Advanced Statistics
One-way ANOVA
Slide #
Discussion
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Good day everyone. This lecture video will focus on one of the comparative
inferential statistics which is the one-way ANOVA or one-way analysis of variance.
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Before we start, bear in mind the following:
1. Do not capture or record any portion of the lecture video.
2. Do not upload any portion of the lecture video in Facebook, messenger,
YouTube, and other media platforms
3. This lecture video is intended only for the consumption of my students.
4. Do not share the link to other students and teachers.
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In this diagram, it indicates that we used One-way ANOVA when comparing
multiple groups for a single variable.
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One-Way ANOVA ("analysis of variance") compares the means of two or more
independent groups in order to determine whether there is statistical evidence that
the associated population means are significantly different. One-Way ANOVA is a
parametric test. Yes, we can also use ANOVA for 2 groups just like in independent
sample t test. But I suggest if you have 2 groups only, you better use independent
sample t test and use ANOVA for 3 or more groups.
F-test is another name for ANOVA.
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The One-Way ANOVA is commonly used to test the following:
 Statistical differences among the means of two or more groups
 Statistical differences among the means of two or more interventions
 Statistical differences among the means of two or more change scores
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Take note that when the normality, homogeneity of variances, or outliers
assumptions for One-Way ANOVA are not met, you may want to run the
nonparametric Kruskal-Wallis test instead.
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This is a published research titled: mathematics college readiness of grade 12
students: basis for instructional enhancement. This study used one-way ANOVA for
objective number 2, particularly in comparing the mathematics college readiness of
the students when grouped according to learning strand with four categories which
are ABM, STEM, HUMSS and GAS. One-way ANOVA was also used to determine
if significant difference exists when grouped according to career track with four
categories such as Academic, Arts and Design, Sports, and TVL. One-way ANOVA
is appropriate for this problem since it involves single variable which is the
mathematics college readiness of the students measured through test scores and 3 or
more groups are involve, specifically 4 groups for learning strand and 4 groups for
career track.
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This is the result of the study. By now, you should know how to interpret computed
p-value since this was already discussed. It shows that there is a significant
difference on the mathematics college readiness of the students when grouped
according to learning strand and academic track. For learning strand, the ABM and
STEM students are significantly more ready compared to GAS and HUMSS strands
as revealed by the posthoc test conducted. Posthoc test will be explained on the next
slides.
Also, academic track students are significantly more college ready than those
students in the art and design, sports and TVL track as revealed by posthoc test. It
could be seen in the second paragraph of the textual interpretation that the findings
could be clinched to the strong academic preparation, sufficient mathematics subject
offerings, and greater instructional exposure of students to math ensure college
readiness for math. This is because STEM and ABM students have more math
subjects compared to other strands and tracks. Again, findings of a study could be
more meaningful if interpreted properly and supported by related studies and
literature.
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This is another published research where one-way ANOVA is used in answering
one of its research problems. The study is titled epistemological beliefs, academic
performance, and teaching competence of pre service teachers by dr. Rudolf
Vecaldo.
Looking into his data analysis, it is indicated that the researcher used one-way
ANOVA in comparing the epistemological beliefs, academic performance and
teaching competence when grouped according to specialization and ethnicity. In his
study, these profile of the respondents has 10 categories for specialization and 6
categories for ethnicity.
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This table shows that there is a significant difference on the students’
epistemological beliefs when grouped according to specialization since the p-value
is less than the significance level.
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This table shows that there is a significant difference on the students’ academic
performance when grouped according to specialization since the p-value is less than
the significance level.
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On the other hand, this table shows that there is no significant difference on the
students’ teaching competence when grouped according to specialization since the
p-value is greater than the significance level.
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When grouped according to ethnicity, there is no significant difference on the
students’ epistemological beliefs since the p-value is greater than the significance
level.
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Same with academic performance, there is no significant difference on the students’
academic performance when grouped according to ethnicity, since the p-value is
greater than the significance level.
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Also with teaching competence, there is no significant difference on the students’
teaching competence when grouped according to ethnicity, since the p-value is
greater than the significance level.
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These are some other examples of research problem in one-way ANOVA. Let us try
to qualify if one-way ANOVA is appropriate in each research problem.
1. Number 1 example is related to medicine, Does a drug work? Does the
average life expectancy significantly differ between the three groups that
received the drug versus the established product versus the control? There
are 3 groups involved in this problem as indicated and the single variable
here is average life expectancy. Thus, one-way ANOVA is appropriate since
we compare 3 groups for a single variable.
2. Number 2 example is related to sociology, Are rich people happier? Do
different income classes report a significantly different satisfaction with life?
In this problem we could use the social classes for the categories of income
classes report such as upper class, upper middle class, lower middle class,
working class and poor, so we are dealing with 5 groups. The single variable
here is the satisfaction of the respondents to life, this should be measured
using a numerical data. Then, one-way ANOVA is appropriate since we
compare the respondents’ satisfaction to life when grouped according to
income classes or social status with 5 categories.
