Lecture 4:Understanding Confidence Intervals Flashcards
What is the difference between hypothesis testing and estimation?
Both use sample statistics to find out something about an unknown larger population
- Hypothesis testing: answers yes/no
- Estimation: answers exactly how much.
What is a sample?
A set of individuals selected from a population
What is Accuracy?
Validity
How closely your result reflects the truth
Accuracy indicates?
Validity
What is Precision?
Reliability/ Reproducibility
Obtaining similar results with repeated measurement/samples
What does Precision indicate?
Reliability/ Reproducibility
What are measures of Accuracy/ Validity?
Sensitivity & Specificity
How are accuracy and precision related to inferential statistics?
- Since we are inferring from a sample to a population, we need to know how closely the sample statistics represents the true population parameter, and how reproducible that specific population statistic is
- The more accurate and precise the statistic, the more representative the sample is to the population
What is meant by confidence interval?
Confidence intervals: one way of expressing the usefulness of research data
Confidence intervals (given as a range around an estimate) provides information about the degree of uncertainty surrounding data from a sample
What is the Standard Error of the mean = SE?
Standard error of the mean is a measure of how much the different sample means differ from each other
Smaller standard error indicates?
That samples are all similar and represent true population mean
Formula for Standard error SE
ππ‘ππππππ πΈππππ=(ππ‘ππππππ πππ£πππ‘πππ/βππππππ π ππ§π)
What is a confidence interval CI?
Aconfidence interval (CI)gives an estimated range of values which is likely to include the mean
CIs are an estimate of the accuracy and precision of the mean
Typically the 95% Confidence Interval is reported β 1.96 Γ SE on either side of the mean = 95% Confidence Interval
For 95% CI, if the population is sampled repeatedly and a CI computed each time, 95% of the time the population mean would fall within the computed CI
True or false?
True
What is the formula to estimate 95% Confidence interval CI?
Mean Β± 1.96 Γ Standard Error of the Mean
AKA
Mean Β±1.96 Γ (ππ‘ππππππ πππ£πππ‘πππ/β(ππππππ π ππ§π))
What is Standard erro?
Standard Error is used to make inferences from sample or several samples to whole population
Standard Error answers the question of what outcomes to expect if you repeat the experiment using a different sample from the larger population
A random sample of 30 men & 30 women (45-65 yrs old), was selected from a community of 55,000. Each individual had their Blood Pressure measured. The results indicate that this sample of 60 had a mean systolic blood pressure of 135 mmHg, with a standard deviation (SD) of 36 mmHg. What is the 95% confidence interval (CI) for this Sample?
A. 99-171 B. 126-144 C. 117-153 D. 130.5-139.5 E. 63-207
Calculate
What is the Width of the confidence interval CI?
WIDTH of the CI is a measure of the Precision of the study
To increase PRECISION (more narrow CI), increase the SAMPLE SIZE
Imprecise data is more prone to Type II error (FN)
To increase PRECISION (more narrow CI), increase the SAMPLE SIZE
True or false?
True
When is the Confidence Interval Ci Significant in Ratios?
If it does not include 1
When is the Confidence interval CI significant for differences?
Is it does not include 0
If CI (confidence interval) is significant?
Then p<0.05
What do P values indicate?
The probability of this result (point estimate) being due to chance if the Null Hypothesis is true
It is either significant or not
What do Confidence Intervals CIs indicate?
CI gives theprecisionof the point-estimate; a wide range is worse than a narrow range
CI allows you to compare different studies
