### SPSS-3-T-tests-and

```SPSS Session 3:
Finding Differences Between Groups
Learning Objectives
• Review Lectures from 8 and 9
• Understand how to test for differences
between two or more groups
• Describe the relationship between variability
and standard deviation of means
• Be able to conduct t-tests and ANOVAs within
SPSS
• From the statistical output, be able to discuss
results of analyses using t-tests and ANOVAs
Review of Lecture 8
• Defined and discussed the theory and rules of
probability
• Calculated probability and created a
probability distribution with example data
• Described the characteristics of a normal
curve and interpreted a normal curve using
example data
Review from Lecture 9
• Defined research hypothesis, null hypothesis and
statistically significance
• Discussed the basic requirements for testing the
difference between two means
• Defined and described the difference between
the alpha value and P value, and Type I and Type
II errors
• Calculated the difference between the means (tratio) using example data through advanced
study
Testing for Differences between Groups
• Often times in social work research, we wish
to know if the differences between two
groups is significant.
• No two groups of people are alike, but are
their dissimilarities important?
• That is to say, are the differences significant or
did these differences likely happen by chance?
– Think about comparing p-value to α.
Testing for Differences between Groups
• Testing for differences between groups of
people on some score or measure is reliant on:
– The average scores for each group on that measure
(mean scores)
– The variability of each group’s scores on that
measure (standard deviation scores)
• Mean and standard deviation scores are very
important when comparing groups
Standard Deviation Scores
• Standard Deviation (SD) is an important piece of
statistical information
• Stand Deviation scores indicate the extent to
which the data cluster around the mean of a
distribution.
• It is the most common score of “data dispersion”
and variability in a particular variable.
• It is often reported in studies with the mean:
– Example, “children in the study were 7.69 years of age
on average (SD=4.85)”.
Deviation Scores
• Deviation is the amount that an individual score
is different from the mean score for that variable.
• Recall that the children in the study were on
average (mean) 7.69 years of age.
• Deviation scores for specific cases then would be:
– A child that is 10 years old would deviate from the
mean by 2.31 years (10 - 7.69 =2.31)
– A child that is 3 years old would deviate from the
mean by -4.69 years (3 - 7.69 = -4.69)
Standard Deviation Scores
• Standard Deviation scores (SD) are the square
root of sum of all squared deviation scores for
all individuals and divided by the total number
of individuals minus one.
 (value m ean)
N 1
2
Standard Deviation Scores and Variability
• Standard Deviation Scores (SD) are important as
they give information about how closely the
values in a distribution cluster around the mean.
• Essentially, this is how much scores in a variable
actually vary!
• The next three slides demonstrate the variability.
• Watch for the Standard Deviation Scores and
changes in the histograms.
Histogram with Large SD scores
• Mean = 50
• SD = 30
Histogram with Medium SD scores
• Mean = 50
• SD = 14
Histogram with SD scores of 0
• Mean = 50
• SD = 0 (no variability)
Group Differences in Child Protection
• In our child protection study, we wanted to for
differences between two groups of parents.
• All parents completed the General Health
Questionnaire, and were categorized as having
clinically scores or not.
• Clinically elevated scores are those where the
parents likely are experiencing severe
psychiatric stress.
Group Differences in Child Protection
• We hypothesized that there would be significant
differences between these two groups of parents
on their mean scores on the Family Environment
Scale (FES) and the Strengths and Difficulty
Questionnaire (SDQ).
• The FES concerns three aspects of their social
environment in their home: Family Cohesion,
Family Expressiveness, and Family Conflict.
• The SDQ total score concerns the parents’ views
of the behaviour and social problems
experienced by their child.
Testing for Differences between Groups
• In order to test for differences between two
groups based on their mean scores on a measure,
we use a statistical test called a t-test.
