Lecture 7

Question 1

Each research question has…

Answer 1

A numerical answer… counts… probabilities… proportions

Question 2

Inference definition

Answer 2

Inference is the formal name given to learning from data using statistical tools

Question 3

What is the parameter?

Answer 3

The numerical measure of the quantity of interest in the population
- parameters are generally unknown, but can be hypothetical
- will never find the parameter

Question 4

Answer 4

Mean of the population

Question 5

Answer 5

Standard deviation for the population

Question 6

Answer 6

Proportion for the population

Question 7

What is a random variable

Answer 7

An unknown quantity that varies in an unpredictable way

Question 8

Random variable once observed we refer to it as…

Answer 8

An observed or realised value

Question 9

Notion of random variables

Answer 9

• random variables are represented by upper case Roman letters
• observed or realised value is represented by lower case Roman letters

Question 10

What does Pr(X=x) mean?

Answer 10

‘The probability that the random variable X takes the value x’

Question 11

Random variables are describes by

Answer 11

Probability distubutions

Question 12

Observed values of random varieables are

Answer 12

Data

Question 13

Random variables are describes by_______
Observed values of random variables are_____

Answer 13

-probability distubutions
-data

Question 14

What is a statstic?

Answer 14

A numerical summary of data

Question 15

What is an estimate

Answer 15

• a special kind of statistic used an as intelligent guess for a parameter

Question 16

Often estimates are denoted by adding a circumflex…

Answer 16

Û is an estimate of the parameter U

Question 17

What is used to denote the parameter of U

Answer 17

Question 18

x is a statistic and an estimate; U is a prarmeter

Answer 18

Yep

Question 19

What is a statistical model

Answer 19

A mathematical description of the way the data are generated

Question 20

What is the statistical model expressed in terms of?

Answer 20

• parameters (Greek characters)
• random variables (capitals)

Question 21

The scientific equations the types of ___ and the _____ we use in our___

Answer 21

The scientific question determines the types of variable and the parameters we use in our model

Question 22

Different types of _____ give rise to different types of ___ (____)

Answer 22

Different types of variables give rise to different types of data (realisations)

Question 23

Variables - continuous

Answer 23

Can be expressed on a continuous scale in which every value is possible

Question 24

Variables - discrete

Answer 24

• can be put in one-to-one correspondence with the counting numbers

Question 25

Variables - categorical

Answer 25

- restricted to one of a set of categories e.g ‘heads’ or ‘tails’

Question 26

Categorical variables - binary

Answer 26

- give rise to categorical data - two - 0-1 data - refers to the codes we use for different outcomes

Question 27

Catagerial data - more then 2

Answer 27

More then two lol - ethnicity isn’t per se a categorical variable because people can identify with more then one

Question 28

When is categorical data nominal

Answer 28

If there is no natural (or relevant) ordering - super market - blood group - prioritised ethnicity

Question 29

When is data ordinal

Answer 29

If there is no natural ordering - exam result - degree of pain - socio-economic deprivation

Question 30

Discrete variables give rise to..

Answer 30

..descrete data

Question 31

With descrete data ________ take only certain _______ ____, typically ____ or _____ numbers

Answer 31

With discrete data, observations take only certain numerical values, typically integers or whole numbers

Question 32

Categorical data has no…

Answer 32

Numerical relationship

Question 33

Why are descrete data not like catergorical data

Answer 33

Because in discrete the numerical representations are always consistent - can be treated as categorical but it discards information about the maginitue of the relationships between the numbers

Question 34

Continuous variables give rise to

Answer 34

Continuous data

Question 35

Continuous data arise from..

Answer 35

… some form of measurement

Question 36

In practice many continuous variables only take positive / negative values

Answer 36

Positive

Question 37

Restrictions on continuous variables

Answer 37

No restriction on values other then that caused by the accuracy of the equipment for recording values However, while the underlying variable may be truely continuous, the data may be coarsened e.g age in years no seconds

Question 38

Wide range of continuous vairiable patterns

Answer 38

Question 39

Ratio

Answer 39

Fraction given by one quantity over another - both quantities have the same units

Question 40

Proportion

Answer 40

Fraction of one quantity when compared to the whole

Question 41

Proportions are often expressed in terms of…

Answer 41

… percentages

Question 42

What are rates

Answer 42

- same as rations but for quantities with different units E.g - number of children per family - number of new diagnoses of HIV in NZ per year - to simplify rates to a ‘per unit’ measure

Question 43

Scores

Answer 43

- obtaining measures of continuous phenomena is not always easy - where exact measurement is not possible a score may be used

Question 44

Scores are treated as..

Answer 44

Ordinal categories rather then continuous data - the responses may be numbered (e.g 0,1,2,3,4) but care must be taken interpreting these as numerical data

Question 45

3 types of censored data

Answer 45

- right censored - left censored - interval-censored

Question 46

What kind of distribution for censored data

Answer 46

- the underlying variable follows a continuous distubution, but some values are not known exactly

Question 47

Right censored data

Answer 47

- the true value is known to be larger then a recorded value E.g: we know that someone lives until at least 31 December 2017

Question 48

left censored data

Answer 48

- the true value is known to be smaller than a recorded value E.g: we know that a measurement is less then a known limit of detection

Question 49

Interval censored data

Answer 49

- the true value is known to lie between two values E.g we know the date of infection with HPV is after a negative and before a positive test 2 days later

Question 50

Censored data is characterised by ____ varieables

Answer 50

Two - e.g: for right censored data one variable gives the last known value and another indicated whether or not the measurement is censored

Question 51

Example of right censored data

Answer 51