructing new instruments)
Item analysis (objective tests)


Cronbach’s alpha is one of the most common psychometric tests
used by survey researchers.
Looks at the internal consistency of the items in a certain scale or
instrument.


In other words, how responses to items in the scale relate to one
another.
What to interpret
The overall alpha value for the scale
 The “alpha if item removed” table


How to interpret
For the Alpha values: > .90 is excellent, .80-.90 is good, .70-.80 is
acceptable, .60-.70 is questionable, between .50-.60 is poor, and
<.50 is unacceptable. If you see a negative  value, then recheck
your data for coding errors.
 For the “alpha if removed” table: Look at the  values that the scale
would have if the item was removed. If dropping an item makes a
meaningful improvement (e.g. from .75 to .80), then consider
dropping the item and rerunning the analysis.

 More
items
 More participants
 Increase the “good” type of redundancy
 Drop poor items (those that affect alpha)
 Clarify item stems
 Double check coding
 PCA
and FA are both dimension reduction
techniques that are used when either
pretesting a new instrument (exploratory) or
gathering validity evidence for an existing
instrument (confirmatory).
 Both methods look at how items cluster
together as latent (not directly measured)
“factors” or “components”.
 Examples: “depression”, “anxiety”, or “sense
of belonging”
 Number
of items
 Number of subjects
 Technique used


PCA
FA
 Extraction


methods
Orthogonal
Oblique
 SO
many others!
Remember:

Just because a finding is not significant does not mean that it is not
meaningful. You should always consider the effect size and
context of the research when making a decision about whether or
not any finding is relevant in practice.