• t-tests use one nominal independent variable (IV)
and one interval/ratio dependent variable (DV)
• In this case:
– GHQ groups (IV): Clinically elevated scores and not
clinically elevated groups (one variable with two
groups)
– FES and SDQ scores (DV): interval/ratio level variables
T-tests Hypotheses
• We hypothesized (research hypothesis) that there
would be significant differences between these two
groups of parents on their mean scores on the Family
Environment Scale (FES) and the Strengths and
Difficulty Questionnaire (SDQ).
• Parents reporting greater stress would also have higher
FES and SDQ scores.
• Our null hypothesis states that there are no significant
differences between these two groups of parents
based on their mean scores on the FES and SDQ
measures.
• We have the data, so time to test!
T-tests Analysis Demonstrated in SPSS
• When conducting a t-test, use the “Analyze”
menu and select “Compare Means”.
• In this case, we select “Independent Samples
t-test” as the parents either have clinically
elevated GHQ scores or they do not.
• Firstly, we identify our DV called here as our
“Test Variable(s)”.
• Find “SDQ_TotalDif” in the list on the left and
select it for the “Test Variable(s)”.
• Next, we identify our IV and the particular
groups of interest.
• Select “GHQ_Cutoff_4” from the list on the left
and select this variable for the “Grouping
Variable”. GHQ scores use a clinical cutoff score
of 4 or more, hence the variable name.
• Now that the IV variable is identified, we have
to tell SPSS which two groups we are using in
the analysis.
• This variable is coded as the following:
– 0 = "Subclinical score, 3 or less"
– 1 = "Clinically elevated score, 4 or more"
• Knowing the coding for each group, select
“Define Groups…”
• Specify the two groups as:
– Group 1: 0
– Group 2: 1
• Click “Continue”
Identify the values for
each group in the
variable based on how
the variable is coded.
After clicking “Continue”,
the “Grouping Variable”
shows the grouping
numbers. Now click “OK”.
T-tests Analysis Results in SPSS
• Now we see the results of the test between the
two parent groups on the SDQ measure.
• The first table give the mean and standard
deviations scores on the SDQ measure for group
of parents with clinically elevated GHQ scores
(42 people) and those without the elevated
scores (53 people).
T-tests Analysis Results in SPSS
• The mean SDQ scores for each group do not
appear significantly different.
• The group with the elevated GHQ scores had a
mean SDQ score of 20.38 (SD=6.868).
• The group of parents without an elevated GHQ
score actually had lower mean SDQ scores of
20.94 (SD=7.202).
• We had hypothesized that parents with elevated
GHQ scores would also rate their children as
having more total difficulties as rated by the SDQ
(research hypothesis).
T-tests Analysis Results in SPSS
• To see if these results likely occurred by
chance, or if there is a statistically significant
difference between these two groups of
parents, we look to the next table for the
results of the t-test.
• From the table below, we see the t-test score of
t=.386 and a p-value of .701 shown here as “Sig.
(2-tailed)” with 93 degrees of freedom (“df”).
• Because the p-value of .701 is greater than our α
= .05 level of significance, we say that we failed to
reject our null hypothesis.
• These results likely happened by chance, and we
cannot confirm our research hypothesis.
T-tests Analysis Results in SPSS
• Our null hypothesis stated that there were no
statistically significant differences between these
two groups of parents based on their SDQ means
scores. From our data, this appears to be the case.
• SDQ scores were not significantly different (t=.386,
df=93, p>.05) between parents with clinically
elevated GHQ scores (mean SDQ scores of 20.38,
SD=6.868) and those parents without clinically
elevated GHQ scores (mean SDQ scores of 20.94,
SD=7.202).
• Parents with increased levels of stress did not rate
their children has having greater behavioural and
social problems when compared to the parents
reporting lower levels of stress.
T-tests Analysis in SPSS: Second Example
• For a second example, we wanted to know if these
same two groups of parents differed in terms of their
family environment.
• We used the Conflict subscale of the Family
Environment Scale as a measure of their family social
environment.
• Our research hypothesis is that the group of parents
with clinically elevated GHQ scores would have
significantly higher FES-Conflict scores when compared
to the group of parents without clinically elevated
scores.
