Sampling, Data Description & Probability

Question 1

Sampling error

Answer 1

when measuring something in a sample of the population, the difference between the sample result and the true underlying population value (if you measured everyone). This error may be the result of biased selection (i.e. sampling bias) or random variation.

Question 2

biased selection (i.e. sampling bias)

Answer 2

sampled subjects are not representative of the population. Bias can be minimized through good study design.

Question 3

random variation

Answer 3

variation due strictly to chance; sample to sample variability that we expect in any study, even with unbiased selection of subjects.

Question 4

Types of samples

Answer 4

Sample of Convenience, Random sample, Stratified sampling

Question 5

Sample of Convenience

Answer 5

take who you can get:

• easy to obtain
• bias may be a problem

Question 6

Random sample

Answer 6

every individual in the population has an equal chance of being in the sample:

• used to ensure that uncontrolled factors do not bias results
• may be difficult to obtain

Question 7

Stratified sampling

Answer 7

sample is drawn within each of two or more strata (groups with common characteristic):
- used to improve accuracy of results in certain circumstances

Question 8

Categorical variables

Answer 8

values fit into natural categories

Examples: gender, disease status, vital status, type of bone break (hairline, simple, etc).

Question 9

discrete variables

Answer 9

ordered numerical data restricted to integer values (count data)
Examples: # of siblings, # of days hospitalized, # of pregnancies

Question 10

continuous variables

Answer 10

numerical data that can take on any value. Often limited by precision of measuring instrument (e.g. height to 1/4 inch)
Examples: age, height, weight, cholesterol, blood pressure

Question 11

Frequency distribution

Answer 11

a table of categories along with their observed frequencies.

a. categories may be natural (e.g. gender, race, type of fracture) or they may be created from continuous variables by grouping values together (e.g. age < 21 yrs, 21-49, 50+)
b. percentages are often included (relative frequencies)
c. may also include cumulative percentages

Question 12

Distribution shapes

Answer 12

Unimodal and symmetric (Mean = Median = Mode), Bimodal, Skewed left (Mean < Median)/right (Mean > Median)

Question 13

Mean (x)

Answer 13

the sum of all observations divided by n, the number of subjects

Question 14

Median

Answer 14

Half the values are below the median and half are above. The middle-most observation of ordered data. If the data are ordered from smallest to largest, the median is

• the observation in the middle of the list if n is odd
• the mean of the two middle observations if n is even

Question 15

Mode

Answer 15

the most frequently occurring observation(s) in the sample

Question 16

Range

Answer 16

difference between the lowest and highest observations

Question 17

Standard Deviation (sd or s)

Answer 17

a measure of the average distance of each observation from the mean

Question 18

Characteristics of a normal distribution

Answer 18

• mean, median, and mode are equal
• approximately:
  68% of its area lies within 1 std. dev. of mean
  95% of its area lies within 1.96 std. dev. of mean
  99% of its area lies within 2.58 std. dev. of mean

Question 19

Normal Range AKA Normal Limits

Answer 19

Can be computed from data and gives an estimate of where a certain percentage (usually 95%) of the population values lie. It is a statistical measure and may not adequately reflect “normal” in a clinical sense.

Question 20

Confidence Interval (CI) AKA Confidence Limits

Answer 20

An interval that describes where the population mean is likely to be with a certain level of confidence (usually 95%). If the interval is narrow then we feel that we have a good estimate of the population mean

Question 21

Pr(Event)/Probability of the event

Answer 21

estimated as (# experiencing event)/(# in the Set)

Question 22

Event

Answer 22

A characteristic defining a subset of our Set (e.g. affliction with a disease)

Question 23

Set

Answer 23

A collection of distinct objects (e.g. a sample of patients)

Question 24

General Multiplication rule

Answer 24

Pr(E1 and E2) = Pr(E1|E2) * Pr(E2). Simple Multiplication Rule (if independent events): Pr(E1 and E2) = Pr(E1) * Pr(E2)
[since, if E1 and E2 are independent events, Pr(E1|E2) = Pr(E1).]

Question 25

General Addition Rule

Answer 25

Pr(E1 or E2) = Pr(E1) + Pr(E2) - Pr(E1 and E2).
Simple Addition Rule (if mutually exclusive): Pr(E1 or E2) = Pr(E1) + Pr(E2)
[since, if E1 and E2 are mutually exclusive, Pr(E1 and E2) = 0.]