What kind of data does chi-squared need, and what does it not accept?

It needs frequencies - actual counts of how many cases fall into each category, such as the number of pebbles pointing in each of four directions, or the number of shoppers coming from each of three zones. It does not accept percentages, proportions, means or measurements; these must be converted back into raw counts before the test can be used. The expected frequency in each category should be at least five, so small samples spread across many categories cannot be tested. This test is an A2 requirement only.

What is the null hypothesis in a chi-squared test?

The null hypothesis states that there is no significant difference between the observed frequencies and the expected frequencies, so that any difference found has arisen by chance - in geographical terms, that there is no pattern and the cases are distributed evenly, or in the proportions the theory predicts. The test then determines whether the observed data depart from that far enough to justify rejecting it. Chi-squared, and therefore this procedure, belongs to the A2 part of the course.

What does a large chi-squared value mean?

A large value means the observed frequencies depart widely from the expected ones, because the calculation accumulates the size of the difference in every category. So the larger the value, the stronger the evidence that a real pattern exists rather than an even or chance distribution. Whether it is large enough to count is decided by comparison with the critical value for the degrees of freedom involved, not by how big the number looks. Chi-squared is an A2 technique.

CCEA A-Level Geography 3910

Processes That Shape Fluvial Environments

Topic overview The drainage basin as an open system Storm hydrographs Factors influencing storm hydrographs Annual hydrographs and river regimes River erosion and transportation Deposition and the Hjulstrom curve Erosional and mixed river landforms Depositional river landforms

Human Interaction in Fluvial Environments

Topic overview Why rivers are channelised, and the methods used Environmentally sensitive and sustainable river management The causes of river flooding The effects of flooding on people, property and land

Global Biomes

Topic overview The global distribution of biomes The tundra biome: climate and soils The temperate grassland biome: climate and soils Climate change and tundra ecosystems

Small-Scale Ecosystems

Topic overview Biotic and abiotic components Ecosystems as open systems Trophic structure and ecological pyramids Nutrient cycling and the nutrient cycling model Plant succession and seral stages Climatic climax and plagioclimax vegetation

The Processes That Shape Our Weather and Climate

Topic overview The global energy balance Vertical and horizontal heat transfer in the atmosphere Ocean currents and the transfer of heat Pressure belts, the Coriolis effect and the pressure gradient The tri-cellular model, the global winds, and where it breaks down Jet streams and the upper westerly winds Global patterns of temperature, pressure, wind and precipitation Factors influencing air temperature

Weather in the British Isles

Topic overview How precipitation forms Air masses affecting the British Isles The polar front and the birth of a depression The life cycle of a depression, and its fronts The sequence of weather as a depression passes Anticyclones in summer and winter Isobars, wind, and the front symbols on a synoptic chart Station circles, recognising systems, and satellite images

Global Weather Issues

Topic overview The Pacific in a normal year: the Walker circulation El Niño events and their global consequences La Niña events and their global consequences How tropical cyclones form The structure of a tropical cyclone The impacts of a tropical cyclone on people and property Managing tropical cyclones: prediction, preparation and response

Population Data

Topic overview Census taking, vital registration, and how the data is collected The reliability of the data, and the use made of it

Population Change

Topic overview Fertility and mortality measures, and why crude rates are crude The demographic transition model The epidemiological transition

Population and Resources

Topic overview Overpopulation, underpopulation and optimum population Malthus and Boserup, and how they hold up Fertility policies, and evaluating one

Settlement Change and the Rural-Urban Fringe

Topic overview Defining rural and urban settlement The rural-urban continuum Issues affecting the rural-urban fringe Greenfield and brownfield development Suburbanisation Counterurbanisation

Planning in Rural Environments

Topic overview Why the countryside needs planning protection ASSIs and SSSIs Areas of Outstanding Natural Beauty National parks A national park for Northern Ireland: the case for, the case against, and the verdict

Urban Challenges in MEDC and LEDC Cities

Topic overview Economic and social deprivation in the MEDC inner city Re-urbanisation in the MEDC city Gentrification and its consequences Urban growth and informal settlements in the LEDC city Service provision in the LEDC city Economic activity and the informal economy in the LEDC city

Measuring Development

Topic overview Why 'development' resists definition Two economic measures: GDP and GNI per capita Two social measures: infant mortality and adult literacy Two composite measures: the HDI and the Gender Inequality Index Using the measures together to describe global contrasts

Reducing the Development Gap

Topic overview The Millennium Development Goals: aims and framework Evaluating two Millennium Development Goals The 2030 Agenda and the Global Goals How the Global Goals build on the Millennium Development Goals Globalisation as a route to development in LEDCs Aid and development in LEDCs, and judging development in one

Emerging Markets

Topic overview What an emerging market is BRICS and MINT: what the labels group, and why they are contested Why emerging markets have grown, and one economy studied

Data Collection

Topic overview Collecting primary data in the field Sampling methods: random, systematic, stratified and pragmatic Point, line and quadrat sampling Ordnance Survey maps and map reading Photographs and satellite images as evidence Synoptic charts and remotely sensed data

