Data Analysis Decision
Matrix
By Dr. Kevin Kaeochinda
Capstone II Workshop
Series
How to use this Data Analysis Matrix:
• Write down your hypothesis and identify your
independent variable(s) (IV) and your
dependent variable(s) (DV)
– IV: Types of treatment (e.g., therapy or no
therapy) and DV: Outcome (e.g., depression)
• How many do you have of each?
– For example:
– Treatment (Therapy or no therapy) is ONE I.V. with
two levels
– Depression is ONE D.V. with one level (although it
is continuous
• Are you measuring the outcome(s) on the same
population or different? If you use two-levels of
Treatment (no therapy and then therapy) on the
same group of people, then your sample would
be “dependent”
• Are they Categorical, Ordinal, or Interval type
variables?
– Categorical/Nominal: Two or more categories but
no true order for the categories (e.g., Male and
Female; Hair color)
– Ordinal: Same as categorical but has a logical
order or value (e.g., First place, second place, third
place, etc.)
– Interval/Continuous: Has order but there’s values
in between (e.g., Income in dollars)
Other things to consider:
• Do you have any groupings?
– Are you going to compare male
versus female, ethnic groups, age
groups, or other grouping (e.g.,
hours spent on Facebook)
– Write down your groups so you can
visually see it.
• For most test, you would also
want to test for parametric
assumptions before conducting a
parametric test (a non-parametric
equivalent would be possible)
– Normality
– Homogeneity of variances
Descriptive & Frequencies
• You should always do a “Frequency” analysis
prior to any other analysis
– Also, break down your analysis based on grouping
to help you get means/modes/medians and
Standard Deviations
• Include a histogram or graphical representation
of the data to get a “feel” of it
• It will help you get the feel of your data
– How many N’s? How many males or females?
Students or non-students? How many missing?
No. of D.V.’s Nature of I.V.
1
Nature of D.V.
Analysis to perform
Interval & Normal
One-Sample t-test
Ordinal or Interval
Wilcoxon Signed Rank Test
Interval & Normal
2 Independent Sample t-test
Ordinal or Interval
Wilcoxon-Mann Whitney test
1 I.V. with 2+ levels
(independent groups)
Interval & Normal
One-way ANOVA
Ordinal or Interval
Kruskal Wallis
1 I.V. with 2+ levels
(dependent/matched
groups)
Interval & Normal
Paired sample t-test
Ordinal or Interval
Wilcoxon signed ranks test
2 or more I.V.
Interval & Normal
Factorial ANOAV
Ordinal or Interval
Ordered logistic regression
Interval & Normal
Correlation
And/Or
Simple Linear Regression
Ordinal or Interval
Non-parametric correlation
Categorical
Simple logistic regression
Interval & normal
Multiple regression
0 I.V.’s
(1 population)
Example.
Whole Sample
1 I.V. with 2 levels
(independent groups)
Example.
Female/Male
Students/Non-students
1 Interval I.V.
1 or more interval I.V.’s
and/or 1 or more
categorical I.V.’s
Analysis of Covariance
(ANCOVA)
Categorical
Multiple logistic regression
Discriminant analysis
2+ D.V.’s
No. of D.V.’s
Nature of I.V.
Nature of D.V.
Analysis to
perform
2+
1 I.V. with 2 or
more levels
(independent
groups)
Interval &
Normal
One-Way
MANOVA
2+ I.V.
Interval &
Normal
Multivariate
Multiple Linear
Regression
0 I.V.
Interval &
Normal
Factor Analysis
0 I.V.
Interval &
Normal
Canonical
Correlation
2+ sets of 2+
The above analyses are advanced.
Please see me about them before
trying to conduct the analyzes boxed
in red
Retrieved and simplified from: http://goo.gl/ohT922
One Sample t-test
• The one-sample t-test is used to determine whether a
sample comes from a population with a specific mean.
This population mean is not always known, but is
sometimes hypothesized. For example, you want to
show that a new teaching method for pupils struggling
to learn English grammar can improve their grammar
skills to the national average. Your sample would be
pupils who received the new teaching method and
your population mean would be the national average
score.