• Our null hypothesis stated that there is no difference
between these groups of parents based on their FESConflict scores.
T-tests Analysis in SPSS: Second Example
• To test this second research hypothesis, we
again select the “Analyze” menu and select
“Compare Means”.
• Again, we use “Independent Samples t-test”
to test for differences between to
independent groups of parents.
T-tests Analysis in SPSS: Second Example
• From the window for “Independent-Samples T
Test”, the previous analysis is shown.
• Because we are interested in testing the new DV
of FES-Conflict scores, we remove
“SDQ_TotalDif” from the list and replace it with
“FES_Conflict” from the list on the right.
• The “Grouping Variable” is still set from the
previous analysis and does not need changing.
• As the analysis is set, we click “OK” for the
results.
T-tests Results in SPSS: Second Example
• From the results in the output window, we see the first
table with the mean and standard deviation scores for
each group.
• We see that the mean FES-Conflict scores for the clinically
elevated group (mean=5.19, SD=2.32) appears to be
higher than the group of parents without clinically
elevated scores (mean=3.87, SD=2.72).
• To find if this difference is statistically significant, we look
to the next table in the output.
• From the table below, we see the t-test score of t=2.511 and a p-value of .014 shown here as “Sig. (2tailed)” with 93 degrees of freedom (“df”).
• Because the p-value of .014 is less than our α = .05
level of significance, we say that succeeded in
rejecting our null hypothesis.
• These results were unlikely to have happened by
chance, and we accept our research hypothesis.
• Our null hypothesis stated that there were no statistically
significant differences between these two groups of
parents based on their FES-Conflict means scores. From
our data, this appears not to be the case.
• FES-Conflict scores were significantly different (t=-2.511,
df=93, p<.05) between parents with clinically elevated
GHQ scores (mean FES-Conflict scores of 5.19, SD=2.32)
and those parents without clinically elevated GHQ scores
(mean FES-Conflict scores of 3.87, SD=2.72).
T-tests Results in SPSS: Second Example
• From the results of this second t-test, we can
conclude that parents with clinically elevated
GHQ scores reported significantly greater
amounts of social conflict in their family
environments.
Analysis of Variance (ANOVA):
Testing for Differences between
Three or More Groups
Analysis of Variance (ANOVA)
• Where T-tests look for differences between
only two groups, Analysis of Variance (ANOVA)
tests for similar differences between three or
more groups.
• The independent variable is a nominal or
ordinal variable with three or more categories
• The dependent variable is a interval/ratio
variable
Analysis of Variance (ANOVA)
• The null hypothesis for an ANOVA test is that
the mean score for each group on a particular
measure will not significant differ from any
other group.
• The research hypothesis is usually that some
group will be significant different from
another group.
• The ANOVA test produces a statistical score
called a “F-value” through a “F test”.
Analysis of Variance (ANOVA)
• The logic behind the ANOVA test is that the
differences within a group of people is less so
than those differences between the three or
more groups.
• ANOVA tests become a comparison of between
group differences and within group differences.
• Hence, it is an ANALYSIS of VARIANCE between
groups compared to VARIANCE within each
group.
• T-tests are actually a mathematically simplified
version of an ANOVA because it only needs to
compare two groups!
The Two Parts of ANOVA
First Step
• ANOVA tests are conducted
in two parts.
• The first step is to test
whether any group is
significantly different from
any other group.
• This first step uses a F-test
and is called an “omnibus”
test meaning an “over all”
test.
Second Step
• If the F-test is significant
(p<.05), it means that there
is one group significantly
different from another.
• The second part of an
ANOVA is to which group(s)
are different.
• This is called a “post hoc”
test meaning “after that”
• Post Hoc tests can be
conducted many different
ways.
ANOVA Examples in Child Protection
• For our child protection study, we wanted to test for
differences between three groups of parents based
on two different measures.
