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What is the association between involvement in high school extracurricular activities and GPAs in high school seniors in Texas?

What is the association between involvement in high school extracurricular activities and GPAs in high school seniors in Texas? This is an ideal question for a one-way ANOVA because:

One-way ANOVA tests can accommodate one independent variable, divisible into as many nominal categories as required. In this case, the independent variable is the extracurricular activity the participants are involved in, divided into sports, student government (student council, yearbook committee), musical group (choir, orchestra, band), and academic groups (Mathletes, language clubs, science clubs). This fits the qualitative, nominal characteristic requirement for the one-way ANOVA independent variable.
The dependent variable must be a ratio or interval scale. The dependent variable in this study is GPA, which is quantitative, continuous ratio data measured from 0-4.0.
One-way ANOVA tests require that the groups in question have a homogeneity of variance, or that the “groups should all have reasonably similar standard deviations”(Sukal, 2013, p. 211).
Finally, one-way ANOVA tests work off of the assumption that the samples are pulled from a population that is normally distributed (Sukal, 2013). The population is high school seniors in Texas, and while not yet confirmed with the actual data collection, it is assumed that the population will yield a normal distribution.

The null hypothesis posits that there is no difference in GPAs across the 4 groups of extracurriculars. It is annotated in the following manner: H0=µsports= µgovt= µmusic= µacademic. Meanwhile, the alternate hypothesis, Ha=µsports ≠µgovt ≠µmusic ≠µacademics, suggests that the differences in GPAs across the extracurricular groups are statistically significant.
Running a statistical t-test with the same data multiple times (to account for the multiple categories within the independent variable) increases the potential for TypeI errors; running a single test with the ANOVA technique controls this inflation (Sukal, 2013). Granted, the ANOVA test itself will not indicate which means are significantly different, but follow-up post-hoc tests can provide that data (Sukal, 2013). Assuming that the groups are meet the homogeneity of variance and normal distribution requirements, Type I errors will be minimal and remain at the original alpha level (p=.05 in most cases) (Laerd Statistics, 2018).
Laerd Statistics. (2018). One-way ANOVA. Retrieved from Laerd Statistics:
Sukal, M. (2013). Research Methods: Applying Statistics in Research. Bridgepoint Education.
Reply Reply to Comment———————————————————————————————————————————————————————————————CLASSMATE #-2—-M. R.
According to Hollenbeck and Klein (1987); Prendergast (1999), “Existing research also indicates that providing rewards for goal attainment can increase effort and strengthen individuals’ goal commitment, which can result in better performance” (as cited by, Presslee, Vance and Webb, 2013, p. 1806). The “one-way repeated measure ANOVA will address my revised question concerning whether or not financial reinforcers (i.e., monthly bonuses) increases employee performance in collection agencies.  According to Sukul (2013), “The “one” in one-way ANOVA indicates that there is just oneIVin this model” (Sukul, 2013).  In regards to my revised research question, there is a great chance that error variability could occur, brought on by other factors that are not influenced by our IV (independent variable).  The IV within my proposed research question can be identified as the financial reinforcers or “monthly bonuses.”  The DV (dependent variables) are identified as the “employees performance.”
My proposed research question is appropriate for this particular statistical test because it concerns itself with IVs with multiple groups unlike an independent t-test.  Sukul (2013) states, “he difference is that the independent t-test allows for an IVwith just two groups, but the IVin ANOVA can be any number of groupsgenerally more than two” (Sukul, 2013). For example, the IVs within my proposed research question can consist of other factors (or confounding variables) that could demonstrate error variance.  These confounding variables can be peoples level of maturity that can be associated with age.  Other confounding variables can be related to individuals level of education, experience, gender or behaviors that are influenced by intrinsic or extrinsic motivation.  Sukul (2013) mentioned that, “Behavior changes that are notrelated to the IVreflect the presence of error variance attributed by other factors known as confounding variables” (Sukul, 2013).
The samples for my research proposal consist of both male and female collectors (DV) which their attributes are considered on ratio scales; discrete as we are dealing with variances that are respectively influenced by our IVs.  For example, between both male and female collectors, what would be the ratio differences between male and female who’s level of performance is motivated by the IV.  Our IV (monthly bonuses) attributes in contrast would be considered using ordinal scales; continuous.
Null Hypothesis:
Because I am only dealing with two groups, my statistical hypothesis in one-way ANOVA is much like the independent t-test.  Depending on if our means for both populations (male and female) are the same, our null hypothesis would therefore express that with both groups, there is not a significant difference between both populations concerning monthly financial reinforcers and increased performance:
H0: μ1 = μ2
Alternative Hypothesis:
The alternative hypothesis would change drastically if I were dealing with 3 or more groups.  According to Sukul (2013), “Things have to change for the alternate hypothesis, however, because with three groups, there is not just one possible alternative” (Sukul, 2013).  Three groups would create more noise and confusion with trying to determine an alternate to reject my null.  Our null hypothesis is therefore represented as; Both male and female are influenced by monthly incentives, therefore, increasing their ongoing performance. This would indicate that there is a significant difference between our IV (financial reinforcers) and our DV (employee increased performance).  However, we predict that there is a higher mean concerning women performance as it relates to our IV, so, our alternative hypothesis would be a prediction (Directional Alternative Hypothesis:
Ha: μ1,μ2
Type of errors:
For my study, I am anticipating new variables to take into consideration which in turns presents the possibilities of type 1 errors in association with what is known as Family-Wise Errors (FWER).  This would be in the result of an inflated hypothesis. According to Sukul (2013), “The other problem is an issue of inflated error in hypothesis testing when doing multiple test known as family-wise error” (Sukul, 2013).  This is actually one of several good reasons of using an omnibus test.  It is important for me, during my study to understand that by using the ANOVA has “the assumption that the groups being compared have similar variances or spreads in their scores (this is called homoscedasticiy)” (Wall Emerson, 2017, p. 194).
Presslee, A., Vance, T. W., & Webb, R. A. (2013). The Effects of Reward Type on Employee Goal Setting, Goal Commitment, and Performance. Accounting Review, 88(5), 1805–1831.
Sukal, M. (2013). Research methods: Applying statistics in research. San Diego, CA: Bridgepoint Education, Inc.
Wall Emerson, R. (2017). ANOVA and t-tests. Journal of Visual Impairment & Blindness, 111(2), 193–196. Retrieved from,cpid&custid=s8856897&db=ccm&AN=121669183&site=ehost-live
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