Podcast
Questions and Answers
Which of the following best describes a scenario where bias could influence sampling?
Which of the following best describes a scenario where bias could influence sampling?
- Measuring the height of all children in the world to estimate the height of all humans. (correct)
- Using a perfectly calibrated scale to weigh lollies in a jar.
- Drawing a random sample from a population where everyone participates.
- Employing statistical methods to correct for measurement errors.
Increasing the sample size in a study is always an effective way to eliminate bias.
Increasing the sample size in a study is always an effective way to eliminate bias.
False (B)
Define the term 'standard error' in the context of sampling distributions.
Define the term 'standard error' in the context of sampling distributions.
Standard error is the standard deviation of the sampling distribution.
In the context of binary variables, the sampling distribution is centered on the ______ proportion when there is no bias.
In the context of binary variables, the sampling distribution is centered on the ______ proportion when there is no bias.
Match the following terms with their description:
Match the following terms with their description:
What is the primary reason for using a random sample from the whole population?
What is the primary reason for using a random sample from the whole population?
If a study is biased, increasing the sample size will correct the bias, leading to a more accurate result.
If a study is biased, increasing the sample size will correct the bias, leading to a more accurate result.
Explain how a convenience sample might introduce bias into a study.
Explain how a convenience sample might introduce bias into a study.
Errors that move us away from the truth, leading to a wrong answer, are often called ______.
Errors that move us away from the truth, leading to a wrong answer, are often called ______.
Match each type of sample with its vulnerability to bias:
Match each type of sample with its vulnerability to bias:
What is the implication of a sampling distribution being centered on the population mean?
What is the implication of a sampling distribution being centered on the population mean?
The standard error always increases as the sample size increases.
The standard error always increases as the sample size increases.
Explain why the normal distribution is important in statistics.
Explain why the normal distribution is important in statistics.
When comparing two groups, the sampling distribution is used to assess whether the observed difference is likely due to ______ or a real effect.
When comparing two groups, the sampling distribution is used to assess whether the observed difference is likely due to ______ or a real effect.
Match each term to its correct formula or conceptual definition:
Match each term to its correct formula or conceptual definition:
If a study on the effectiveness of a new drug only includes participants who are likely to respond positively, what type of bias is most likely affecting the results?
If a study on the effectiveness of a new drug only includes participants who are likely to respond positively, what type of bias is most likely affecting the results?
A large standard error indicates that the sample mean is a very precise estimate of the population mean.
A large standard error indicates that the sample mean is a very precise estimate of the population mean.
Describe the impact of increasing sample size on the shape of the sampling distribution, assuming the central limit theorem applies
Describe the impact of increasing sample size on the shape of the sampling distribution, assuming the central limit theorem applies
In a scatterplot with a regression line, the ______ represents the predicted value of the dependent variable when the independent variable is zero.
In a scatterplot with a regression line, the ______ represents the predicted value of the dependent variable when the independent variable is zero.
Match the statistical measures with their interpretation in the context of a research study:
Match the statistical measures with their interpretation in the context of a research study:
Which scenario would most likely result in a biased estimate of the average income of adults in a city?
Which scenario would most likely result in a biased estimate of the average income of adults in a city?
If a study shows a statistically significant difference between two groups, bias is ruled out as a possible explanation of the results.
If a study shows a statistically significant difference between two groups, bias is ruled out as a possible explanation of the results.
Explain how the distribution shape of the population affects the sampling distribution when small sample sizes are used.
Explain how the distribution shape of the population affects the sampling distribution when small sample sizes are used.
In a regression equation y = a + bx, the variable b represents the ______, indicating how much y changes for each unit change in x.
In a regression equation y = a + bx, the variable b represents the ______, indicating how much y changes for each unit change in x.
Match each statistical term with its characteristic:
Match each statistical term with its characteristic:
A researcher is studying the prevalence of a rare disease in a population but can only access data from a few specialized clinics. What type of bias is most concerning?
A researcher is studying the prevalence of a rare disease in a population but can only access data from a few specialized clinics. What type of bias is most concerning?
A perfectly random sample guarantees that the sample mean will be exactly equal to the population mean.
A perfectly random sample guarantees that the sample mean will be exactly equal to the population mean.
What steps can researchers take during study design to minimize the potential for selection bias?
What steps can researchers take during study design to minimize the potential for selection bias?
When animal studies do not check for the effects in pregnancy of a drug which then causes birth defects, this is an example of ______.
When animal studies do not check for the effects in pregnancy of a drug which then causes birth defects, this is an example of ______.
Match the following scenarios to the most relevant statistical concept:
Match the following scenarios to the most relevant statistical concept:
In a study comparing a drug against a placebo, what would be most helpful in the study?
In a study comparing a drug against a placebo, what would be most helpful in the study?
A study can not have bias if there is a large group size
A study can not have bias if there is a large group size
How might a convenience sample not be representative of the population which means a biased result?
How might a convenience sample not be representative of the population which means a biased result?
When non-respondents differ systematically from respondents, then this is vulnerable to ______.
When non-respondents differ systematically from respondents, then this is vulnerable to ______.
Match the sample with its vulnerability to bias:
Match the sample with its vulnerability to bias:
Flashcards
What is Type 1 error in statistics?
