Lecture 4:Understanding Confidence Intervals

Question 1

What is the difference between hypothesis testing and estimation?

Answer 1

Both use sample statistics to find out something about an unknown larger population

• Hypothesis testing: answers yes/no
• Estimation: answers exactly how much.

Question 2

What is a sample?

Answer 2

A set of individuals selected from a population

Question 3

What is Accuracy?

Answer 3

Validity

How closely your result reflects the truth

Question 4

Accuracy indicates?

Answer 4

Validity

Question 5

What is Precision?

Answer 5

Reliability/ Reproducibility

Obtaining similar results with repeated measurement/samples

Question 6

What does Precision indicate?

Answer 6

Reliability/ Reproducibility

Question 7

What are measures of Accuracy/ Validity?

Answer 7

Sensitivity & Specificity

Question 8

How are accuracy and precision related to inferential statistics?

Answer 8

• 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

Question 9

What is meant by confidence interval?

Answer 9

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

Question 10

What is the Standard Error of the mean = SE?

Answer 10

Standard error of the mean is a measure of how much the different sample means differ from each other

Question 11

Smaller standard error indicates?

Answer 11

That samples are all similar and represent true population mean

Question 12

Formula for Standard error SE

Answer 12

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐸𝑟𝑟𝑜𝑟=(𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛/√𝑆𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒)

Question 13

What is a confidence interval CI?

Answer 13

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 – 1.96 × SE on either side of the mean = 95% Confidence Interval

Question 14

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?

Answer 14

True

Question 15

What is the formula to estimate 95% Confidence interval CI?

Answer 15

Mean ± 1.96 × Standard Error of the Mean

   AKA 

Mean ±1.96 × (𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛/√(𝑆𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒))

Question 16

What is Standard erro?

Answer 16

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

Question 17

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

Answer 17

Calculate

Question 18

What is the Width of the confidence interval CI?

Answer 18

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)

Question 19

To increase PRECISION (more narrow CI), increase the SAMPLE SIZE

True or false?

Answer 19

True

Question 20

When is the Confidence Interval Ci Significant in Ratios?

Answer 20

If it does not include 1

Question 21

When is the Confidence interval CI significant for differences?

Answer 21

Is it does not include 0

Question 22

If CI (confidence interval) is significant?

Answer 22

Then p<0.05

Question 23

What do P values indicate?

Answer 23

The probability of this result (point estimate) being due to chance if the Null Hypothesis is true

It is either significant or not

Question 24

What do Confidence Intervals CIs indicate?

Answer 24

CI gives theprecisionof the point-estimate; a wide range is worse than a narrow range

CI allows you to compare different studies

Question 25

What is more informative?

A. Aspirin reduces risk of heart attack in patients with cardiovascular disease by 25% (p < 0.05)

B. Aspirin reduces risk of heart attack in patients with cardiovascular disease by 25% (95% CI 15%-35%)

C. Aspirin reduces risk of heart attack in patients with cardiovascular disease by 25% (95% CI 2%-48%)

Answer 25

B

Check the answer

Question 26

What is the Power of a sample size?

Answer 26

Ability to reject the Null Hypothesis when it is False

Question 27

Bigger samples usually result in more narrow confidence intervals because the standard error of their mean is smaller

True or false?

Answer 27

True

Question 28

What is the alpha level?

Answer 28

The maximum p value accepted

Question 29

What is the beta level ?

Answer 29

The power desired

Question 30

What is the expected effect size?

Answer 30

The difference between the groups