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A statistical method for making
simultaneous comparisons between three or
If we are only comparing two means,
ANOVA will produce the same results as
the t test for independent & dependent
The t-test can only be used to test differences
between two means.When there are more than two
means, it is possible to compare each mean with
each other mean using many t-tests.
But conducting such multiple t-tests can lead to
severe complications and in such circumstances
we use ANOVA.Thus, this technique is used
whenever an alternative procedure is needed for
testing hypotheses concerning means when there
are several populations.
When you choose to analyses your data using a
one-way ANOVA, part of the process involves
checking to make sure that the data you want to
analyses can actually be analyses using a one-way
You need to do this because it is only appropriate
to use a one-way ANOVA if your data "passes“
following assumptions that are required for a one
way ANOVA to give you a valid result.
Dependent variable should be measured at the interval
or ratio level.
Independent variable should consist of two or more
categorical, independent groups.
Should have independence of observations.
There should be no significant outliers.
Dependent variable should be approximately normally
There needs to be homogeneity of variances.
One of the principle advantages of this
technique is that the number of
observations need not be the same in each
Additionally, layout of the design and
statistical analysis is simple.
A manager wants to raise the productivity at his company by
increasing the speed at which his employees can use a
particular spreadsheet program. As he does not have the skills
in-house, he employs an external agency which provides
training in this spreadsheet program.
They offer 3 courses: a beginner, intermediate and advanced course.
He is unsure which course is needed for the type of work they do at
his company, so he sends 10 employees on the beginner course, 10
on the intermediate and 10 on the advanced course.
When they all return from the training, he gives them a problem to
solve using the spreadsheet program, and times how long it takes
them to complete the problem. He then compares the three courses
(beginner,intermediate, advanced) to see if there are any
differences in the average time it took to complete the problem.
SPSS generates following quite a few
tables in its one-way ANOVA analysis.
Multiple Comparisons Table
The descriptives table (see below) provides some very useful
descriptive statistics, including the mean, standard deviation and
95% confidence intervals for the dependent variable (Time) for each
separate group (Beginners, Intermediate and Advanced), as well as
when all groups are combined (Total).These figures are useful when
you need to describe your data.
This is the table that shows the output of the ANOVA analysis and
whether we have a statistically significant difference between our
group means.We can see that the significance level is 0.007 (p =
.007), which is below 0.05. and, therefore, there is a statistically
significant difference in the mean length of time to complete the
spreadsheet problem between the different courses taken.This is
great to know, but we do not know which of the specific groups
differed. Luckily, we can find this out in the Multiple Comparisons
Table which contains the results of post-hoc tests.
From the results so far, we know that there are significant differences between the groups
as a whole.The table below, Multiple Comparisons, shows which groups differed from
each other.The Tukey post-hoc test is generally the preferred test for conducting post-
hoc tests on a one-way ANOVA, but there are many others.We can see from the table
below that there is a significant difference in time to complete the problem between the
group that took the beginner course and the intermediate course (p = 0.021), as well as
between the beginner course and advanced course (p = 0.011). However, there were no
differences between the groups that took the intermediate and advanced course (p =
There was a statistically significant difference between
groups as determined by one-way ANOVA
(F(2,27) = 6.087, p = .007).
A Tukey post hoc test revealed that the time to
complete the problem was statistically significantly
lower after taking the intermediate
(23.0 ± 2.8 min, p = .021) and advanced
(22.6 ± 3.8 min, p = .011) course compared to the beginners
course (27.2 ± 3.0 min).
There were no statistically significant differences between the
intermediate and advanced groups (p = .960).