Description

Question

You conduct a survey of a sample of 25 members of this  year’s graduating business students and find that the  average GPA is 3.2. The standard deviation of the sample  is 0.4. Over the last 10 years, the average GPA has been  3.0. Is the GPA of this year’s students significantly different  from the long-run average? At what alpha level would it be  significant?

I have decided that I am going to conduct a sample of this years graduating class of the business students.  I have found that the average GPA is 3.2 and the standard deviation on that sample is 0.4.  Over the last 10 years in the department, the average GPA has been 3.0.  I wanted to  find if the GPA from this year’s class is significantly different from the average and at what alpha level would the findings be significant.

Type of Test

To determine how these three things are related to each other, I would use the parametic test method.  This would allow me to analyze the data over a period of time.  While the samples are independent of each other, they are related in the program and the college that they are offered in.

Parametric data has an underlying normal distribution such that the variable in question, when plotted, demonstrates a predictable and symmetrical bell-shaped graph, a so-called Gaussian distribution. The principal advantage of data of this type is that since the shape of its distribution is known, inferences may be drawn about values that lie within any part of the distribution curve. These distributions are defined by parameters, namely the mean and standard deviation and it is possible to predict critical values such as those that encompass 68.27%, 95.45% and 99.73% of the values of the variable; 1, 2 and 3 standard deviations respectively (Grech & Calleja, 2018).

This type of test will allow us to bell curve both GPA’s and show us where the major differences between the classes were.  It will also show us the major differences at different years, allowing us to find out if outside interference had a part in influencing the GPA of the students in each class.

Was There a Major Difference?

Looking at the data, no there is not a major difference in the average of the GPA from this year’s graduating class and the classes that have been there over the past 10 years at the university.  The deviance rate of the sample is 0.4 and the two GPAs fall well within the measuring difference or room for error in the GPA of each class.  The GPA would have had to have been 0.3 points higher or lower, at .0.7 for there to be a major difference in the GPA of each class.

Alpha Level

When figuring out the alpha level in research you have to look at three things, the level that you are currently at, in this case 3.2 GPA, the historical data 3.0 and the variation that was involved in the research 0.4.  So, for the alpha level to really have an effect on the research or the hypothesis, it would been to fall outside the normal level of deviance.  The GPA would need to be 3.5, or on the lower end a 2.7 to have a major impact on the hypothesis.  You should not adjust the alpha level to make your research more prevalent or less prevalent as it will nullify any results that you find.

We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers (Trafimow & et. al, 2018).

Conclusion

The type of research model that you use and the way you set your hypothesis can have great effects on your research as a whole.  If you do not follow the parameters of the tests, it will make your assumptions off base.  In the bible, it tells us that we are to do our works as in the eyes of the Lord.  It also tells us that we should work our land, or research and that the Lord will reward us for it.  “Those who work their land will have abundant food, but those who chase fantasies have no sense.” (Proverbs 12:11, ESV)

References

Grech, V., & Calleja, N. (2018). WASP (write a scientific paper): Parametric vs. non-parametric tests. Early Human Development, 123, 48-49. doi:10.1016/j.earlhumdev.2018.04.014

Trafimow, D., Amrhein, V., Areshenkoff, C. N., Barrera-Causil, C. J., Beh, E. J., Bilgiç, Y. K., . . . Velasco-Forero, S. (2018). Manipulating the alpha level cannot cure significance testing. Frontiers in Psychology, 9(MAY)

 

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