One-Way ANOVA Demonstration
One-Way ANOVA Demonstration
Program Transcript
MATT JONES: This week we're going to be introducing you to one-way ANOVA.
This is a comparisons-of-means test. Let's go to SPSS to see how we'll perform
this specific test. To perform the one-way ANOVA in SPSS, we start up at the
Analyze tab. If we click that, we get a dropdown menu.
Since one-way ANOVA over is a comparisons-of-means test, we can move our
cursor down to Compare Means, scroll across, and we see that one-way ANOVA
is down at the bottom. If we click on that, a dialog box is opened up, where we
have a Dependent List and a Factor. For one-way ANOVA, our dependent
variable needs to be a metric level variable. That is it's an interval or ratio level of
measurement. This is important because one one-way ANOVA compares means
across a factor.
The factor is our grouping variable. This needs to be a categorical variable.
Typically, one-way ANOVA is used with grouping variables that have three or
more levels or attributes to them. In this case, let's go ahead and test whether the
means of the socioeconomic status index differ across a respondent's highest
degree.
To begin with, well, we'll go ahead, and we'll put socioeconomic status index into
our Dependent List box. So you can see off to the left are choice of variables.
Socioeconomic Status is down towards the bottom of our Variable list. If I place
my cursor over it, we'll see it highlighted. You'll also note, again, a little scale
ruler off to the left, which indicates that this is an interval-ratio-level variable.
Once I click on that variable, it's highlighted. I can just simply click on the arrow
box, which moves that variable over into the Dependent List. Now I need to make
sure and enter my factor as well. I'll scroll up till I find Respondents Highest
Degree. I can see that it's right here. I can hover over this variable and then
highlight it.
Again, click on my arrow that places it into the Factor box. For basic omnibus
ANOVA test, we are finished. We can go ahead and click OK and examine our
output. This is the SPSS one-way ANOVA omnibus output. You can see here
Respondent Socioeconomic Index is our dependent variable.
SPSS provides us with information about between-groups and within-groups
variance. The between-groups variance is a squared deviations between the
groups. The within-groups variance, also known as unexplained variance, is the
variance within the sample. A ratio of the mean square of between groups to
within groups is how we obtain the F-value. The F statistic is a critical value that
determines the significance of our test.
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One-Way ANOVA Demonstration
Here we can see that the significance level is 0.000. This significance level is
well below the conventional threshold of 0.5. Therefore we can reject the null
hypothesis that there are no differences in socioeconomic status index across
respondents highest degree. To find out where possible differences lie, we have
to perform a post-hoc test.
To perform a post-hoc test, we once again go back up to our Analyze, Compare
Means, One-Way ANOVA. We can click on Post-Hocs, in here you'll see that
there are a variety of options provided for you. We have equal variances
assumed and equal variances not assumed. At this point, we don't know that
whether we have equality of variances, and this is something that we specifically
have to test for.
But as you're performing the one-way ANOVA test, you can choose an equal
variances assumed test, an equal variances not assumed test, and then on your
output, go to the appropriate test after examining the variances. So we can click
on a Bonferroni Test for equal variances and also Games-Howell for equal
variances not assumed. Click Continue.
If we click our Options box, this is how we determine whether we have
homogeneity of variances, or said another way, equality of variances. As you
know from your reading, this is an assumption of the one-way ANOVA test. If we
click on that and activate this test, going to hit Continue and then click OK. Right
away you'll see that we get quite a bit more output than we had before.
Our first piece of output is the test of homogeneity of variances, also known as a
Levene's test. This tests the null hypothesis of homogeneity of variances. Here, if
you look at the significance level, you'll see that we are at 0.000, which is well
below the threshold of 0.05. This means we reject our null hypothesis that
variances are equal. Therefore, we have to assume that the variances are not
equal in the one-way ANOVA.
As we noted before, the overall test, also sometimes referred to as the omnibus
test, is significant. Since the omnibus test is significant, we know that at least one
of the means differs from another. Therefore we need to examine our post-hoc
tests to determine which means differ. Again, moving with the assumption of
inequality of variances, we have to move down to our Games-Howell all Post-
Hoc test.
If you remember, we chose Bonferroni as a test for equality of variances, but
tested for the equality of variances and found they were not equal. The Games-
Howell test performs a pairwise comparison for all levels of our variable. Here
you'll see less than high schools compared to high school, less than high school
to junior college, less than high school to bachelor, less than high school to
graduate, and so forth, until all possible combinations are achieved.
©2016 Laureate Education, Inc.
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One-Way ANOVA Demonstration
The next column shows us our mean difference. We can see that on the
socioeconomic status index, our dependent variable, those with less than high
school have a mean score of 10.08 units lower than high school. If we move over
to our significance level, we see that, indeed, this pairwise comparison is
statistically significant a at the 0.05. Therefore there is a statistically significant
difference between those with less than high school and those with a high school
degree.
