Podcast
Questions and Answers
What is the primary purpose of pre-lecture material in the context of a university course?
What is the primary purpose of pre-lecture material in the context of a university course?
- To serve as a complete substitute for attending lectures.
- To provide a detailed summary of the lecture after it has occurred.
- To help students prepare for and take notes during the lecture. (correct)
- To replace the lecture content entirely.
According to the material presented, distributing course resources for any purpose beyond private study or research is permitted without charge.
According to the material presented, distributing course resources for any purpose beyond private study or research is permitted without charge.
False (B)
What is the primary objective regarding the learning outcomes of the lecture?
What is the primary objective regarding the learning outcomes of the lecture?
- To understand the history of statistical analysis.
- To apply statistical concepts to research and compare study findings with expected results. (correct)
- To memorize statistical formulas.
- To conduct original statistical research.
What constitutes a sampling distribution?
What constitutes a sampling distribution?
A 95% confidence interval definitively captures the population mean or proportion 100% of the time.
A 95% confidence interval definitively captures the population mean or proportion 100% of the time.
When comparing sample results to expected outcomes, what is the role of sample variability?
When comparing sample results to expected outcomes, what is the role of sample variability?
When comparing the findings of a study with expected results, the initial step involves collecting data before making any assumptions.
When comparing the findings of a study with expected results, the initial step involves collecting data before making any assumptions.
In the context of analyzing M&M color distribution, what conclusion was drawn when real-world sample data was compared to an assumption of equal color distribution?
In the context of analyzing M&M color distribution, what conclusion was drawn when real-world sample data was compared to an assumption of equal color distribution?
Which of the following is a common objective in health sciences when comparing groups?
Which of the following is a common objective in health sciences when comparing groups?
When comparing the heights of people from the north and south islands, the sampling distribution assumes there is a significant difference in height between the two groups.
When comparing the heights of people from the north and south islands, the sampling distribution assumes there is a significant difference in height between the two groups.
In a comparison of injury proportions between lime scooters and motorcycles, what initial assumption is typically made before looking for evidence?
In a comparison of injury proportions between lime scooters and motorcycles, what initial assumption is typically made before looking for evidence?
When assessing whether lime scooters or motorcycles are more dangerous, what aspect is critical to consider regarding the question being asked?
When assessing whether lime scooters or motorcycles are more dangerous, what aspect is critical to consider regarding the question being asked?
The presence of sample ______ impacts the reliability of conclusions drawn from a sampling distribution.
The presence of sample ______ impacts the reliability of conclusions drawn from a sampling distribution.
If the proportion of injuries is higher for lime scooters than motorcycles we can definitively conclude that scooters are more dangerous.
If the proportion of injuries is higher for lime scooters than motorcycles we can definitively conclude that scooters are more dangerous.
How does sample variability affect the construction and interpretation of a sampling distribution?
How does sample variability affect the construction and interpretation of a sampling distribution?
What was the conclusion regarding the effect of fluoride consumption on IQ, based on the Dunedin study data?
What was the conclusion regarding the effect of fluoride consumption on IQ, based on the Dunedin study data?
In statistical hypothesis testing, outcomes falling within the 'grey tails' of a distribution are typically considered consistent with the null hypothesis.
In statistical hypothesis testing, outcomes falling within the 'grey tails' of a distribution are typically considered consistent with the null hypothesis.
In the ACL example, a 95% confidence interval that excludes zero suggests evidence of a meaningful ______ between early intervention and rehab.
In the ACL example, a 95% confidence interval that excludes zero suggests evidence of a meaningful ______ between early intervention and rehab.
In research, what is the significance of the initial question or assumption made before collecting data?
In research, what is the significance of the initial question or assumption made before collecting data?
In the context of comparing outcomes, focusing solely on injuries provides a comprehensive view, negating the need to consider more severe outcomes like fatalities.
In the context of comparing outcomes, focusing solely on injuries provides a comprehensive view, negating the need to consider more severe outcomes like fatalities.
