STAT 3001 – Week 5 Discussion – Using t Tests

STAT 3001 – Week 5 Discussion – Using t-Tests

The issue of medication dosing for children who have Attention Deficit Hyperactivity Disorder (ADHD) is something parents and practitioners alike struggle with on a daily basis. ADHD is considered a brain chemistry problem and thought to be directly related to the naturally low levels of specific neurotransmitters in a certain individual, which help carry nerve impulses to specific areas of the brain for certain functions (Carver, n.d.). Pharmaceutical companies claim that the manufacturing process produces consistent uniformity of their medication. However, many parents will tell you that despite strict adherence to dose administration times and amounts and accounting for many other variables such as activity, nutrition, and fluid intake, the medication absorption and efficacy can vary greatly from day to day.

I wanted to evaluate one medication, Methylphenidate hydrochloride extended-release, which my son is taking for treatment of his ADHD, to see if the variation in the time it takes the pill to dissolve in water (dissolution) and be available for absorption could be a contributing factor to his behavior difference from day to day. According to a manufacturer, Methylphenidate hydrochloride extended-release is a central nervous system stimulant intended for once-a-day administration with an expected lasting duration of twelve hours and is soluble (able to be dissolved) in water (“CONCERTA® (methylphenidate HCl) Extended-release Tablets CII,” n.d.).

STAT 3001 – Week 5 Discussion – Using t-Tests

The results would be substantial when considering the length of time it takes to become available to enter the bloodstream and its efficacy before changing the drug regimen based on perceived ineffectiveness. It would be of interest to me as a parent and a nurse practitioner to know that, variables considered, the variation in medication absorption and its lasting duration may vary by manufacturer. This would be necessary to explain to parents of children with ADHD when deciding whether to prescribe generic or brand-name Methylphenidate hydrochloride extended-release after comparing data from multiple pharmaceutical companies.

t-Test Hypothesis Testing – Step One

Manufacturer XYZ claims the mean dissolution time is forty-eight (48) minutes for its version of Methylphenidate hydrochloride extended-release. Using the quantitative variable of time, I randomly selected a total of thirty tablets (n=30) from six random batches of Manufacturer XYZ’s inventory (5 from each batch). Placing each one in a glass bowl with 500 ml of water at a temperature of 98.6 degrees Fahrenheit, I measured the time it took the tablet to dissolve completely in the water. At the alpha (a) = 0.01 level, is there sufficient evidence to support my claim that the dissolution times are greater than forty-eight (48) minutes? Proving this may indicate there is a potential variation in the uniformity of the medication production, which would likely have a direct effect on the availability of the drug for absorption.

Figure 1. Histogram of Dissolution Time (in water) of Methylphenidate hydrochloride extended-release tablets

H_o: µ = 48 minutes dissolution time H_a: µ > 48 minutes dissolution time

t-Test Hypothesis Testing – Step Two

Sample Size, n:          30

Mean:                    47.73333

Standard Deviation, s:   1.855715

Alternative Hypothesis: µ > µ(hyp)

Figure 2. t-Test hypothesis testing of Methylphenidate hydrochloride extended-release dissolution time.

Test Statistic, t: -0.7871 Critical t:                       2.4620

P-Value:           0.7812

98% Confidence interval: 46.89918 < µ < 48.56748

t-Test Hypothesis Testing – Step Three

P-value: 0.7812. The P-value represents the likelihood of observing a test statistic at least as large as the one calculated, assuming the null hypothesis is true. Since the P-value of 0.7812 is greater than the 0.01 significance level at which we were testing, it indicates the sample results are not unusual and likely could have occurred by chance. In this particular case, we cannot reject the null hypothesis (Bennett, Briggs, & Triola, 2009).

STAT 3001 – Week 5 Discussion – Using t-Tests

t-Test Hypothesis Testing – Step Four

Since the P-value of 0.7812 is greater than the significance (alpha) level of 0.01, the sample data does not support the rejection of the null hypothesis; therefore, there is evidence to support the manufacturer’s claim that the mean dissolution time is forty-eight (minutes). This confirms the dissolution testing results submitted by Manufacturer XYZ and affirmed by the Federal Drug Administration (FDA) in the fiscal year 2016 (FY16) as having passed the testing process(“Drug quality sampling and testing programs: FY16 Drugs,” 2016). The variation in my son’s behavior, despite the same daily dosing and schedule, is likely due to one or more other variables besides the dissolution time and rate of availability of the medication.

One Sample t-Test for Means

The one-sample t-test is used when we want to know whether the sample obtained comes from a particular population but we don’t have all of the population information available to us, such as the population standard deviation (“One-sample t-Test,” n.d.). In other words, this would help me answer the question, “Is my sample mean statistically different from the known manufacturer’s mean?”. It would be able to help me answer my research question, “At the alpha. (a) = 0.01 level, is there sufficient evidence to support the claim that the dissolution times are greater than forty-eight (48) minutes?” because I only had one sample of the medication to compare to the manufacturers’ population. Since this is a two-tailed test, it would also be able to explain whether my test sample was equal to or not equal to the manufacturer’s claimed mean of forty-eight minutes for the population using a single sample.

As long as my resulting sample value falls within the area under the curve and between the critical values, it explains with a selected confidence level, that my results from this sample support the null hypothesis claim by the manufacturer that the dissolution time is forty-eight minutes for the entire population of Methylphenidate hydrochloride extended-release tablets. If the test statistic was less than -2.7564 or more than 2.7564, then I would be able to reject the null hypothesis and state that the mean dissolution time is not equal to forty-eight minutes, thus refuting the manufacturer’s claim. However, since my sample t value was -0.7871, it fell within the area under the curve, and I can say with a 99% confidence level that my results support the null hypothesis and there is not sufficient evidence to support my claim that the dissolution times are greater than forty-eight (48) minutes.

Test Statistic, t: -0.7871 Critical t:                       ±2.7564

P-Value:           0.4376

99% Confidence interval: 46.79945 < µ < 48.66721

Figure 3. One-sample mean t-Test of Methylphenidate hydrochloride extended-release dissolution time.

References

Bennett, J. O., Briggs, W. L., & Triola, M. F. (2009). Statistical reasoning for everyday life (3rd ed.). Boston, MA: Pearson Education, Inc.

Carver, J. M. (n.d.). Attention-deficit hyperactivity disorder (ADHD). Retrieved May 4, 2017, from http://www.drjoecarver.com/clients/49355/File/Attention- Deficit%20Hyperactivity%20Disorder%20(ADHD).html

CONCERTA® (methylphenidate HCl) extended-release tablets CII. (n.d.). Retrieved from https://www.accessdata.fda.gov/drugsatfda_docs/label/2007/021121s014lbl.pdf

Drug quality sampling and testing programs: FY16 Drugs. (2016). Retrieved from https://www.fda.gov/Drugs/ScienceResearch/ucm407277.htm

Hunt, R. D. (2006). Functional roles of norepinephrine and dopamine in ADHD. Medscape Psychiatry. Retrieved from http://www.medscape.org/viewarticle/523887

One-sample t-Test. (n.d.). Retrieved May 5, 2017, from http://www.psychology.emory.edu/clinical/bliwise/Tutorials/TOM/meanstests/tone.htm

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Post by Day 3 a 1- to 2-paragraph write-up including the following:

Describe your research question, and explain its importance.

Describe how you would use the four-step hypothesis test process to answer your research question.

Explain how using a t-test could help you answer your research question.