As we move down our output, we can examine all of these pairwise comparisons.
Again, less than high school to junior college, there is a difference of 17.38, and it
is statistically significant. If we move to a less than high school to bachelor's, we
can see that the difference increases. Again, it is statistically significant, and the
same is true for less than high school to graduate.
Moving through our output, we can go ahead and examine all of these pairwise
comparisons, move over to our significance column, and see that they are indeed
all statistically significant. You'll notice on the main difference that SPSS also
puts an asterisk next to each mean difference to highlight or flag those
differences that are statistically significant. We can conclude from our output and
our post-hoc tests that there is indeed a difference in socioeconomic status index
across respondents highest degree and that all pairwise comparisons are
statistically significant, concluding that the higher a respondent's degree, the
higher their socioeconomic status index on average.
And that concludes our SPSS demonstration on one-way ANOVA. As a couple of
parting thoughts, be sure and remember that your dependent variable in one-way
ANOVA needs to be a metric variable, that is an interval ratio level of
measurement. Your independent variable, or your factor, needs to be a
categorical variable. This is because one-way ANOVA of is a comparison-of-
means test.
Also, it's very important to test the assumption for homogeneity of variances, so
be sure and look at that Levene's test. If you have any further questions, be sure
and use your textbook. And also, your instructor is a very valuable resource.
©2016 Laureate Education, Inc.
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6210 Week 7 Discussion: How To Complete The Week 7 Discussion Requirement
Review the Week 7 Course Materials
Use the General Social Survey (GSS) dataset for this Discussion.
There is nothing special or mysterious about ANOVA. It is only a series of t-tests that SPSS runs
simultaneously to provide both speed and statistical power. For example, if you want to know if there is
a difference in the dependent ratio variable, Size of Place in 1000S, based on the independent nominal
variableRace of Respondent (with 3 levels, black, white, other), do the following:
Open the GSS data set, select Analyze, select One-way ANOVA, drag Size of Place into the Dependent
List box, drag Race of Respondent into the Factor box, select Post Hoc, select an appropriate Post Hoc
test from the Equal Variances Assumed box, click Continue, click OK.
Review the Sig. value in the Between Groups row in the SPSS Output under ANOVA and decide to reject
or fail to reject the null hypothesis.
If you reject the null and determine that the ANOVA is statistically significant, review the Multiple
Comparisons Output below the ANOVA Output.** This Output compares each level of the IV to every
other level of the IV and tells us if the comparison is statistically significant.
For example, the first 2 rows of the Multiple Comparisons Output
compares white to black and white to other and tells of if there is a statistically significant difference
in Size of Place between black and white and white and other. In this case, both comparisons are
statistically significant because the respective Sig. values are less than .05.
Since there are only 3 levels of the IV there are only 3 comparisons that we are interested in
reviewing, white/black, white/other, black/other. Note:black/white is the same
as white/black, white/other is the same as other/white and black/other is the same as other/black.
**Note: If you fail to reject the null and find that the ANOVA is not statistically significant, then there is
no need to review Multiple Comparisons… …so don’t.
For your discussion post, follow this outline and use each point as a header::
-Identify the dependent variable (DV) and its Level of Measurement (Hint: it must be interval or ratio)
-Identify the independent variable (IV) and its Level of Measurement (Hint: The IV must be nominal
and it must have 3 or more levels)
-Write a research question (RQ)** that can be addressed by a One-way ANOVA. Use this format:
Is there a difference in the DV based on the IV? For example:
Is there a difference in Size of Place in 1000s based on Race of Respondent?
**Note: a question is an interrogative sentence that ends with a question mark. Keep your RQ simple
and concise.
-Write the null hypothesis for your question. Use this format:
There is no difference in (insert DV) based on (insert IV).
-State the research design that aligns with the RQ.
-State the means test used to address the RQ. You have only 1 choice here: One-way ANOVA.
-Decide if the ANOVA is statistically significant and decide to reject or fail to reject the null hypothesis
based on the significance finding.
-If the ANOVA is significant, calculate the effect size.** For a One-way ANOVA effect size is measured
by = eta-squared. Calculate eta-squared this way:
Go to the ANOVA Output.
Go to the Between Groups row and select the value in the Sum of Squares column.
Go to the Total row and select the value in the Sum of Squares column.
Divide the Between Groups Sum of Squares by the Total Sum of Squares. The result of this division is
eta-squared and it must have a value between 0 and 1.
Explain the meaning of effect size.
Decide if the effect is small, medium, or large.
If the ANOVA is not significant the effect size is meaningless… …so don’t calculate it… …just don’t.
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