Match the following statistical concepts with their applications in research:
Match the following statistical concepts with their applications in research:
What does it mean to conclude that there is 'no evidence' that fluoride reduces IQ?
What does it mean to conclude that there is 'no evidence' that fluoride reduces IQ?
In the ACL example, if the 95% confidence interval for the difference in knee score is (0.6 to 9.9), this indicates that there is evidence for a difference, because zero is not ______ in the interval.
In the ACL example, if the 95% confidence interval for the difference in knee score is (0.6 to 9.9), this indicates that there is evidence for a difference, because zero is not ______ in the interval.
In comparing groups, give an example of something besides injuries or fatalities, that could reasonably influence a conclusion about whether the groups are dangerous?
In comparing groups, give an example of something besides injuries or fatalities, that could reasonably influence a conclusion about whether the groups are dangerous?
How would external validity influence the confidence of conclusions drawn from a study?
How would external validity influence the confidence of conclusions drawn from a study?
Match each study element with its importance in outcome interpretation::
Match each study element with its importance in outcome interpretation::
How do initial assumptions impact how we look at a sampling distribution?
How do initial assumptions impact how we look at a sampling distribution?
Can any death rates definitively mean one item is more dangerous than another? Why or Why not?
Can any death rates definitively mean one item is more dangerous than another? Why or Why not?
You wish to compare a new medicine to a placebo. You create a distribution based on no difference between the groups. What's the next step?
You wish to compare a new medicine to a placebo. You create a distribution based on no difference between the groups. What's the next step?
Match each study element with its impact on interpretations:
Match each study element with its impact on interpretations:
If the width of a distribution changes, can you measure what happened with the new sample?
If the width of a distribution changes, can you measure what happened with the new sample?
Lime scooters have more injuries than motorcycles. Thus, lime scooters are more dangerous.
Lime scooters have more injuries than motorcycles. Thus, lime scooters are more dangerous.
What is the goal for 'the question matters'?
What is the goal for 'the question matters'?
Where is the original of the study from Dunedin mentioned in the text?
Where is the original of the study from Dunedin mentioned in the text?
The null hypothesis suggests the assumption we are testing against.
The null hypothesis suggests the assumption we are testing against.
The gray tails is which hypothesis?
The gray tails is which hypothesis?
Match some of the assumptions from the graphs:
Match some of the assumptions from the graphs:
Regarding flouride in water. If our goal is to claim there is a negative side-effect to flouride addition, what hypothesis would we want to support?
Regarding flouride in water. If our goal is to claim there is a negative side-effect to flouride addition, what hypothesis would we want to support?
Smaller sampling rates usually equate to larger confidence intervals.
Smaller sampling rates usually equate to larger confidence intervals.
Flashcards
What is a population?
What is a population?
A group of individuals or items sharing common traits from which samples are drawn.
What is a sample?
What is a sample?
A subset of a population used to make inferences about the entire group.
What is a sampling distribution?
What is a sampling distribution?
The distribution of a statistic across multiple samples from the same population.
What is a confidence interval?
What is a confidence interval?
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What is 95% Confidence?
What is 95% Confidence?
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What is the initial assumption?
What is the initial assumption?
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What is Bias?
What is Bias?
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What is Error?
What is Error?
