statistics

key terms

Population

The whole set of items that are of interest

Census

Observes or measures every member of a population

Advantages of a census

It should give a completely accurate result

Disadvantage of a census

Time consuming and expensive
Hard to process large quantity of data

Sample

A selection of observations taken from a subset of the population which is used to find out information about the population as a whole

Advantages of a sample

Less time consuming
Fewer people have to respond
Less data than a census

Disadvantage of a sample

The data may not be as accurate
The data may not be large enough toggle information about the population

Sampling Units

Individual units of a population

Sampling Frame

A list of individually named or numbered sampling units

Simple Random Sample

A sample where every sampling unit has an equal chance of being chosen

Advantages of Simple Random Sample

Free of bias
Easy and cheap to implement
Each sampling unit has equal chance of selection

Disadvantage of Simple Random Sample

A sampling frame is needed
Not suitable when the population size is very big

Systematic Sampling

A method of sampling where the required elements are chosen at regular intervals from an ordered list

Advantages of Systematic Sampling

Simple and quick to use
Suitable for large samples

Disadvantages of Systematic Sampling

A sampling frame is needed
It can introduce bias if sampling frame is not random

advantages of Stratified Sampling

Sample accuracy reflects the population structure
guarantees proportional representation of groups within a population

Disadvantages of Stratified Sampling

Population must be classified into distinct strata

Selection within each stratum can be time consuming and expensive if sample size is large

A sampling frame is needed

Stratified Sampling

A method of sampling where the population is divided into mutually exclusive strata and a random sample is taken from each

The number sampled in a stratum

(Number in stratum/number in population)* overall sample size

Quota Sampling

A method of sampling where a researcher selects a sample that reflects the characteristics of the whole population

Advantages of Quota Sampling

Allows a small sample to still represent the whole population
No sampling frame required
Quick, easy and inexpensive
Allows for easy comparison between different groups in the population

Disadvantages of Quota Sampling

Not random sampling can produce bias
Population must be divided into groups which can be costly or inaccurate
Non-responces are recorded as such

Opportunity Sampling

A method of sampling where the people sampled are those who are available at the time the study is carried out and who fit the criteria you are looking for

Advantages of Opportunity Sampling

Easy to carry out
Inexpensive

Disadvantages of Opportunity Sampling

Unlikely to provide a representative sample
Highly dependent on individual researcher

Quantitative Variables/Data

Variables or data associated with numerical observations

Qualitative Variables/Data

Variables or data associated with non-numerical observations

Continuous Variable

A variable that can take any value in a given range

Discrete Variable

A variable that can take only specific values in a given range

Class Boundaries

The maximum and minimum values that belong in each class

Midpoint

The average of the class boundaries

Class Width

The difference between the upper and lower class boundaries

Interpercentile range

The difference between the values for 2 given percentiles.

Cleaning the data

The process of removing anomalies from a data set.

bivariate data

Data which has pairs of values for two variables

Correlation

A measure of the linear relationship between two variables

regression line

a line of best fit, y \= a+bx

mutually exclusive events

events that have no sample points in common , P(A or B) \= P(A) + P(B)

independent events

The outcome of one event does not affect the outcome of the second event , P(A and B) \= P(A) x P(B)

tree diagram

A diagram used to show the total number of possible outcomes

probability distribution

Describes the probability of any outcome in the sample space.

binomial distribution

When there are a fixed number of trials
There are 2 possible outcomes (success or failure)
There is a fixed probability of success
The trials are independent of each other

the null hypothesis

The hypothesis you assume to be correct

alternative hypothesis

Tells us about the parameter if your assumption is wrong

critical region

the area in the tails of the comparison distribution in which the null hypothesis can be rejected

mutually exclusive

Events have no outcomes in common, they can't happen at the same time

independent

When one event has no effect on another

If events A and B are independent…

P(A intersection B)= P(A)x P(B)

P(A|B)=P(A)

If events A and B are mutually exclusive

P(A intersection B)= 0

P(A union B)= P(A)+P(B)

When A and B are not mutually exclusive, P(A union B)=

P(A)+ P(B)- P(A intersection B)