ALL of stats chapter1... even lds

What is a census?

an observation of every member within a population

What is a 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 census

Should give a completely accurate result

Disadvantages of a census

Time consuming, expensive

Cannot be used when the testing process destroys the item

Hard to process large quantitiy of data

Advantages of a Sample

Less time consuming, Less expensive

Easier to process smaller quantitiy of data

Fewer people have to respond

Disadvantages of a Sample

Data may not be as accurate

Sample may not be large enough to give information about small sub-groups of the population.

What is a sampling unit

The individual unit of a population e.g. A person

Sampling units are often individually named or numbered to form a list. This is called a sampling frame

What is random sampling and what are the methods of it?

Random sampling is when each member of the population has an equal chance of being selected to be included in a sample. The sample should therefore be representative of the population. It also allows the removal of bias from a sample

Methods:

Simple random sampling

Systematic sampling

Stratified sampling

Simple random sampling

a simple random sample of size n is one where every sample of size n has an equal chance of being selected.

A sampling frame is needed, usually a list of people or things. Each member is allocated a unique number and a selection of these numbers are chosen at random either through generating random numbers or lottery sampling.

What is lottery sampling

Members of the sampling frame could be written on tickets and placed into a “hat”. The required number of tickets would then be drawn out creating a simple random sample of size required number of tickets / required number of members.

Systematic sampling

The required elemnts are chosen at regular intervals from an order list. e.g. if a sample of size 20 was required from a population of 100, you would take every fifth person as 100/20 = 5

THE FIRST PERSON TO BE CHOSEN SHOULD BE CHOSEN AT RANDOM.

Stratified sampling

population is divided into mutually exclusive strata (males and females for example) and a random sample is taken from each

the number of people we should sample from each stratum =

(number in stratum / number in popuilation) * overall sample size

Advantages of simple random sampling

Free of bias

easy and cheap to implement for small populations and small samples

each sampling unit has a known and equal chance of selection

Disadvantages of simple random sampling

Not suitable when the population size or the sample size is large as it is potentially time consuming, disruptive and expensive

A sampling frame is needed

Advantages of Systematic sampling

simple and quick to use

suitable for large samples and large populations

Disadvantages of Systematic sampling

A sampling frame is needed

it can introduce bias if the sampling frame is not random

Advantages of Stratified sampling

Sample accurately reflects the population structure

guarantees proportional representation of groups within a population

Disadvantages of Stratified sampling

Population must be clearly classified into distinct strata

When selecting within each stratum, not suitable when the population size or the sample size is large as it is potentially time consuming, disruptive and expensive and a sampling frame is also needed.

Quota sampling

an interviewer or researcher selects a sample that reflects the characteristics of the whole population

Opportunity sampling

taking the sample from people who are available at the time the study is being carried out and who fit the criteria you are looking for

Quota sampling advantages

allows a small sample to still be representative of the population

no sampling frame required

quick, easy and inexpensive

allows for easy comparison between different groups within a population

Quota sampling disadvantages

non random sampling can introduce bias

population must be divided into grups which can be costly or innacurate

increasing scope of study increases number of gorups which adds time and expense

non responses are not recorded as such

Opportunity sampling advantages

easy to carry out

inexpensive

opportunity sampling disadvantages

unlikely to provide a representative sample

highly dependant on individual researcher

Quantitative variables / Quantitative data

Variables or data associated with numerical observations

e.g. shoe size (number)

Qualitative variables / Qualitative data

Variables or data associated with non numerical observations

e.g. Hair colour

Continuous variables

A variable that can take any value in a given range

e.g. time can be 2 seconds, 2.1 seconds, 2.01 seconds

Discrete variables

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

e.g. Age - must be integer. Or number of boys in a classrom - must be integer

what is midpoint and class width in a grouped frequency table

the average of the class boundaries.

the difference between the upper and lower class boundaries

UK Weather Stations (5)

Camborne, Heathrow, Hurn, Leeming, Leuchars

Overseas Weather Stations (3)

Beijing (China), Jacksonville (Florida, USA), Perth (Australia)

Time Periods Covered

May to October 1987 and May to October 2015

Total Number of Variables (UK Stations)

11 variables

Total Number of Variables (Overseas Stations)

4 variables only (Temperature, Rainfall, Pressure, Wind Speed)

Daily Mean Temperature Unit & Precision

Degrees Celsius (°C), recorded to 1 decimal place

Daily Total Rainfall Unit & Precision

Millimetres (mm), recorded to 1 decimal place

Trace Rainfall (tr) Definition

Amount less than 0.05 mm; treated as 0 in calculations

Daily Total Sunshine Unit & Precision

Hours, recorded to 1 decimal place

Daily Maximum Relative Humidity Unit & Meaning

Percentage (%); values above 95% are associated with mist and fog

Daily Mean Windspeed Unit & Measurement

Knots (kn), alongside descriptive Beaufort scale terms

Daily Maximum Gust Unit

Knots (kn), representing maximum instantaneous speed over 24 hours

Wind Direction Unit & Convention

Degrees relative to true North (and cardinal directions); direction the wind is blowing from

Cloud Cover Unit

Oktas (eighths of the celestial dome covered by cloud, ranging from 0 to 8)

Visibility Unit & Scale

Decametres (dm where 1 dm = 10 m); fog is less than 100 dm, mist is less than 200 dm

Daily Mean Pressure Unit & Adjustment

Hectopascals (hPa); adjusted to sea level to remove altitude effects

Missing Data Representation

Recorded as 'n/a' or a dash ('-') depending on the variable and sheet

Geographical Trend: Temperature

Southern UK locations (like Heathrow) are warmer; northern/coastal sites are cooler

Geographical Trend: Wind & Coastlines

Coastal locations generally experience higher average wind speeds than inland stations

Comparison Between 1987 and 2015

2015 experienced generally higher average temperatures and wind speeds than 1987

Total Days in Dataset (Single Station/Year)

184 days (May to October: 31 + 30 + 31 + 31 + 30 + 31)Systematic Sampling Interval

Knots to MPH Conversion

1 knot is approximately 1.15 mph (or 1 mph ≈ 0.869 knots)

Major Data Limitation

Data only covers May to October (summer/autumn), so conclusions cannot be reliably generalized to a full calendar year