What is Type 1 error in statistics?
Errors that increase uncertainty in our answers, leading to more variability.
What is Type 2 error in statistics?
What is Type 2 error in statistics?
Errors that shift our results away from the true value; often called bias.
What is sampling bias?
What is sampling bias?
Selecting a sample in a way that systematically favors some outcomes over others, leading to a non-representative sample.
What is a sampling distribution?
What is a sampling distribution?
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What is standard error?
What is standard error?
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What is population mean (μ)?
What is population mean (μ)?
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What is population standard deviation (σ)?
What is population standard deviation (σ)?
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What is sample mean (x̄)?
What is sample mean (x̄)?
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What is sample standard deviation (s)?
What is sample standard deviation (s)?
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What is population proportion?
What is population proportion?
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What is sample proportion?
What is sample proportion?
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What is a normal distribution?
What is a normal distribution?
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What is a regression line?
What is a regression line?
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What is the intercept in regression?
What is the intercept in regression?
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What is the slope in regression?
What is the slope in regression?
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What is the regression equation?
What is the regression equation?
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How can a study be affected by 'bias'?
How can a study be affected by 'bias'?
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What is Thalidomide?
What is Thalidomide?
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How can each distribution be summarized?
How can each distribution be summarized?
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How is the sampling distribution described?
How is the sampling distribution described?
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How is sample distribution for binary variables described?
How is sample distribution for binary variables described?
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What is a normal distribution?
What is a normal distribution?
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What range does 95% of the sample lie within?
What range does 95% of the sample lie within?
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Study Notes
Errors in Statistics
- Errors make answers more uncertain, increasing variability.
- Errors can shift results away from the true value and are called bias.
- Variability when sampling is unavoidable when taking samples
- Bias should be avoided so as not to get the wrong answer in a study!
- Random sampling helps avoid bias, assuming participation from the entire population.
Bias in Studies
- Errors/bias can skew study results.
- Bias often stems from how individuals are selected for a study.
- Increasing the sample size will not remove bias from a study.
- Biased samples may not represent the intended population
Populations and Samples
- The population of interest depends on study objectives.
- A sample should reflect the target population.
- Samples can be affected by the exclusion of certain population groups.
Importance of Avoiding Bias
- Thalidomide, a drug from the 1950s, was found to cause birth defects because initial animal studies did not test for effects during pregnancy.
- Complete drug testing is vital to avoid bias.
- Identifying bias is crucial because it can significantly affect results.
- Study design is vital for statistical interpretation.
Sampling Fundamentals
- Prior discussions covered sampling, populations, samples, and variability.
- Sampling videos present populations, samples, and their distributions in three panels.
- Each distribution is characterizable by center and spread.
Continuous Variables Terminology
- Population is described by its mean (μ) and standard deviation (σ).
- A sample can be described by its mean and standard deviation.
- Sampling distributions center around the population mean when unbiased.
- Standard error refers to the standard deviation of the sampling distribution.
Binary Variables Terminology
- A population is described by a proportion.
- A sample is described by a proportion.
- The sampling distribution is centered on the population proportion when unbiased.
- Standard error = variability/standard deviation of the sampling distribution
Sample Size Importance
- Sample size significantly impacts the sampling distribution.
Population Shape Impact
- Sampling distributions approximate a normal distribution regardless of the original population's shape
Population Variability
- Different populations can have different degrees of variability
Comparing Two Groups
- Common in health sciences: Comparing Drug A versus Drug B or Drug A versus placebo.
- Comparing risk factors for a disease in smoking versus non-smoking and females versus non-females.
Research Question Example
- Is there a height difference between North and South Island residents?
- Samples are taken from populations with identical heights and those with a 5cm difference to study sampling effects.
Scenario 1: No Height Difference
- The average height is identical between two groups.
- The sample size is 100.
Scenario 2: Height Difference of 5cm
- There is a 5cm height difference between two groups on average.
- The sample size is 100.
- One dataset is shifted by 5cm compared to the other.
Normal Distribution
- Symmetrical bell-shaped curve describing sampling distribution is known as ‘normal distribution’.
- Statisticians use normal distribution because of known distributions
- Having a mean and standard deviation allows for shape depiction
- Distribution falls within defined limits
Properties of Normal Distribution
Sample Size and Normal Distribution
- Large sample sizes (30+) lead to a sampling distribution which follows this normal distribution/symmetric bell curve.
- Approximately 95% of sample means fall within 1.96 standard errors of the population mean
- In sampling distributions, standard error represents a standard deviation.
Scatterplots and Regression Lines
- Regression line formula y = a + b × x describes the relationship between variables.
- 'a 'is the intercept and 'b' the slope.
- Height = a + b × leglength
Knee Injuries in New Zealand (2000-2005)
- ACC claims between July 1, 2000, and June 30, 2005, included 238,488 knee ligament injuries.
- ACL surgeries (Anterior Cruciate Ligament) numbered 7375.
- Average cost per injury: Nonsurgical ($885.31), ACL surgery ($11,157.35).
Lecture 13 Summary
- Explored when bias impacts sampling.
- Reviewed properties of normal curves
- Discussed sampling distribution following a normal curve is expected
- Explained sample size and its affect on sampling distribution spread
- Outlined sampling distribution to compare two groups
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