Flashcards in Chapter 6 - Estimation Deck (18):

1

## Two types of statistical inference

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- estimation

- hypothesis testing

2

## Estimation

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- concerned with estimating the values of specific population parameters (point estimates)

- sometimes, interval estimation is carried out to specify a range

3

## Hypothesis testing

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

4

## Random sample

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- 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

5

## Simple random sample

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

6

## Study population

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- the group we want to study

the random sample is selected from the study population

7

## Randomized clinical trials

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- 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

8

## Methods of randomization

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- random selection

- random assignment (block randomization)

9

## Stratification

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- 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

10

## Blinding

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- 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

11

## Design features of RCTs

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- 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

12

## Estimation of the mean of a distribution

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- the minimum variance unbiased estimator of the population mean is the sample mean

- population mean = expected value

13

## Standard error of the mean

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- 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

14

## Central-limit theorem

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- 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

15

## Interval estimation

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- 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

16

## t distribution

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- 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

17

## Factors affecting the length of a CI

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- 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

18