Chapter 6 - Estimation

Question 1

Two types of statistical inference

Answer 1

• estimation

- hypothesis testing

Question 2

Estimation

Answer 2

• concerned with estimating the values of specific population parameters (point estimates)
• sometimes, interval estimation is carried out to specify a range

Question 3

Hypothesis testing

Answer 3

• concerned with testing whether the value of a population parameter is equal to some specific value

Question 4

Random sample

Answer 4

• a selection of members of the population so that each member is independently chosen and has a known nonzero probability of being selected
• a popular alternative to random sampling is cluster sampling

Question 5

Simple random sample

Answer 5

• a random sample where each group member has the same probability of being selected

Question 6

Study population

Answer 6

• the group we want to study

the random sample is selected from the study population

Question 7

Randomized clinical trials

Answer 7

• optimal study design in clinical research
• used for comparing different treatments, in which patients are assigned to a particular treatment by some random mechanism
• randomization = the process of assigning treatments to patients
• patients assigned to different treatment modalities will be smaller if the sample sizes are large
• if sample sizes are small, then patient characteristics of treatment groups may not be comparable

Question 8

Methods of randomization

Answer 8

• random selection

- random assignment (block randomization)

Question 9

Stratification

Answer 9

• patients are subdivided into subgroups, or strata, according to characteristics thought important for patient outcome(s)
• separate randomization lists are maintained for each stratum
• typical characteristics = age, sex, overall clinical condition

Question 10

Blinding

Answer 10

• double blind = neither the physician nor the patient knows what treatment the patient is getting
• single blind = the patient is blinded as to treatment assignment but the physician is not
• unblinded = both the physician and patient are aware of the treatment assignment

Question 11

Design features of RCTs

Answer 11

• gold standard = randomized double-blind study
• this prevents biased reporting of outcome
• however, it may not always be feasible
• in some cases, the side effects may strongly indicate actual treatment received

Question 12

Estimation of the mean of a distribution

Answer 12

• the minimum variance unbiased estimator of the population mean is the sample mean
• population mean = expected value

Question 13

Standard error of the mean

Answer 13

• the standard error represents the estimated standard deviation obtained from a set of sample means from repeated samples of size n from a population with underlying variance
• it is not the standard deviation of an individual observation
• as sample size increases, the variability of the mean (standard error) decreases
• variance can be affected by experimental technique

Question 14

Central-limit theorem

Answer 14

• the skewness of the distribution can be reduced by transformation data using the log scale
• the central-limit theorem can then be applicable for smaller sizes
• as sample size increases, the distribution of the sample mean becomes approximately normally distributed

Question 15

Interval estimation

Answer 15

• interval estimation involves specifying a range within which parameter values are likely to fall
• 95% of the Z values from the repeated samples of size n will fall between the interval of -1.96 and 1.96

Question 16

t distribution

Answer 16

• standard deviation is rarely known in practice, and n is often small
• when n is small, it is not safe to assume that it is normally distributed
• this problem was solved by William Gossett (Student)
• the t distribution is not unique, but is a family of distributions with the parameter of degrees of freedom
• t distribution becomes very similar to the normal distribution as the degrees of freedom increases

Question 17

Factors affecting the length of a CI

Answer 17

• as the sample size increases, the length of the CI decreases
• as the standard deviation increases, the length of the CI increases (cannot really be controlled)
• as the confidence desired increases, the length of the CI increases

Question 18

Chi-square distribution

Answer 18

• used to find the sampling distribution of the sample variance , in order to obtain an interval estimate of the population variance
• only takes on positive values and is always skewed to the right
• n is equal to or greater than 3, the distribution has a mode greater than 0
• the skewness diminishes as n increaes