RUNNING HEAD: ANOVA 1
ANOVA:
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ANOVA 2
Essay 1
The one-way between-subjects ANOVA test determines if the means of two or more
groups are statistically significantly different (Cardinal and Aitken 2006). An example of a
hypothetical study that would require this test is one in which a researcher wants to ascertain
which of three employee training methods, use of simulators, instructor-led training, and on-
the-job training, is effective. The findings would inform how a company can train its
employees to improve their overall skills.
Therefore, employees would randomly be included in the three groups. Specifically,
the groups would be employees to be trained using simulators, those to be trained using the
on-the-job training method, and those to be trained by an instructor. After the training
session, the employees would be required to take a test to ascertain their performance after
undergoing the training session. The average scores would then be analyzed to determine if
they significantly differ.
Null hypothesis
H0: There is no statistically significant difference in the mean performances of the
three groups of employees.
Alternative hypothesis
Ha: There is a statistically significant difference in the mean performances of the
three groups of employees.
Even though the test results will indicate whether the performances significantly
differ, it does not show which groups' performances significantly differ. In other words, the
one-way between-subjects ANOVA test is omnibus. Thus, it does not indicate the specific
means that are significantly different, but only shows that there is statistically significant
difference between the means (Mrkvička et al. 2020).
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A factor that would affect the reliability of the results is the sample size. For this
reason, it would be essential for the researcher to ensure that they have a desired sample size
with characteristics similar to those of the population—a good sample size results in a low
type 1 error of between 0.01 and 0.05 (Serdar et al. 2021). Thus, the aim would be to have a
statistical power between 0.8 and 0.9.
Essay 1
As mentioned above, ANOVA tests are omnibus. Therefore they fail to show which
specific groups of interest significantly differ (Mrkvička et al. 2020). Post hoc procedures
enable researchers to find out the specific differences. However, the procedures are only
relevant if the ANOVA test results show that there is a significant difference between the
means of two or more groups.
The two common post hoc procedures for comparing means in an ANOVA are
Turkey's HSD (Honest significant difference) test and Games Howell's post hoc test. Turkey's
HSD is preferred if the assumption of homogeneity of variances is met (Mahajan 2016). The
procedure tests the pairwise differences among the means while controlling the likelihood of
making a type 1 error. On the other hand, if the assumption of homogeneity of variances is
not met, then the most preferred test is the Games Howell post hoc test. In other words, it is a
nonparametric approach that does not assume equal sample sizes and variances (Mahajan
2016).
The two common post hoc procedures, Turkey's HSD and Games Howell post hoc
test, differ from planned contrasts (Mahajan 2016). Specifically, unlike planned contrasts in
which a researcher defines the independent linear comparisons between specific levels in
advance, the post-hoc approaches are used after obtaining a significant result. In other words,
in planned contrasts, internal references can be evident even when there is no overall
significance. On the other hand, when using post-hoc approaches, the researcher must first
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ascertain that there is a significant difference between the means of the groups (Mahajan
2016).
When using the ANOVA test to analyze data, MS between and MS within are some
terms evident in the output results. MS, in this case, stands for mean square. MS-between is
the variance between the groups of interest, while MS within is the variance within the
groups themselves. Therefore, it is evident that MS-between can be influenced by the
differences among the means of groups under study. However, the differences among the
means of groups do not influence MS-within. For these reasons, the researcher would want
the MS between to be larger.
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References
Cardinal, Rudolf N, and Michael R. F Aitken. 2006. ANOVA for the Behavioural Sciences
Researcher. Mahwah, N.J.: L. Erlbaum.
Mahajan, Anjali. 2016. "Post Hoc Tests In Analysis Of Variance". Indian Journal of
Occupational and Environmental Medicine 20 (2): 121. doi:10.4103/0019-
5278.197552.
Mrkvička, Tomáš, Mari Myllymäki, Milan Jílek, and Ute Hahn. 2020. "A One-Way ANOVA
Test for Functional Data with Graphical Interpretation". Kybernetika, 432-458. Doi:
10.14736/kyb-2020-3-0432.
Serdar, Ceyhan Ceran, Murat Cihan, Doğan Yücel, and Muhittin A Serdar. 2021. "Sample
Size, Power and Effect Size Revisited: Simplified and Practical Approaches In Pre-
Clinical, Clinical And Laboratory Studies". Biochemia Medica 31 (1): 27-53.
doi:10.11613/bm.2021.010502.