Data Processing

Topic overview Geographical information systems, and mapping techniques Annotated sketch maps, and the graph types Triangular graphs Mean, median, mode and range Spearman's rank correlation Nearest neighbour analysis Chi-squared (A2 only)Location quotient (A2 only)Developing investigative skills, and the conventions of mapping and graphical work

Fieldwork Skills and Techniques

Topic overview Framing a geographical question and designing the enquiry Fieldwork safety, hazards and contingency planning Choosing and justifying sampling techniques for an investigation Collecting quantitative and qualitative evidence Describing and evaluating data collection methods Presenting evidence in cartographic, diagrammatic and graphical form Choosing and applying statistical techniques Analysing evidence and drawing conclusions Evaluating methods, evidence and the limitations of conclusions

Planning and Recording an Investigation

Topic overview Choosing an issue, hypothesis or question Identifying appropriate sources and methods Describing the study area, stating aims, and recording data

Plate Tectonics: Theory, Margins and LandformsTectonics

Topic overview The structure of the Earth and the driving mechanism The evidence for continental drift and plate tectonics Constructive margins: processes, ocean ridges and rift valleys Conservative margins: processes and why they build nothing Destructive margins: subduction, trenches and island arcs Collision margins and fold mountains Matching landform to margin: the classic confusions

Volcanic Activity and Its ManagementTectonics

Topic overview Magma composition, viscosity and eruption style Volcanic activity at constructive margins Volcanic activity at destructive margins Hot spots and intraplate volcanic activity Hazards of volcanic activity Benefits of volcanic activity Preparing for volcanic activity: monitoring, planning and protection Responding to volcanic activity and evaluating the response

Seismic Activity and Its ManagementTectonics

Topic overview The nature of a seismic event Seismic waves: P, S and L waves Seismic shaking and its impacts Liquefaction Tsunamis Attempts to predict seismic events Preparing for seismic activity Responding to seismic activity and evaluating the response

Locations and Climates of the Major Tropical BiomesTropical

Topic overview The Hadley cell and the ITCZ Tropical forest: distribution, climate and biomass Tropical grassland: distribution, climate and biomass Hot desert, and the tropical biomes compared

Management and Sustainability in Arid and Semi-Arid Tropical EcosystemsTropical

Topic overview Why irrigation is needed, and the methods used The benefits of irrigation and its environmental problems The socio-economic problems of irrigation, and the solutions

Management and Sustainability in the Tropical Forest EnvironmentTropical

Topic overview Trophic structure, the nutrient cycle, and why clearance is so damaging The zonal soil of the tropical forest Large-scale development and its threats to the forest ecosystem Attempts to achieve sustainable development in the tropical forest

Coastal Processes and FeaturesCoastal

Topic overview Waves and wave energy Wave refraction and coastal alignment Marine erosion, transport, longshore drift and deposition Landforms of high-energy coasts Landforms of low-energy coasts

Regional Coastlines: Submergence, Emergence and Rising Sea LevelCoastal

Topic overview Eustatic and isostatic change Coastlines of submergence Coastlines of emergence Rising sea level and the threat of climate change

Coastal Management and SustainabilityCoastal

Topic overview Environmental Impact Assessment and Cost-Benefit Analysis Sediment cells and Shoreline Management Plans Hard engineering strategies Soft engineering strategies Choosing and evaluating a management strategy

Natural Climate Change: Evidence, Causes and the Arrival of the HoloceneClimate

Topic overview Evidence for past climate change: ice cores, pollen and ocean-floor deposits Causes of long- and medium-term climate change The end of the last glaciation and the arrival of the Holocene

Lowland Glacial LandscapesClimate

Topic overview Ice sheet formation and glacial and fluvioglacial processes Landforms of glacial deposition: till, drumlins, moraines and erratics Landforms of fluvioglacial deposition: eskers and outwash plains Socio-economic development in lowland post-glacial environments

Current Global Climate Change: Human Causes and ImpactsClimate

Topic overview The greenhouse effect and the enhanced greenhouse effect Evidence for recent climate change and its links to human activity Present and potential impacts of climate change

Managing Global Climate ChangeClimate

Topic overview Mitigation: reducing greenhouse gas emissions and capturing carbon Adaptation: reducing vulnerability to climate change International action: the Kyoto Protocol, the IPCC and progress so far

Cultural Groups, Social Inequality and LandscapeCultural

Topic overview Why cultural groups exist Differences between cultural groups Cultural nationalism and its expression Social inequality: exclusion and discrimination as distinct mechanisms Inequality by ethnicity, race, religion, gender, sexuality and class Social constructions of nature and landscape

MigrationCultural

Topic overview Push and pull factors: economic, social, political, cultural and environmental Barriers to migration, and its implications for services, the economy and stability Voluntary and forced migration, and immigration as a political issue

The Geographies of CyberspaceCultural

Topic overview Cyberspace, economic change and cultural globalisation Minority cultures, virtual communities and the digital divide

Sustainable Development in SettlementsPlanning

Topic overview Sustainability, and the urban ecological footprint Carbon footprints and waste management Energy consumption and water supply

