Biostatistics- WA 5
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University of the People *
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CPH 4510
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Jan 9, 2024
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1
Sampling and Hypothesis Testing
Sampling and Hypothesis Testing
Department of Health Science, University of The People HS 4510 – 01 Biostatistics
Adaugo Eziyi
December 20
th
, 2023
2
Sampling and Hypothesis Testing
Sampling and Hypothesis Testing
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.
Write a null and alternative hypothesis for this study.
Null Hypothesis (
H
0
): The soft drink has sugar levels that are within the acceptable range.
Alternative Hypothesis (
H
1
): The Soft drink has higher sugar levels than what is acceptable.
Explain in words what a Type 1 error would mean in this situation.
A type 1 error is made “when we reject the null hypothesis when it is actually true” (University of The People, 2023) In this situation, a type 1 error would mean that the soft drink has higher sugar levels than what is acceptable, even though it does not.
Explain in words what a Type 2 error would mean in this situation.
Type 2 error is made “when we accept the null hypothesis when it is false” (University of The People, 2023). In this situation, a type 2 error would mean failing to conclude that the soft drink has higher sugar levels than what is acceptable, even though it does.
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:
3
Sampling and Hypothesis Testing
Type 1 error
Type 1 Error: The significance level also known as alpha, “is the probability of rejecting the null hypothesis when it is true” (Minitab, 2015). By decreasing the level of significance from 0.05 to 0.01, you are making it stricter. This means that the probability of committing a type 1 error which is rejecting the null hypothesis when it is actually true, decreases— meaning, you become more conservative in claiming statistical significance.
Type 2 error
Type 2 Error: Type 2 error occurs when we accept the null hypothesis when it is false. Decreasing the level of significance from 0.05 to 0.01 does not directly affect the type 2 error rate. However, as the level of significance decreases and become stricter, the chances of committing a type 2 error tends to increase. This is because you are setting a higher bar for rejecting the null hypothesis making it harder to detect a true effect if it is present.
Power
Power: Power is the probability of “rejecting the null hypothesis when it is false” (University of The People, 2023). By decreasing the level of significance, you are decreasing the probability of rejecting the null hypothesis, both for when it is true (type 1 error) and when it is false (type 2 error). As a result, this reduction in the probability of rejecting the null hypothesis decreases the statistical power of your study. Lower power means a lower ability to detect true effects, which can increase the chances of false negatives.
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Sampling and Hypothesis Testing
3.
You were asked to investigate the association between smoking among mothers and infant low birth weight. You were asked to calculate a measure of association like an
Odds Ratio together with the confidence intervals. They asked you to calculate a 90% confidence interval instead of a 95% confidence interval.
Will the lowering of the confidence interval from 95% to 90% increase or decrease the chance of making Type 1 error? Lowering the confidence interval from 95% to 90% will increase the chance of making a type 1 error. A type 1 error occurs when we reject the null hypothesis when it is true. By using a lower confidence interval, we are more likely to reject the null hypothesis and conclude that there is a significant association between smoking and infant low birth weight, even if the association may not truly exist.
Will this affect the probability of making
Type 2
error? In this case, a probability of committing a type 2 error which is made when we accept the null hypothesis when it is false, is unaffected by changing the confidence interval. This probability is determined by factors such as sample size, effect size, and statistical power.
How will this affect the
power
of the study? Explain your answer.
When we decrease the confidence interval (from 95% to 90%), we are effectively increasing the precision or our estimate. However, this comes at the cost of wider confidence intervals and lower statistical power. Power refers to the probability of rejecting the null hypothesis when it is false. By using a smaller confidence interval, we are decreasing the range of plausible effect
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Sampling and Hypothesis Testing
sizes, making it more challenging to detect smaller or more subtle associations. Therefore, lowering the confidence interval to 90% may decrease the power of the study, making it less likely to detect true associations.
4.
Design a research project that investigates an outcome over time, with three measurements done: at baseline, 2 months, and 4 months following an intervention.
State the research question.
Research Question: Does the implementation of exercise intervention over a 4-month period impact the risk of developing cardiovascular diseases?
In this study, implementation of exercise is expected to affect the risk of developing cardiovascular disease. Risk of developing cardiovascular diseases will be checked for before the
intervention begins, at 2-months, and 4-months following the intervention. The risk of developing cardiovascular disease would be measured and compared over the period of 4-
months.
Write the null and alternative hypothesis.
Null Hypothesis (
H
0
): There is no significant difference in the risk of developing cardiovascular
diseases between individuals who receive exercise intervention and those who do not over a 4-
month period.
Alternative Hypothesis (
H
1
): The Implementation of exercise intervention over a 4-month period significantly reduces the risk of developing cardiovascular diseases compared to those who do not receive intervention.
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Sampling and Hypothesis Testing
Discuss the effect size you will be investigating in this study.
Effect of Size: The effect of size being investigated in this study would be the magnitude of the difference in the risk of developing cardiovascular diseases between the group receiving exercise
intervention and the group not receiving exercise intervention.
Explain in words what a type 1 error would mean in this study.
Type 1 Error: In this study, a Type 1 error would occur if we rejected the null hypothesis (assuming there is significant difference in the risk of developing cardiovascular diseases) when, in fact, there is no true difference between the two groups. This would cause a false positive conclusion, suggesting that exercise intervention has an impact on reducing the risk of cardiovascular diseases when it actually does not.
Explain in words what a type 2 error would mean in this study.
Type 2 Error: In this study, a Type 2 error would occur if we failed to reject the null hypothesis (assuming no significant difference) when, in fact exercise intervention does have a significant effect on reducing the risk of developing cardiovascular diseases. This would result in a false negative conclusion, suggesting that exercise intervention has no impact on reducing the risk of cardiovascular diseases when it actually does.
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Sampling and Hypothesis Testing
References
Minitab Blog Editor. (2015, March 19). Understanding hypothesis tests: Significance levels (alpha) and P values in statistics.
Minitab Blog. Retrieved December 18, 2023, from https://blog.minitab.com/en/adventures-in-statistics-2/understanding-hypothesis-tests-
significance-levels-alpha-and-p-values-in-statistics?hs_amp=true
University of the People. (2023). Biostatistics.
Unit 5 reading assignment. Retrieved from https://my.uopeople.edu/pluginfile.php/1812007/mod_book/chapter/474939/Unit
%205_CPH%204510%20Biostatistics_Reading%20Assignment.pdf