Lecture 7- Terminology

Question 1

What does the type of variable used effect?

Answer 1

The tools we use to analyze it

Question 2

What are the three main types of variables?

Answer 2

• Continuous: expressed on a continuous scale in which every value is possible
• Discrete: can be put in a one to one correspondence with counting numbers (whole)
• Categorical: restricted to one of a set of distinct categories e.g. heads or tails

Question 3

What is binary categorical data?

Answer 3

This is the simplest data type that can arise from a categorical variable
There is only two categories to choose from
e.g. you are either a smoker or non-smoker, athlete or not athlete

Question 4

Why is binary categorical data sometimes called 0-1 data?

Answer 4

Because the two categories are given arbitrary numbers for representation e.g. 1 represents the patients with the outcome and 0 represents those without the outcome

Question 5

Are there cases where we need more than two categories of categorical data? What are the further divisions that occur at this level?

Answer 5

Yes, often e.g. blood types
The term nominal is used if there is not relevant ordering of the data
Ordinal is used if there is an ordering/ rank

Question 6

In what case where we are using a number scale is data not numerical?

Answer 6

For categorical ordinal categories we often use number as a scale/ ranking. However, this doesn’t mean the data is numerical e.g. pain levels. If it was numerical we could say someone who rated double someone else’s score experienced twice the pain which we can’t do.

Question 7

How is discrete numerical data different from categorical data which uses a number scale?

Answer 7

Because numbers only take on discrete (whole) data values spaces between the numbers is always consistent so we can make claims like 2x as many (comparisons)

Question 8

Continuous data arises from…..

Answer 8

taking a measurement (e.g. height), there is a full scale of numbers.

Question 9

True or false continuous data is more often positive than negative…

Answer 9

T

Question 10

What is an example of making continuous data discrete? (coarsening)

Answer 10

When we say our age in full years

Question 11

Does continuous numerical data give rise to only 1 pattern of distribution?

Answer 11

No, because any measurement is possible often there is a lot of variation in the pattern that can be seen from a graph

Question 12

What is an example of when multimodal data would arise?

Answer 12

Measuring height- would get a mode for each gender

Question 13

What is a ratio?

Answer 13

Fraction given by one quantity over another. Both quantities have the same units

Question 14

What is a fraction?

Answer 14

Fraction of one quantity when compared to the whole

Question 15

What are rates?

Answer 15

Ratios for quantities of different units

Question 16

What happens when it is too hard to obtain measures of a continuous phenomena?

Answer 16

A score is used

Question 17

What is censored data? What are the types?

Answer 17

Underlying data follows a continuous distribution but some values are not known exactly

Types:
-Right censored - the true value is known to be larger than a recorded
value

• Left censored - the true value is known to be smaller than a recorded
  value
• Interval-censored - the true value is known to lie between two values

Censored data are categorized by two variables, e.g. for right censored
data one variable gives the last known value and another indicates whether
or not the measurement is censored.

Question 18

What are parameters?

Answer 18

The numerical measure of the quantity of interest in a population. They are generally unknown but can be hypothetical

Question 19

What is a random variable?

Answer 19

An unknown quantity that varies in a unpredictable way. Like flipping a coin.

Once observed we refer to an observed or realized value

Question 20

Upper case roman letters represent…

Answer 20

Random variables

Question 21

Lower case roman letters represent…

Answer 21

Observed or realised values

Question 22

Random variables are described in…

Answer 22

probability distributions

Question 23

what is a statistic?

Answer 23

A numerical summary of data

Question 24

What is an estimate?

Answer 24

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

Question 25

What does adding a circumflex do?

Answer 25

Estimates are denoted by adding a circumflex. This implies that the value is an estimate for the parameter value.