EAB - Estimation And Significance Tests And P-Values

Question 1

what is a pro of using a sample?

Answer 1

Can use a sample to obtain a confidence interval

Question 2

what is a con of using a sample

Answer 2

Cannot deduce exact population value from a sample

Question 3

what is a confidence interval

Answer 3

Range within which population value is likely to be

Question 4

what is sampling error

Answer 4

when different samples give different estimates

Question 5

what is sampling distribution

Answer 5

Sample estimates (e.g.: means),calculated from multiple samples from the same population, will then have a distribution of differing values that is known as the ‘sampling distribution’.

Question 6

Which sample mean gives the most precise estimate of population mean?
A: Random sample of 50 men, standard deviation 10
B: Random sample of 1000 men, standard deviation 10

Answer 6

B

THE MORE DATA = MORE PRECISE THE ESTIMATE

Question 7

Which sample mean gives the most precise
estimate of population mean?
A: Random sample of 200 men, standard deviation 20
B: Random sample of 200 men, standard deviation 5

Answer 7

B

LOWER STANDARD DEVIATION = MORE PRECISE ESTIMATE

Question 8

What is standard error?

Answer 8

A standard error (SE) is an indication of the extent of the sampling error

Question 9

How can Standard Error be calculated

Answer 9

standard deviation divided by the square root of the sample size

SE= SD /sqrt𝑁

Question 10

what does standard error tell us

Answer 10

Standard error tells us how much a sample mean tends to vary from the population mean (true mean).

It provides an estimate of the precision of the sample mean.

Question 11

what does a smaller SE mean

Answer 11

Question 12

what does a larger SE mean

Answer 12

Question 13

What range can the true population estimate be expected to lie in?

Answer 13

• True (population) estimate can be expected to lie in the range:
• sample mean – 1.96 standard errors to
• sample mean + 1.96 standard errors in 95% of calculations

Question 14

What are the 4 assumptions in calculating confidence interval?

Answer 14

• Normal data or large sample
• The sample is chosen at random from the population
• The observations are independent of each other
• The sample is not small (at least 60)

Question 15

Answer 15

Question 16

How do you calculate proportion?

Answer 16

It is the same formula of sample mean -/+ 1.96 standard error.

Question 17

What are the 4 assumptions of proportion?

Answer 17

• the sample is chosen at random from the population
• the observations are independent of each other
• the proportion with the characteristic is not close to 0 or 1
• np and n(1-p) are each greater than 5 (large sample)

Question 18

What is the standard error for proportion?

Answer 18

• Multiply the proportion with the characteristic by the proportion without the characteristic
  
  • p(1-p)
• Divide by the sample size
  
  • p(1-p)/n
• Take the square root to deduce the SE
  
  • sqrt(𝑝×(1−𝑝)/𝑛)
• Worked through example.
  
  • Out of 7074 men, 1981 smoked cigarettes.
  • Proportion smoking = 0.28 (28%)
  • Standard error of proportion = 0.0053
  • 95% confident that true proportion is in the range:
    0.28 - 1.96 x 0.0053 to 0.28 + 1.96 x 0.0053
  • i.e. in the range 27% to 29%

Question 19

what is the difference in the 95% confidence interval between a large sample and proprotion

Answer 19

• for the mean from a large sample the 95% confidence interval is:
  
  • sample mean -1.96 standard errors
    to
    sample mean + 1.96 standard errors
• for a proportion the 95% confidence interval is:
  
  • sample proportion -1.96 standard errors
    to
    sample proportion + 1.96 standard errors

Question 20

what decreases standard error?

Answer 20

as sample size increases, standard error decreases

Question 21

what is the null hypothesis

Answer 21

The NH states that “No relationship exists between the variables and outcomes of the a study”

we then ask… does the sample data provide sufficient evidence to REJECT the null hypothesis

Question 22

what is a p-value

Answer 22

provides a way of weighing evidence against the null hypothesis

p value is a probability that lies between 0 and 1

The smaller the p-value, the stronger the evidence against the Null Hypothesis

Question 23

what does it mean if the p value is LESS THAN 0.05 (p<0.05)

Answer 23

^ provides good evidence to REJECT null hypothesis,

therefore a real difference or association DOES exist

and the result is STATISTICALLY SIGNIFICANT

Question 24

what does it mean if the p value is MORE THAN or EQUAL TO 0.05 (p>0.05)

Answer 24

^ provides INSUFFICIENT EVIDENCE to reject null hypothesis,

therefore a real difference or association DOES NOT exist,

and the result is NOT STATISTICALLY SIGNIFICANT

Question 25

What is clinical signficance

Answer 25

the difference observed is large enough to be clinically meaningful

Question 26

in general, why are 2 sided tests used and not 1 sided tests

Answer 26

1 sided tests do not distinguish between ‘no effect’ and ‘a harmful effect’

Question 27

does an increase or decrease in the SAMPLE SIZE bring it closer to the mean?

Answer 27

increase sample size = estimate closer to mean

Question 28

does an increase or decrease in the SPREAD OF DATA bring it closer to the mean?

Answer 28

decrease spread of data = estimate closer to mean

Question 29

decreasing the SD does what?

Answer 29

lower spread of data

Question 30

increasing the SD does what?

Answer 30

higher spread of data