Topic 6 DQ 1:2
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Linguistics
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Jan 9, 2024
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DQ 1
Review the four "ANOVA" videos in the Calculations section of the "Statistics Visual
Learner" media piece.
Explain why factorial designs with two or more independent variables (or factors) can
induce errors when interpreting data. Give an example.
Factorial designs in experimental research, which involve investigating the impacts of multiple
independent variables on a dependent variable, offer powerful insights but pose challenges that
may lead to data interpretation errors (GCU, n.d.). Interaction effects are a primary concern,
where one independent variable's effect depends on the level of another, making interpretations
complex and potentially misleading. For instance, in a study examining the effects of sleep and
caffeine intake on cognitive performance, a failure to consider the interaction between sleep and
caffeine levels could misrepresent the individual effects of each.
Distinguishing between main effects (average influence of each independent variable) and
interaction effects (combinations of variables' impacts) is crucial but needs to be clarified.
Misinterpreting one as the other can yield erroneous conclusions. Additionally, factorial designs
often necessitate larger sample sizes to detect effects accurately, as inadequate samples can lead
to underpowered studies and increased Type II errors. Additionally, using multiple independent
variables and levels increases the risk of conducting numerous statistical tests, elevating the
chance of Type I errors (Rogers & Revesz, 2019). Researchers should apply adjustments for
multiple comparisons or suitable statistical techniques to mitigate this issue. Lastly, as factorial
designs grow in complexity with more independent variables and levels, the interpretation of
results becomes intricate, requiring careful consideration of practical implications.
Factorial designs with multiple independent variables can introduce errors in data interpretation
due to interaction effects, the distinction between main and interaction effects, concerns about
statistical power and sample size, the potential for multiple comparisons, and the complexity of
interpretation. Researchers must meticulously design their studies, conduct thorough data
analysis, and accurately report their findings to ensure valid conclusions.
References
GCU. (n.d.).Statistical Visual Learner. GCU. Retrieved from http://lc.gcumedia.com/hlt362v/the-
visual-learner/assets/anova.pdf
Rogers, J., & Revesz, A. (2019). Experimental and quasi-experimental designs. In
The Routledge
handbook of research methods in applied linguistics
(pp. 133-143). Routledge.
https://www.taylorfrancis.com/chapters/edit/10.4324/9780367824471-12/experimental-quasi-
experimental-designs-john-rogers-andrea-révész
DQ 2
Explain how the ANOVA impacts a Type I error. How might a Type I error change when
comparing groups two at a time using the t-test for independent groups?
ANOVA (Analysis of Variance) and t-tests for independent groups are statistical methods for
comparing group means in hypothesis testing. Still, they employ different strategies to control
the overall Type I error rate. When it comes to ANOVA, it is employed to simultaneously
compare means among three or more groups by assessing whether the null hypothesis, which
posits that all group means are equal, can be rejected (Weissgerber et al., 2018). If the null
hypothesis is rejected, indicating that not all means are similar, post-hoc tests like Tukey's HSD
or Bonferroni correction are often employed to compare pairs of groups and pinpoint the
differences. ANOVA is designed to manage the overall Type I error rate, representing the
probability of making at least one Type I error in multiple comparisons. By applying these post-
hoc tests and correction techniques, researchers can control this global error rate, thus
diminishing the risk of committing multiple Type I errors when conducting multiple group
comparisons.
Equally, t-tests for independent groups compare two groups at a time. When multiple t-tests are
performed across various pairs of groups, the likelihood of making a Type I error in each specific
comparison increases. This is because, for each t-test, a significance level (usually set at 0.05) is
established, representing the probability of making a Type I error in that particular comparison.
The more t-tests conducted, the greater the potential for committing a Type I error. For example,
if you wish to compare three groups in all possible pairs, three t-tests, each with its alpha level,
would be carried out. The cumulative probability of making at least one Type I error across all
three comparisons is higher than the alpha level used for each test.
ANOVA manages the overall Type I error rate when comparing means among multiple groups by
implementing control measures at the experiment-wise level using post hoc tests and correction
techniques (Weissgerber et al., 2018). On the other hand, t-tests for independent groups, when
applied between pairs of groups, each have their alpha levels, which heightens the risk of
encountering multiple Type I errors if adjustments, like Bonferroni correction, are not applied.
Researchers must exercise caution when conducting multiple t-tests and contemplate modifying
alpha levels to mitigate the possibility of making a Type I error in any individual comparison.
Reference
Weissgerber, T. L., Garcia-Valencia, O., Garovic, V. D., Milic, N. M., & Winham, S. J. (2018).
Why we need to report more than'Data were Analyzed by t-tests or ANOVA'.
Elife, 7
, e36163.
https://elifesciences.org/articles/36163
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