Biostatistics Lecture 10: Confidence Interval
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Questions and Answers

What does a 95% confidence interval indicate regarding the true population mean?

  • 95% of the population values fall within this interval.
  • We are 95% confident that the true population mean falls within the calculated interval. (correct)
  • There is a 95% chance that the sample mean is equal to the true population mean.
  • There is a 5% chance that the true population mean falls outside the calculated interval.

In a study comparing a new drug to a placebo, the drug shows a 95% CI of [-1.50, -0.19] for the mean change in a specific marker. What does this suggest?

  • The drug has no effect, since the confidence interval includes negative values.
  • The drug increases the marker, as the confidence interval does not include zero.
  • The results are inconclusive because the P-value is needed to interpret the confidence interval.
  • The drug likely decreases the marker, as the entire confidence interval is below zero. (correct)

A researcher calculates a confidence interval for the average weight loss after a new diet program. How would increasing the sample size, while keeping all other factors constant, likely affect the confidence interval?

  • Narrow the confidence interval. (correct)
  • The effect on the confidence interval cannot be determined.
  • Widen the confidence interval.
  • Not affect the confidence interval.

Which value is NOT needed to calculate a confidence interval?

<p>P-value (C)</p> Signup and view all the answers

If the confidence level is increased from 95% to 99%, what happens to the width of the confidence interval, assuming all other factors remain constant?

<p>The width increases. (C)</p> Signup and view all the answers

What is the relationship between α (alpha) and the confidence level?

<p>Confidence level = 1 - α (D)</p> Signup and view all the answers

A study reports a 95% confidence interval for the mean difference in blood pressure between a treatment group and a control group as [2 mmHg, 8 mmHg]. Which of the conclusions is most appropriate?

<p>The treatment significantly increases blood pressure because the entire interval is above zero. (C)</p> Signup and view all the answers

A researcher wants to estimate the average height of students at a university. They collect a random sample and calculate a 90% confidence interval. What does a 90% confidence level mean in this context?

<p>If the researcher repeats the sampling process many times, 90% of the calculated intervals would contain the true average height of all students. (B)</p> Signup and view all the answers

Flashcards

Inferential Statistics

The branch of statistics that uses sample data to make inferences and draw conclusions about a population.

Hypothesis

A statement about a population parameter that we want to test.

Statistical Tests

A statistical procedure used to determine whether there is enough evidence to reject a null hypothesis.

P-value

The probability of obtaining results as extreme as, or more extreme than, the observed results, assuming the null hypothesis is true.

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Types of Errors

Incorrect decisions in statistical testing: Type I (false positive) and Type II (false negative).

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Confidence Interval (CI)

A range of values that is likely to contain the true population parameter with a certain level of confidence.

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Interval Estimation

Estimating a population parameter using a range of values.

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Confidence Interval (Definition)

The range within which the true population mean is likely to lie, with a specified probability (e.g., 95%).

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Study Notes

  • The lecture covers Mathematics and Biostatistics for Level 1 students, specifically Lecture 10

Confidence Interval

  • Confidence intervals provide an interval estimation, contrary to point estimation
  • Defined as the range in which the true mean of the population lies, associated with a certain probability
  • If a 95% confidence interval is given, one can be 95% sure that the true value of the parameter lies within the interval

Calculating the Confidence Interval

  • The formula to calculate the confidence interval (CI) is: CI = x̄ ± z ⋅ (s / √n)
    • x̄ represents the mean value
    • *z *represents the z-value for the confidence level
    • s is the standard deviation
    • n is the sample size
  • The result provides a lower and upper limit for the interval
  • The formula can also be expressed as Point estimate ± Margin of error

Confidence Level Details

  • Confidence level is denoted by (1 – α) 100%
  • Confidence levels of 95% or 99% are frequently used as the probability

Practical Example

  • When measuring the heights of 40 randomly chosen men, with a mean height of 175 cm and a standard deviation of 20 cm, the calculation for a 95% confidence interval is:
    • CI = 175 ± 1.96 ⋅ (20 / √40) = 175 cm ± 6.2 cm
    • which means: from 168.8 to 181.2 cm (Margin of error is 6.2 cm)
  • Therefore, the CI = [168.8, 181.2]
  • With 95% confidence, the mean population will lie between 168.8 to 181.2 cm

Reference Example

  • In a study on empagliflozin versus placebo and linagliptin versus placebo in young people with type 2 diabetes:
    • The mean HbA1c change from baseline at week 26 was -0.84% in the empagliflozin group versus placebo (95% CI –1.50 to −0.19, p=0.012)
    • The corresponding change from baseline for linagliptin versus placebo was -0.34% (95% CI – 0.99 to 0.30, p=0.29)
    • Empagliflozin provided clinically relevant placebo-corrected reductions in HbA1c, whereas linagliptin did not

Confidence Interval Representation

  • A 95% confidence interval represents the range of values most likely to contain the population parameter with 95% confidence

Lower Endpoint

  • The lower endpoint of a confidence interval can be described as the point estimate minus the margin of error

Upper Endpoint

  • The upper endpoint of a confidence interval can be described as the point estimate plus the margin of error

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Description

Lecture on confidence intervals for level 1 Biostatistics students. It explains how confidence intervals provide an interval estimation, indicating the range where the true population mean lies with a certain probability. It details the formula for calculation, CI = x̄ ± z ⋅ (s / √n).

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