RUNNING HEAD: ONE WAY ANOVA 1 ONE WAY ANOVA 8 One-Way ANOVA Stacy Hernandez PSY7620 Dr. Lorie Fernandez Capella University Data Analysis and Application (DAA) The one way ANOVA is used to determine whether there are any significant differences between the means of two or more independent groups. In this sample, the file grades.sav is used with section (independent variable) and quiz3 (dependent variable). Data File Description 1. The one way ANOVA is used to determine whether there are any significant differences between the means of two or more independent groups. 2. In this sample, the file grades.sav is used with section (independent variable) and quiz3 (dependent variable). 3. The sample size (N) is 105. Testing Assumptions The dependent variable, quiz3, is measured at the interval or ratio level (meaning continuous). The dependent variable (quiz3) in this case, is therefore continuous since it ranges from one to 10. The independent variable (section) should consist of two or more categorical independent groups. In this case, the independent variable (section), has three groups, therefore it meets this assumption. There should be independence of observation, meaning that there is no relationship between the observations in each group or between the groups themselves. There should be no significant outliers, although there are single data points within the data that do not follow a normal pattern. Therefore, the outliers found will a negative effect on the one-way ANOVA, reducing the validity of the results. Note the above boxplot indicates outliers in section two, with the id of 21. The dependent variable (quiz3) should approximately have a normal distribution for each category of the independent variable (section). The null hypothesis is that the data is of a normal distribution, that the mean (average value of the dependent variable) is the same for all groups. Ho – the observed distribution fits the normal distribution. The alternative hypothesis is that the data does not have a normal distribution; the average is not the same for all groups. Ha – the observed distribution does not fit the normal distribution. It is observed that the data is not normally distributed. Most sections have quiz3 values between five and nine note this is a visual estimate. Note that the largest group also has the largest value of quiz3. The statistics from the histogram of quiz3 reveal that the Mean is 8.05; the Standard Deviation is 2.322, with a total number N of 105. Descriptive Statistics N Minimum Maximum Mean Std. Deviation Skewness Kurtosis Statistic Statistic Statistic Statistic Statistic Statistic Std. Error Statistic Std. Error quiz3 105 0 10 8.05 2.322 -1.177 .236 .805 .467 section 105 1 3 2.00 .797 .000 .236 -1.419 .467 Valid N 105 When looking at skewness, for a perfectly normal and symmetrical distribution, it has a value of zero (Warner, 20 ...

1. RUNNING HEAD: ONE WAY ANOVA 1
ONE WAY ANOVA
8
One-Way ANOVA
Stacy Hernandez
PSY7620
Dr. Lorie Fernandez
Capella University
Data Analysis and Application (DAA)
The one way ANOVA is used to determine whether there are
any significant differences between the means of two or more
independent groups. In this sample, the file grades.sav is used
with section (independent variable) and quiz3 (dependent
variable).
Data File Description
1. The one way ANOVA is used to determine whether there are
any significant differences between the means of two or more
independent groups.
2. In this sample, the file grades.sav is used with section
(independent variable) and quiz3 (dependent variable).
3. The sample size (N) is 105.
Testing Assumptions

2. The dependent variable, quiz3, is measured at the interval or
ratio level (meaning continuous). The dependent variable
(quiz3) in this case, is therefore continuous since it ranges from
one to 10. The independent variable (section) should consist of
two or more categorical independent groups. In this case, the
independent variable (section), has three groups, therefore it
meets this assumption. There should be independence of
observation, meaning that there is no relationship between the
observations in each group or between the groups themselves.
There should be no significant outliers, although there are
single data points within the data that do not follow a normal
pattern. Therefore, the outliers found will a negative effect on
the one-way ANOVA, reducing the validity of the results.
Note the above boxplot indicates outliers in section two, with
the id of 21.
The dependent variable (quiz3) should approximately have
a normal distribution for each category of the independent
variable (section). The null hypothesis is that the data is of a
normal distribution, that the mean (average value of the
dependent variable) is the same for all groups.
Ho – the observed distribution fits the normal distribution.
The alternative hypothesis is that the data does not have a
normal distribution; the average is not the same for all groups.
Ha – the observed distribution does not fit the normal
distribution.
It is observed that the data is not normally distributed. Most
sections have quiz3 values between five and nine note this is a
visual estimate. Note that the largest group also has the largest
value of quiz3. The statistics from the histogram of quiz3
reveal that the Mean is 8.05; the Standard Deviation is 2.322,
with a total number N of 105.
Descriptive Statistics