Urban Design, Planning and Management for SustainabilityPlanning

Topic overview Eco-towns, eco-cities, residential space and defensible space How greenfield and brownfield development relate to sustainability Retail parks, leisure facilities and open space

Traffic and TransportPlanning

Topic overview The sustainability of transport by sea, air and land Public transport, integrated networks, and restrictions on car use Pedestrian and cycling policies, and judging a traffic management strategy

Defining EthnicityEthnic

Topic overview Race, nationality, language and religion as defining factors Ethnicity as socially constructed and self-ascribed Role, residential concentration, age and gender in perceived identity

Processes That Create and Maintain Ethnic DiversityEthnic

Topic overview Colonisation, annexation and international migration Segregation as a process maintaining diversity Multiculturalism as a process maintaining diversity Economic, social and spatial outcomes of ethnic diversity

Ethnic ConflictEthnic

Topic overview The causes of ethnic conflict The nature of ethnic conflict Social, economic and territorial outcomes of ethnic conflict Ethnic cleansing, international intervention and peace processes

The Changing Nature of TourismTourism

Topic overview The growth of mass tourism as a global industry Positive social and economic impacts of tourism The pleasure periphery and the Butler model of resort development

Challenges and Management of Mass TourismTourism

Topic overview The challenges arising from mass tourism Strategies to reduce the negative impacts of mass tourism

Ecotourism: Opportunities, Challenges and RegulationTourism

Topic overview Defining ecotourism The benefits of ecotourism The negative impacts of ecotourism Regulating ecotourism internationally

Decision Making in Geography

Topic overview What a decision-making exercise asks of you Adopting and maintaining a role Reading maps as evidence Reading photographs as evidence Reading statistics and data as evidence Reading reports and written sources as evidence Reading infographics and diagrams as evidence Processing and presenting supplied quantitative data Interpreting and evaluating the information provided Examining conflicting values Considering alternative choices Making and justifying a recommendation on greater overall benefits Structuring and supporting the decision

Data Processing

Chi-squared (A2 only)

3 things to know
Unit AS 3

Overview

Data does chi-squared need, null hypothesis in a chi-squared test and degrees of freedom in a chi-squared test.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What does the chi-squared test do, and at which level of the course is it required?

Key term

What are degrees of freedom in a chi-squared test, and how are they found?

Key term

How do you use the provided chi-squared table to reach a conclusion?

Questions from this subtopic

Each one with the model answer underneath.

1
What does the chi-squared test do, and at which level of the course is it required?
Model answer
Chi-squared tests whether the frequencies actually observed in a set of categories differ significantly from the frequencies that would be expected if there were no pattern - that is, whether the difference between what you found and what chance predicts is bigger than chance alone can explain. It is required only at A2: chi-squared is one of the two techniques reserved to the second year of the course, so an AS student is not examined on it, while an A2 student must be able to choose it, apply it and interpret the result.
2
What kind of data does chi-squared need, and what does it not accept?
Model answer
It needs frequencies - actual counts of how many cases fall into each category, such as the number of pebbles pointing in each of four directions, or the number of shoppers coming from each of three zones. It does not accept percentages, proportions, means or measurements; these must be converted back into raw counts before the test can be used. The expected frequency in each category should be at least five, so small samples spread across many categories cannot be tested. This test is an A2 requirement only.
3
What is the null hypothesis in a chi-squared test?
Model answer
The null hypothesis states that there is no significant difference between the observed frequencies and the expected frequencies, so that any difference found has arisen by chance - in geographical terms, that there is no pattern and the cases are distributed evenly, or in the proportions the theory predicts. The test then determines whether the observed data depart from that far enough to justify rejecting it. Chi-squared, and therefore this procedure, belongs to the A2 part of the course.
4
What are degrees of freedom in a chi-squared test, and how are they found?
Model answer
Degrees of freedom describe how many of the category totals are free to vary once the overall total is fixed, and they determine which row of the significance table you use. For a single row or column of categories they are the number of categories minus one. For a table with rows and columns they are the number of rows minus one, multiplied by the number of columns minus one. Getting them wrong sends you to the wrong critical value and reverses the conclusion. This is A2 content.
5
How do you use the provided chi-squared table to reach a conclusion?
Model answer
Work out the degrees of freedom, then find that row in the table and read the critical value in the column for the significance level you are using, normally the 95 per cent or 0.05 level. Compare your calculated chi-squared value with it. If the calculated value is equal to or greater than the critical value, the difference between observed and expected is significant and the null hypothesis is rejected; if it is smaller, the difference could have arisen by chance and the null hypothesis stands. Since the formula and tables are supplied in the examination, the marks lie in choosing the test, using the table correctly and stating what the result means. Chi-squared is required at A2 only.
6
What does a large chi-squared value mean?
Model answer
A large value means the observed frequencies depart widely from the expected ones, because the calculation accumulates the size of the difference in every category. So the larger the value, the stronger the evidence that a real pattern exists rather than an even or chance distribution. Whether it is large enough to count is decided by comparison with the critical value for the degrees of freedom involved, not by how big the number looks. Chi-squared is an A2 technique.

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