Chapter 6 - Estimation Flashcards Preview

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Flashcards in Chapter 6 - Estimation Deck (18):

Two types of statistical inference

- estimation
- hypothesis testing



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


Hypothesis testing

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


Random sample

- 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


Simple random sample

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


Study population

- the group we want to study
the random sample is selected from the study population


Randomized clinical trials

- 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


Methods of randomization

- random selection
- random assignment (block randomization)



- 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



- 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


Design features of RCTs

- 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


Estimation of the mean of a distribution

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


Standard error of the mean

- 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


Central-limit theorem

- 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


Interval estimation

- 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


t distribution

- 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


Factors affecting the length of a CI

- 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


Chi-square distribution

- 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