• Using the Previous Involvement variable, we have all
of the cases categorized in one of the following ways:
– Cases with a history of occasional child protection
involvement
– Cases with a long standing history of child protection
involvement
– Cases with no history of child protection involvement
ANOVA Examples in Child Protection
• Based on these three groups of parents and cases, we wanted
to test for differences between them on two measures:
1. Family Environment Scale – Family Cohesion
– We would expect that families with long standing or occasional
involvement would have less family cohesion than families with no
prior involvement with child protection services.
2. General Health Questionnaire – Total Score
– We would expect that families with long standing or occasional
involvement would have higher levels of psychological distress
compared to families with no prior involvement with child
protection services.
• The null hypothesis for each test is that there are no
differences between the three groups of cases based on any
measure or score.
ANOVA Example: 1. Family Cohesion
• Testing for differences between these three
groups of cases based on the FES – Cohesion
scores.
• We need to find “Compare Means” under the
“Analyze” menu.
• Under “Compare Means”, select “One-Way
ANOVA”
ANOVA Example: 1. Family Cohesion
• Once “One-Way ANOVA” is selected a new
window for ANOVA will appear
ANOVA Example: 1. Family Cohesion
• First, we need to add the Dependent Variable
which is the FES – Cohesion scores to the
“Dependent List”.
• Find this variable on the list on the left and add it
to this list.
ANOVA Example: 1. Family Cohesion
• Now we need to add the Independent Variable to
the “Factor” list.
• The Independent Variable is the groups of cases
called “Previous_Involvement”
ANOVA Example: 1. Family Cohesion
• This ANOVA test will now search for differences
between the three groups, but it will not yet test
for where exactly the differences exist.
• This is the “omnibus test” portion.
• We need to ask the ANOVA test also to conduct
the “post hoc” test to find which group or groups
are significantly different from other groups.
• We do this by selecting a post hoc test from the
“Post Hoc” option on the right.
ANOVA Example: 1. Family Cohesion
• After selecting the “Post Hoc” button, a new
menu will appear.
• This lists all of the options for any number of
post hoc tests.
• One of the most common post hoc tests is
called the “Tukey” post hoc test.
• Select this test and press “Continue”
ANOVA Example: 1. Family Cohesion
ANOVA Example: 1. Family Cohesion
• In the “Options” menu, a few more valuable
pieces of the analysis need to be added to our
ANOVA.
• The three most common are the following:
– “Descriptive”: provides the mean and standard
deviation scores for each group in the analysis
– “Homogeneity of variance test”: tests a major
assumption of ANOVA
– “Means plot”: provides a chart of each groups mean
and gives a good visual of the results
• Click “Continue” and then “OK”
ANOVA Example: 1. Family Cohesion
ANOVA Example: 1. Family Cohesion
• Results!
• The first table provides the descriptive statistics
for each “previous involvement” group based on
the “FES – Cohesion” measure.
• Importantly, this table also provides the overall
descriptive statistics for the “FES – Cohesion”
measure.
ANOVA Example: 1. Family Cohesion
• We can see that each “previous involvement” group
has different scores on the FES – Cohesion measure.
• Question: Are these differences statistically significant
(p<.05) or did they happen by chance (p>.05) ?
ANOVA Example: 1. Family Cohesion
• The “ANOVA” table gives the results of the F-test.
• The F-test is a comparison of variation in each
group compared to the variation between
groups.
• If the variation between groups is comparatively
greater then the variation within the groups,
then this test is more likely to be statistically
significant.
ANOVA Example: 1. Family Cohesion
• The ANOVA table does give a statistically
significant result.
• The “Sig.” value is our p-value for this test, and is
well below our significant level standard of α=.05.
• We reject the null hypothesis.
ANOVA Example: 1. Family Cohesion
• We now know that significant differences exist
between at least one group based on the FESCohesion scores, and that this difference was
unlikely to have been due to chance.
• The problem is that we don’t yet know which group
or groups were significantly different!
• Solution: This is why we need a second part which is
the “Post Hoc – Tukey” test to show us exact which
significant between group differences exist.