3. Number 3 example is related to management studies, What makes a
company more profitable? A one, three or five-year strategy cycle? This
problem has 3 groups being compared – the one-year strategy cycle, threeyear strategy cycle, and five-year strategy cycle. The single variable here is
the company’s profit. Hence, one-way ANOVA is appropriate to use since
we would like to compare the company’s profit when grouped according to
their strategy cycle with 3 categories such as the one-year strategy cycle,
three-year strategy cycle, and five-year strategy cycle.
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These are other examples to better understand when to use one-way ANOVA.
1. Is there a significant difference in the achievement test scores of grade 10
students when grouped according to their parents’ highest educational
attainment (elementary graduate, secondary graduate, college graduate)?
There are three groups involved here, students whose parents are elementary
graduate, secondary graduate, and college graduate. The single variable here
is the achievement test scores of the students. Thus, one-way ANOVA is
appropriate to use since we compare 3 groups in a single variable which is
the achievement test score.
2. Is there a significant difference on the enrolees’ CSU CAT scores when
grouped according to the desired course in college (CTED, CHM, CBEA,
CAHS)? There are 4 groups involved here, students’ desired course in
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college which are CTED, CHM, CBEA, and CAHS. The single variable
involve is the enrolees’ CSU CAT scores. Thus, one-way ANOVA is
appropriate to use.
3. Is there a significant difference on the students’ satisfaction to the service of
Registrar when grouped according to year level (first year, second year, third
year, fourth year)? This research problem involves 4 groups, students’ year
level which are first year, second year, third year, and fourth year. The single
variable is the students’ satisfaction to the service of registrar which should
be measured through numerical data. Then, one-way ANOVA is appropriate
since we compare 4 groups in a single variable.
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Now, I will teach you how to interpret SPSS output of one-way ANOVA. SPSS is a
software used in treating data. SPSS stands for Software Package for the Social
Sciences. I personally used this software in treating because of its accuracy and it is
user friendly.
However, since this software is not installed in your personal computer, I will just
teach you how to interpret and locate the important data needed in the tables since
when using SPSS, there are lot of tables being presented and it is important to
determine only the essential data.
Also, you apply the steps in hypothesis testing once you learn to locate the
necessary data such as p values, degrees of freedom, computed value, mean,
standard deviation and other necessary data. But before we start let us have a quick
review on what one-way ANOVA is.
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One-way ANOVA is a generalized version of the independent samples t-test:
it examines differences among three or more groups on a
quantitative/numerical (numerical/interval/ratio) variable.
After ANOVA is conducted, one must determine which groups differ
significantly using post-hoc or multiple comparisons tests.
You have to select a test of homogeneity of variance to examine equal
variances.
You have then to choose a post-hoc based on whether equal variances are
assumed (Scheffe), and one based on whether equal variances are not
assumed (Games-Howell).
Based on results of test of homogeneity of variance, you will select the more
suitable posthoc test, if a significant ANOVA result is found.
Post-hoc tests allow you to determine where significant differences lie.
When the ANOVA is found to be significant, one must examine which two
groups differ significantly from the total number of groups: so post-hoc tests
look at mean differences between different pairs: e.g. given three groups:
BSED, BEED, BTVTED, you will examine differences such as BSED
versus BEED, BSED versus BTVTED, and BEED versus BTVTED.
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There are many post-hoc tests to choose from when doing an ANOVA.
Post-hoc tests are done based on whether equal variances are assumed, or
not. This assumption is also for ANOVA (like the t-test).
The Scheffe post-hoc test should be selected when equal variances assumed
but the GamesHowell post-hoc test should be selected if not.
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Let us take this example (read the research question).
The null hypothesis for this research problem is: There is no significant difference
on the tourists’ overall satisfaction with the destination when grouped according to
age.
(Read the second to fifth bullet)
In this case, we have 4 categories or groups for age, 18-25, 26-40, 41-60, and over
60.
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Read the slide
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Read the slide
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This is how it looks for the table where you can see the p-value, degree of freedom
and F value, it is not included in my reference but I included it here because this is
the most essential table for ANOVA. The p-value here is in SIG which is 0.001.
This means that there is a significant difference on the tourists’ overall satisfaction
with the destination when group according to age.
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Read the slide
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These are the things you need to present on your table when reporting the results of
independent sample t test
(Read the bullet)
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This is sample write up for our research problem
(Read the slide)
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I strongly recommended that you watch the following video so that you know how
how to run data in SPSS when dealing with one-way ANOVA. The links will also
be posted in our FB group.
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Thank you for listening my dear students and that ends my lecture for one-way
ANOVA. I hope you can now distinguish when to use one-way ANOVA given a
research problem. Keep safe my dear students.
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