3. N
Minimum
Maximum
Mean
Std. Deviation
Skewness
Kurtosis
Statistic
Statistic
Statistic
Statistic
Statistic
Statistic
Std. Error
Statistic
Std. Error
quiz3
105
0
10
8.05
2.322
-1.177
.236
.805
.467
section
105
1
3
2.00
.797
.000
.236
-1.419

4. .467
Valid N
105
When looking at skewness, for a perfectly normal and
symmetrical distribution, it has a value of zero (Warner, 2013).
There tends to be a quantification of how symmetrical the
distribution is (Warner, 2013). In this sample, the skewness is -
1.177. This presents an indication of an asymmetrical
distribution with a long tail to the left, or a Left Skewed
Distribution. The Kurtosis is an indicator used in distribution
analysis to see if there is a sign of a flatter (Platykurtic) than an
ideal normal distribution (Warner, 2013). If the distribution has
a sharper or steeper peak in the center than an ideal distribution,
it is considered leptokurtic (Warner, 2013). The kurtosis here is
.805 (a normal distribution corresponds to a value of 3); hence
indicating that it is a Platykurtic distribution.
Tests of Normality
section
Kolmogorov-Smirnova
Shapiro-Wilk
Statistic
df
Sig.
Statistic

5. df
Sig.
quiz3
1
.440
33
.000
.550
33
.000
2
.156
39
.018
.909
39
.004
3
.223
33
.000
.853
33
.000
a. Lilliefors Significance Correction
Considering that the data is smaller than 2000 elements, using
the Shapiro-Wilk test is best. The p-value is 0.000 for section
one; therefore the null hypothesis will be rejected. The p-value
is 0.004 for section two, hence the rejection of the null
hypothesis. The p-value for section three is 0.000; the null
hypothesis will also be rejected. The reason for the rejection of
the null hypotheses is that the data is not normally distributed
for all the groups
Test of Homogeneity of Variances

6. quiz3
Levene Statistic
df1
df2
Sig.
1.576
2
102
.212
The homogeneity of variances refers to the assumption that the
variances of populations being compared are equal (using
ANOVA). They can be tested by using the Levene test (Warner,
2013). There is a need for homogeneity of variances, the
Levene tests for the null assumption that the population
variances are equal (Warner, 2013).
Ho – Population variances are equal
Ha – Population variances are not equal
In the above Levene statistic, it shows a sig value of .212,
which is clearly above .05, the preselected alpha level, therefore
the decision, is not to reject the Ho. This clearly shows that the
homogeneity was not violated.
It is clear that most of the assumptions of the one-way
ANOVA have been met. The dependent variable, quiz3, has a
range of one through 10, so therefore it is continuous. The
independent variable, section, has three categorized groups.
These groups do not have a relationship between the categorical
groups. The assumption of a lack of outliers in section 2 has
not been fully met. There is an existence of outliers in section
two as represented by circles and in section 1 represented by
stars.
Analyzing the Levene test there was the discovery that
there is homogeneity of variances. Although the assumption of
normality of data has not been met by the three groups, no
surprise due to real world data being used. Over all it is
concluded that the assumptions are met.
Research Question

7. · Will there be a significant difference between the sections of
the quiz given?
Hypotheses
· Null Hypothesis – There is no difference in quiz3 by the
sections.
· Alternative Hypothesis – There is a difference in quiz the by
section.
Alpha Level
· Alpha level is 0.05
Interpretation
Means Plot
The ANOVA means plot will provide a visual representation of
the group means and their linear relationship (Warren, 2013).
The mean score on quiz3 of section 1 (9.00) is appeared to be
significantly different from those of section 2 (7.62) and section
3 (7.61) when we observe the descriptive statistics and the mean
plot. The results of ANOVA indicated that the differences
among the means scores on quiz3 for the 3 sections were only
due to chance causes, actually there is no effect of the section
in which the student is studying on the score, F (2, 102) =
3.058, p = 0.051 > 0.05.
Case Processing Summary
Cases
Included
Excluded
Total
N
Percent

8. N
Percent
N
Percent
quiz3 * section
105
100.0%
0
0.0%
105
100.0%
Report
quiz3
Section
Mean
N
Std. Deviation
1
9.00
33
2.107
2
7.62
39
2.098
3
7.61
33
2.549
Total
8.05
105
2.322
ANOVA