ANOVA Example: 1. Family Cohesion
• The “Multiple Comparisons” table starts to give
us a picture of which groups are different.
ANOVA Example: 1. Family Cohesion
• This table shows you each group compared to
every other group, and it provides a further test
to show you if these two groups significantly
differ.
ANOVA Example: 1. Family Cohesion
• Another table, labeled “Tukey HSD” gives you
subsets of groups.
• If the groups have similar scores on the FES –
Cohesion measure, they will appear on the same
subset column.
• Groups that are significantly different will appear
in different columns.
ANOVA Example: 1. Family Cohesion
• The “Tukey HSD” table from this analysis
indicates that each group significantly differs
because each sits in a separate column.
ANOVA Example: 1. Family Cohesion
The chart at the end of
the results gives us a
good visualization of the
mean FES – Cohesion
scores for each “previous
involvement” group.
ANOVA Conclusion: 1. Family Cohesion
• From this analysis, we can say that each “previous
involvement” group had significantly different FES – Cohesion
scores (F=33.96, df= 2, 92, p<.05). We rejected our null
hypothesis.
• Those families with long standing involvement in child
protection services had significantly lower FES scores (mean =
2.23, SD = 1.64) than both the families with occasional
involvement (mean = 5.10, SD = 2.21) and families with no
prior involvement (mean = 7.19, SD = 2.02). Families with
occasional involvement also had significantly different FES –
Cohesion scores then the families with no prior involvement.
• We can say that families with greater previous involvement in
child protection services reported that their families were less
cohesive. This is an important finding concerning the family
environment for these parents and children receiving services.
ANOVA Example:
2. General Health Questionnaire (GHQ)
• Our finding about those families with varying degrees of
previous child protection involvement raised further
questions.
• We wanted to know if these same families, grouped by
their degree of previous child protection involvement, also
reported significantly different General Health
Questionnaire scores (GHQ), which is a measure of
psychological distress.
• We would expect that families with greater degrees of
previous involvement would have significantly higher GHQ
mean scores (research hypothesis).
• Our null hypothesis for this analysis would again state that
no significant differences between these groups exist
based on their GHQ mean scores.
ANOVA Example: 2. GHQ scores
• To complete this analysis, we return to the
“Analyze” menu, select “Compare Means”, and
then “One-Way ANOVA”
ANOVA Example: 2. GHQ scores
• Replace “FES_Cohesion” with “GHQ_TotalScore”
ANOVA Example: 2. GHQ scores
• On “Post Hoc” menu, leave “Tukey” selected.
ANOVA Example: 2. GHQ scores
• Under the “Options” button, leave these
options selected.
• Press “Continue” and then “OK” to conduct
analysis
ANOVA Results: 2. GHQ scores
• The first table is the descriptive statistics for each previous
involvement group and their GHQ scores.
• The group without previous involvement appears to have
a much lower mean than the other two groups. The other
two groups do not appear significantly different.
• The question remains if the differences between the
groups is significantly different.
ANOVA Results: 2. GHQ scores
• From the “ANOVA” table, we can see that the pvalue listed under “Sig.” is well above our
significance level of α=.05.
• In this case, we failed to reject our null
hypothesis.
ANOVA Results: 2. GHQ scores
• From the post hoc analysis, the Tukey test shows
all families existing in the same subset.
ANOVA Results: 2. GHQ scores
• Here is the chart showing the means. While
there appears to be a significant visual
difference, our statistical test indicates that these
differences were likely to happen by chance.
ANOVA Results: 2. GHQ scores
• GHQ scores do not significantly differ between
groups of families separated by their previous
involvement with child protection services (F=.516,
df=2,92, p>.05).
• We failed to reject our null hypothesis. These
differences likely happened by chance and not due
to a real difference between these groups of families
based on their GHQ scores.
• Parent and carer psychological distress, while high,
appears not to be associated with previous
involvement in child protection services. Perhaps
families currently involved with services all
experience high levels of distress regardless of the
degree of prior involvement.
```