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Study Notes
Learning Objectives
- Apply statistical concepts from previous lectures to outline the use of statistics in research
- Compare the findings of a study with expected results
Key Concepts
- Sampling involves a population, a sample, and a sampling distribution
- Confidence intervals indicate a 95% confidence level that the true population mean or proportion falls within the interval
- Variability in the sampling distribution can be determined using the sample results
Comparing Study Findings with Expectations
- Start with an assumption, illustrated by the example of equal color distribution in M&M's
- Gather a sample and determine expected results if the assumption holds true
- Compare your sample data to the expected data
- Draw a conclusion based on the comparison
- With M&M's, one might conclude that the color distribution isn't equal and the proportion of yellow is under 16.7%
Comparing Groups
- Comparing groups is common in health sciences
- Examples include comparing the effectiveness of a new drug to current treatments or determining if smoking increases lung cancer rates
- Other comparisons include physiological characteristics of people with and without a disease, and the likelihood of falling asleep in lectures when taking a statistics course
Height Difference Example
- Examines if there is a difference in height between people from the North and South Islands
- Considers the sampling distribution with no height difference between north and south islanders
- It is assumed that there is no height difference between the two groups on average
- A sample size of 100 is used
- Sampling distribution can be estimated based on the sample size and variability
Injury Comparison: Motorcycles vs. Lime Scooters
- In 2018, there were 273 ACC claims in Auckland & Christchurch from 150,000 lime scooter riders over ~2 months
- The proportion of injuries from lime scooters was 273/150,000, which equals 0.00182 or 0.182%
- In 2016, 1,205 motorcyclists were injured in road crashes
- There were an estimated 700,000 people in NZ with a motorcycle license
- Proportion of injuries from motorcycles was 1205/700,000, which equals 0.00172 or 0.172%
- It is initially assumed that there is no difference
Injury Analysis
- Proportion injuries from lime scooters = 0.00182 (or 0.182%)
- Proportion injuries from motorcycles = 0.00172 (or 0.172%)
- Difference in proportion = Proportion injuries lime – Proportion injuries motorcycle
- = 0.00182 - 0.00172
- = 0.000099 or 0.0099% (using unrounded proportions)
- There is no evidence that lime scooters and motorcycles have a different proportion of riders who have an injury
Death Analysis
- Proportion riders died in lime scooters crashes = 0 / 150 000, which equals 0 or 0%
- In 2016, 52 motorcyclists were killed in road crashes in NZ
- There were an estimated 700 000 people in NZ with a motorcycle license
- Proportion died from motorcycles = 52 / 700 000, which equals 0.0000743 or 0.007%
- Proportion deaths from lime scooters = 0 or 0%
- Proportion deaths from motorcycles = 0.00007 (or 0.007%)
- Difference in proportion = Proportion deaths lime – Proportion deaths motorcycle
- = 0 - 0.00007
- = -0.00007 or -0.007%
- There is evidence of a difference in the proportion of riders dying
- The proportion of motorcycle riders dying in crashes is higher than the proportion of lime scooter riders dying in crashes
Fluoride and IQ claims
- The text questions if claims that fluoridation of water reduces IQ are valid.
- Biostatistics can be used to answer these questions of fluoride
- The initial assumption is no difference in IQ exists between those who drink fluoridated water and those who do not.
- Studies can be compared based on this assumption
Dunedin Study Data
- The Dunedin study followed a cohort of people over time
- Exposure to water fluoridation before the age of 5 was measured and then intelligence measured at age 13
- 891 people lived in an area with water fluoridation, and 99 did not
- Intelligence was measured on the Wechsler IQ scale
- The mean IQ was 100.0, with a standard deviation of 15.1 in the fluoridated area
- The mean IQ was 99.8, with a standard deviation of 14.5 in the non-fluoridated area
- Difference in means = 100.0 – 99.8 = 0.2
- There is no evidence that fluoride reduces (or increases) IQ
ACL Reconstruction
- The text poses a question of whether there is evidence of a difference in primary outcome (knee function/symptoms) between rehab+ optional reconstruction vs early reconstruction.
- An example difference in knee score was 5.3 with 95% CI (0.6 to 9.9)
- There is evidence of a difference in knee score with early ACL reconstruction having better scores
- Mean difference 5.3 95% CI (0.6 to 9.9)
Statistics in Research
- The research question and the assumption made are important for understanding the result
- Bias and errors that can creep in should be considered.
- It is essential to consider whether you believe the results or if there are important errors or bias that could be changing the results
Summary
- There are examples of applying statistical concepts in research
- The findings of a study can be compared with expected results
- The research question matters, which is illustrated with the variable 'dangerous'
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