In SPSS
• Analyze >> Compare Means >> One-Sample T-test
• Transfer your Dependent Variable (in this case,
dep_score) to the Test Variable(s) box.
• Click OK
Population
mean to
compare to
the sample
mean
Click here to continue >>
One Sample t-test cont’d.
• How to interpret your output
The write-up:
• Dep_score is Dependent Score
• “A single-sample t-test was conducted to compare the
weight of all participants in their Dependent Scores to
the average Dependent Score of students at MCU. The
results were significant, t(9)=4.47, p<.001.”
<< Click here to go Back to beginning
Wilcoxon Signed Rank Test
•
•
Equivalent to the dependent t-test
For example, you could use a Wilcoxon signed-rank test to
understand whether there was a difference in smokers' daily
cigarette consumption before and after a 6 week hypnotherapy
program (i.e., your dependent variable would be "daily cigarette
consumption", and your two related groups would be the cigarette
consumption values "before" and "after" the hypnotherapy
program).
In SPSS
• Analyze >> Nonparametric >> Related Samples (scan data option)
• In Objective tab: Customize Analysis
• Fields tab: Move the Pre and Post test over to Test Fields
Click here to continue >>
Wilcoxon Signed Rank Test cont’d
•
In the Settings tab: tick Wilcoxon matched-pairs signed rank (2
samples)
•
Click the Run button on the bottom
•
In the output, double-click the Window under Hypothesis Test
Summary
Click here to continue >>
Wilcoxon Signed Rank Test cont’d
•
The Model Viewer will open up and you will see this on the rightside
The write-up:
• Pre-test: Health problems before smoking
• Post-test: Health problems after starting smoking
• “A Wilcoxon Signed-ranks test indicated that using cigarettes
(M=1.9, SD=1.20) contributed to increase in health problems than
non-smokers (M=4.2, SD=1.99), Z = 55.00, p < .01.”
<< Click here to go Back to beginning
Independent Samples T-test
• In this analysis, you’re attempting to compare one IV
(e.g., Gender) with two independent levels (e.g.,
Female and Male) to a DV (Writing score).
In SPSS
•
Analyze >> Compare Means >> Independent Samples t-Test
•
•
Writing is the Testing Variable(s) – The DV
Grouping Variable is Gender with 1,2 – The IV
• You should get the following output:
Click here to continue >>
Independent Samples T-test cont’d
• First, look at Levene’s Test for Equality of Variances. If
it is non-significant, then you will need to report the ttest in the row of “Equal variances assumed”. If it is
significant, then you will need to report the t-test in
the row of “Equal variances not assumed”
• This example’s Levene’s test is non-significant, so we
assume equal variances
The write-up
• “An independent samples t-test was used. There was
a significant difference in the writing scores between
female (M=88.2, SD=4.81) and males (M=73.2,
SD=10.52), t(8)=2.90, p < .05.
<< Click here to go Back to beginning
Wilcoxon-Mann Whitney test
• This is similar to the independent samples t-test when
you have ordinal variables.
• For example, you could use the Mann-Whitney U test
to understand whether attitudes towards pay
discrimination, where attitudes are measured on an
ordinal scale, differ based on gender (i.e., your
dependent variable would be "attitudes towards pay
discrimination" and your independent variable would
be "gender", which has two groups: "male" and
"female").
In SPSS
•
Analyze >> Nonparametric Tests >> Independent Samples
• Objective tab: Customize analysis should be ticked
• Fields tab: Move your DV (AttitudePay) which is
attitude towards pay discrimination to the Test Fields:
and Gender to the Groups.
Click here to continue >>
Wilcoxon-Mann Whitney test cont’d
• Settings tab: Tick Customize Tests, then tick MannWhitney U (2 samples)
• Click Run
• Double-click on the table below in the Output window
to open up the Model Viewer
Click here to continue >>
Wilcoxon-Mann Whitney test cont’d
• In the Model Viewer’s right side, you should see this:
• Reporting: “A Mann-Whitney U test was used to test for
group differences in attitudes to pay rate discrimination.
