Data Collection Statistics and Errors

Question 1

sample

Answer 1

subset of elements

Question 2

population

Answer 2

all possible elements

Question 3

It is important to choose a sample that is

Answer 3

random and representative.

Question 4

Randomisation

Answer 4

prevents bias arising from a subjective choice of units.

Question 5

Good data –

Answer 5

i.e. statistically valid data – should also be replicable.

Question 6

Independent variable (factor):

Answer 6

The presumed cause in an experimental study

Question 7

Dependent variable (response):

Answer 7

The presumed effect in an experimental study

Question 8

Controlled variable:

Answer 8

An unrelated variable that an investigator does not wish to examine in a study.

Question 9

Continuous variable:

Answer 9

A variable that is not restricted to particular values (other than limited by the accuracy of the measuring instrument), e.g. temperature, velocity, pressure…

Question 10

Discrete variable:

Answer 10

A variable having only integer or ‘stepped’ values. For example, number of attempts to learn a task, number of days it rains in a month, number of rooms in a building…

Question 11

data=

Answer 11

pattern + residuals

Question 12

Pattern:

Answer 12

how two variables are (seemingly) related.

Question 13

Residuals:

Answer 13

data points deviating from the proposed pattern.
Also called outliers
Do not ignore or remove outliers – they can contain valuable information

Question 14

quoting errors

Answer 14

Only defined constants (e.g. 𝑐,𝜋,𝑒…) possess exact values (i.e. do not need to be quoted with errors)
For anything else, we need to quote errors!

Question 15

experimental errors 4

Answer 15

Error’ is an indication of uncertainties in an experiment or measurement.
In effect, all you can determine in an experiment is an estimate.
Even an unbiased and consistent experiment will possess some error margins.
These errors, however, should become smaller with more repeats.

Question 16

There are two main types of errors:

Answer 16

Systematic errors
e.g. if this guy’s tattoo artist was bad
Random errors
e.g. if he keeps flexing & extending his wrist while you measure

Question 17

repetition leads to

Answer 17

different outcomes that have statistical regularity.

Question 18

3 common causes of random error

Answer 18

Fluctuating ambient conditions (temperature, pressure etc.)
Human error.
An instrument is only as good as the person reading it!
Chaos!

Question 19

systematic error 3

Answer 19

Systematic errors in general are typically caused by faulty (or badly calibrated) equipment or a badly designed experiment.
They can be dangerous as they cannot be measured by repeating the experiment with the same equipment.
As such, if we are to identify systematic errors, we need to have a good understanding of the nature of the experiment and the instruments involved.

Question 20

standard deviation definition

Answer 20

provides a measure of how much, on average, the individual values in a data set of repeated measurements differ from the mean (i.e. the ‘assumed’ value).

Question 21

standard deviation equation

Answer 21

𝜎_𝑥= √(1/𝑁 ∑_(𝑖=0)^𝑁▒(𝑥_𝑖−𝑥̅ )^2 )

𝑥̅ is the mean value of x for a given data set, meaning that (𝑥_𝑖−𝑥̅ ) gives the ‘individual deviation’ of each value from the mean.
The standard deviation is then simply the sum of the squared individual deviations.

Question 22

quoting numbers sensibly

Answer 22

only keep significant figures up to the 1st digit of the error

Question 23

standard error

Answer 23

𝑆𝐸=𝜎_𝑥̅ =𝜎_𝑥/√𝑁, where n is the number of observations or measurements.
What happens as N→∞?
Tends to 0
More measurements smaller error

Question 24

error propagation addition and subtraction

Answer 24

Absolute error of result is simply the sum of the two original absolute errors.

Question 25

error propogation Multiplication or division

and powers

Answer 25

look at slides