9. quiz3
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
43.652
2
21.826
4.305
.016
Within Groups
517.110
102
5.070
Total
560.762
104
Degrees of Freedom
There are two degrees of freedom between the group’s
estimate of variance, and 102 degrees of freedom within the
group’s variance.
F Value
The F value is 4.305
P Value
The p value is 0.016. This is less than the α level therefore we
reject Ho.
Calculated Effect Size

10. The effect size is the size of an effect; it is shown that there is a
significant difference between groups. The difference in means
between:
· 1 and 2 is 1.385
· 1 and 3 is 1.394
· 2 and 1 is -1.385
· 2 and 3 is 0.009
· 3 and 1 is -1.394
· 3 and 2 is -0.009
This is shown in the Post-Hoc Tet below.
Multiple Comparisons
Dependent Variable: quiz3
Tukey HSD
(I) section
(J) section
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
1
2
1.385*
.533
.029
.12
2.65
3
1.394*

11. .554
.036
.08
2.71
2
1
-1.385*
.533
.029
-2.65
-.12
3
.009
.533
1.000
-1.26
1.28
3
1
-1.394*
.554
.036
-2.71
-.08
2
-.009
.533
1.000
-1.28
1.26
*. The mean difference is significant at the 0.05 level.
Post-Hoc Test
If the significance is less than the alpha level of 0.05, there

12. would be a need to reject the null hypothesis. Therefore, in all
the cases with the exception of two the null hypothesis will be
rejected.
Conclusion
After performing the one-way ANOVA, the significance
was less than the alpha level. Hence, it is valid to say that the
null hypothesis is rejected.
Strengths
The one-way ANOVA can be used to compare data for
more than two groups. It has the ability to have control over
Type I errors. The one-way ANOVA also displays a robust
design, which increases statistical power because it is a
parametric test. It provides the overall test of equality of group
of means.
Limitations
Just as the one-way ANOVA has it strengths, it also had its
weaknesses, or limitations. The greatest one would be that it
does require a population distribution that is normal. If the null
hypothesis is rejected, it means at least one group differs from
the others, but with the one-way ANOVA, and multiple groups,
and can become difficult to determine which group is different.
The test also assumes equality of variances, and all assumptions
need to be fulfilled.

13. References
Warner, R. M. (2013). Applied statistics from bivariate through
multivariate techniques (2nd ed.). Thousand Oaks, California,
United States: Sage Publications.
One-Way ANOVA
Resources
· One-Way ANOVA Scoring Guide.
· DAA Template.
· SPSS Data Analysis Report Guidelines.
· IBM SPSS Step-by-Step Guide: One-Way ANOVA.
· Copy/Export Output Instructions.
· APA Style and Format.
As with your previous assignments, you will complete this
assignment with the DAA Template. Links to additional
resources are available in the Resources area.
Reminder: The format of this SPSS assignment should be
narrative with supporting statistical output (table and graphs)
integrated into the text in the appropriate places (not all at the
end of the document).
You will analyze the following variables in the grades.sav data
set:
· section
· quiz3
Step 1: Write Section 1 of the DAA.
· Provide the context of the grades.sav data set.
· Include a definition of the specified variables (predictor,
outcome) and corresponding scales of measurement.
· Specify the sample size of the data set.
Step 2: Write Section 2 of the DAA.
· Analyze the assumptions of the one-way ANOVA.
· Paste the SPSS histogram output for quiz3 and discuss your
visual interpretations.
· Paste SPSS descriptives output showing skewness and kurtosis

14. values for quiz3 and interpret them.
· Paste SPSS output for the Shapiro-Wilk test of quiz3 and
interpret it.
· Report the results of the Levene test and interpret it.
· Summarize whether or not the assumptions of the one-way
ANOVA are met.
Step 3: Write Section 3 of the DAA.
· Specify a research question related to the one-way ANOVA.
· Articulate the null hypothesis and alternative hypothesis.
· Specify the alpha level.
Step 4: Write Section 4 of the DAA.
· Begin by pasting SPSS output of the means plot and providing
an interpretation.
· Also report the means and standard deviations of quiz3 for
each level of the section variable.
· Next, paste the SPSS ANOVA output and report the results of
the F test, including:
· Degrees of freedom.
· F value.
· p value.
· Calculated effect size.
· Interpretation of the effect size.
· Finally, if the omnibus F is significant, provide the SPSS post-
hoc (Tukey HSD) output.
· Interpret the post-hoc tests.
Step 5: Write Section 5 of the DAA.
· Discuss the conclusions of the one-way ANOVA as it relates
to the research question.
· Conclude with an analysis of the strengths and limitations of
one-way ANOVA.
Submit your DAA Template as an attached Word document in
the assignment area.