Females’ level of attitude to pay discrimination (M=3.0,
SD=1.58) was not significantly different than males (M=2.6,
SD=1.52), U = 10.50, z = -.430.”
<< Click here to go Back to beginning
One-Way ANOVA
• A one-way analysis of variance (ANOVA) is used when
you have a categorical independent variable (with two
or more categories) and a normally distributed
interval dependent variable and you wish to test for
differences in the means of the dependent variable
broken down by the levels of the independent
variable.
• For example, if you wanted to test whether high
school, college, or Sunday soccer players differ in
training time
In SPSS
• Analyze >> Compare Means >> One-way ANOVA
• TrainingTime (DV) goes in the Dependent List and
Soccer (IV) goes into the Factor list.
• Click the Post-Hoc button and make sure Tukey is
selected. This will be important after the intial test.
• Press OK
Click here to continue >>
One-Way ANOVA cont’d
•
•
You will need to look at two boxes in the Output.
The first one is whether there are any differences in the
group:
•
If the first box is significant, then we can also report from
the second box:
•
Reporting for two boxes: “A one-way ANOVA was conducted
to compare the effect of Soccer Player Type on Training Time
in High School, College, and Sunday soccer players. There
was a significant effect of soccer player type on training
time, [F(2,7)=159.92, p<.001]. Post-hoc comparison using
the Tukey HSD test indicated that College soccer players had
significantly greater training times (M=19.5,SD=1.73) than
High School soccer players (M=7.33,SD=1.15) and Sunday
soccer players (M=1.00,SD=.00). It was also found that High
School soccer players had greater training times than Sunday
soccer players.”
<< Click here to go Back to beginning
Kruskal Wallis Test
• The Kruskal-Wallis H test (sometimes also called the
"one-way ANOVA on ranks") is a rank-based
nonparametric test that can be used to determine if
there are statistically significant differences between
two or more groups of an independent variable on a
continuous or ordinal dependent variable
• For example, your D.V. is Exam performance on a
continuous scale of 0-100 and I.V. is Work with three
independent groups (levels) of On-campus, Offcampus, and No Work groups.
In SPSS
• Analyze >> NonParametric >> Independent Samples
• Objective tab: Customize analysis
• Fields tab: TestScores (DV) in Test Fields, Work (IV) in
Groups
Click here to continue >>
Kruskal Wallis Test
• Settings tab: tick Kruskal-Wallis 1-Way ANOVA (k
samples)
• Click Run
• In the Output window, double-click this window to get
the Model Viewer to open up
Click here to continue >>
Kruskal Wallis Test
• In the model viewer, you should see this:
• Reporting: “A Kruskal Wallis H Test was conducted.
There were no statistically significant difference
between Worker types (H(2)=5.80, p = .06), with mean
rank of 7 for On-campus, 2 for Off-campus, and 7 for
No Work.”*
– * You can get the “Mean rank” by mousing over the groups in
the graph above.
<< Click here to go Back to beginning
Paired sample t-test
• The dependent t-test (called the paired-samples t-test
in SPSS) compares the means between two related
groups on the same continuous, dependent variable.
• For example, students entering an anxiety workshop
with pre-scores being anxiety levels before the
program and post-scores being anxiety levels
afterward (both measures on continuous scale of 0100).
In SPSS
• Analyze >> Compare Means >> Paired Sample t-Test
• PreAnxiety and PostAnxiety variables are entered as
one pair (Variable 1 and Variable 2)
• Click OK
Click here to continue >>
Paired sample t-test cont’d
• The output window:
• The write-up: “A paired-samples t-test was conducted
to test whether students entering an anxiety reducing
program had significantly less anxiety afterward. A
pre-test on anxiety level (M=61.0,SD=26.45) and posttest on anxiety level (M=30.3,SD=18.92) was recorded.
There was a significant difference between pre- and
post-test levels of anxiety, t(9)=9.36, p <.001.”
<< Click here to go Back to beginning