Unit 5 Written Assignment Research Statistics
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Unit 5. Written Assignment
UNIVERSITY OF THE PEOPLE
HS 4510-01 Biostatistics
AY-2024-T2
Instructor: Adaugo Eziyi
Date: 20/12/2023
1.
A consumer group suspects that a soft drink has higher sugar levels than what is acceptable. They hire a researcher to investigate this issue.
The researcher can formulate the following hypotheses for this study:
Null hypothesis: The mean sugar level of the soft drink is equal to or lower than the acceptable level.
Alternative hypothesis: The mean sugar level of the soft drink is higher than the acceptable level.
A Type 1 error would occur if the researcher rejects the null hypothesis when it is true. This means that the researcher would conclude that the soft drink has higher sugar levels than what is acceptable, when in fact it does not.
A Type 2 error would occur if the researcher fails to reject the null hypothesis when it is false.
This means that the researcher would conclude that the soft drink has acceptable sugar levels,
when in fact it has higher sugar levels than what is acceptable (Creswell, & Creswell, 2018).
2.
In a research study, you decided to change the significance level from the standard 0.05 to 0.01. Explain how this would influence:
Type 1 error: A type 1 error is the probability of rejecting the null hypothesis when it is true. By lowering the significance level, you are making the criterion for rejecting the null hypothesis more stringent. This means that you are less likely to make a type 1 error, or a false positive. The type 1 error rate is equal to the significance level, so
by changing it from 0.05 to 0.01, you are reducing the type 1 error rate from 5% to 1% (Illowsky, et al., 2022).
Type 2 error: A type 2 error is the probability of failing to reject the null hypothesis when it is false. By lowering the significance level, you are making the criterion for rejecting the null hypothesis more difficult to meet. This means that you are more likely to make a type 2 error, or a false negative. The type 2 error rate is influenced by
the significance level, the effect size, and the sample size. Generally, a lower significance level requires a larger effect size and/or a larger sample size to achieve the same power (Illowsky, et al., 2022).
Power: Power is the probability of correctly rejecting the null hypothesis when it is false. By lowering the significance level, you are decreasing the power of your test, unless you increase the effect size and/or the sample size accordingly. Power is equal to 1 minus the type 2 error rate, so by changing the significance level from 0.05 to 0.01, you are reducing the power of your test, assuming everything else remains constant (Illowsky, et al., 2022).
3.
Lowering the confidence interval from 95% to 90% means that we are less confident that the true value of the odds ratio is within the interval. This also means that we are more likely to reject the null hypothesis, even if it is true. This increases the chance of
making a Type 1 error, which is the error of falsely concluding that there is an association between smoking and low birth weight when there is none (Illowsky, et al., 2022).
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On the other hand, lowering the confidence interval from 95% to 90% decreases the chance of making a Type 2 error, which is the error of falsely concluding that there is no association between smoking and low birth weight when there is one. This is because we are more likely to detect a significant difference between the exposed and unexposed groups, even if the difference is small (Illowsky, et al., 2022).
The power of the study is the probability of correctly rejecting the null hypothesis when it is false. Lowering the confidence interval from 95% to 90% increases the power of the study, because it reduces the probability of making a Type 2 error. However, this comes at the cost of increasing the probability of making a Type 1 error, which may lead to false positive results and misleading conclusions (Illowsky, et al., 2022).
4.
One possible research project that investigates an outcome over time is to examine the
effect of a mindfulness-based intervention on stress levels among college students. The research question is: Does a mindfulness-based intervention reduce stress levels among college students over time? The null hypothesis is: There is no difference in stress levels among college students who receive a mindfulness-based intervention and those who do not receive any intervention over time. The alternative hypothesis is: There is a difference in stress levels among college students who receive a mindfulness-based intervention and those who do not receive any intervention over time. The effect size that will be investigated in this study is the mean difference in stress levels between the two groups at each time point, measured by a standardized scale. A type 1 error would mean that the study concludes that there is a difference in stress levels between the two groups when there is actually no difference in the
population. A type 2 error would mean that the study fails to detect a difference in stress levels between the two groups when there is actually a difference in the population (Illowsky, et al., 2022).
References:
Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). SAGE Publications.
Illowsky, B., Dean, S., Birmajer, D., Blount, B., Boyd, S., Einsohn, M., Helmreich, Kenyon, L., Lee, S., & Taub, J. (2022). Introductory statistics. OpenStax. https://openstax.org/books/statistics/pages/6-introduction