How are degrees of freedom found for a chi-square goodness-of-fit test?

Degrees of freedom equal the number of categories minus one. Two categories therefore give one degree of freedom.

With one degree of freedom, what is the critical chi-square value at the 0.05 level?

The critical value is 3.84. A calculated value below that is not significant at the 95% level.

Is a calculated chi-square of 2 with one degree of freedom significant at the 0.05 level?

A value of 2 falls below the critical value of 3.84, so the result is not significant. The difference from the expected pattern could reasonably have arisen by chance.

Eduqas A-Level Geography A110QS

Coastal LandscapesLandscape

Topic overview The coast as a system: inputs, outputs, stores and transfers Sediment sources, sediment cells and dynamic equilibrium Tides, currents and wave types High and low energy coastal environments Fetch, wave refraction and wave reflection Lithology and structural geology at the coast Sub-aerial weathering and mass movement at the coast Marine erosion processes Cliffs, wave-cut platforms, geos and blowholes Headlands, bays and the cave to stump sequence Coastal transport and longshore drift Coastal deposition, flocculation and sediment sorting Beaches, spits and bars Tombolos, cuspate forelands and sandy coastlines Coastal sand dunes and aeolian processes Estuarine coastlines, tidal flats and salt marshes Coral reefs and mangrove coastlines Storms, seasons and sea level change Coastal processes and human activity Human impacts and coastal management

Glaciated LandscapesLandscape

Topic overview The glacier as a system: inputs, outputs, stores and transfers The glacial budget, mass balance and feedback The Quaternary Ice Age and the Little Ice Age Cold-based and warm-based glaciers Glacier ice movement and types of flow Types of ice mass and their distribution Freeze-thaw weathering and glacial erosion processes Factors affecting the rate of glacial erosion Cirques, arêtes and pyramidal peaks Glacial troughs, ribbon lakes, hanging valleys and truncated spurs Roches moutonnées, crag and tail and striations Glacial and fluvioglacial transport Till and types of moraine Drumlins and lowland glacial deposition Ice-contact fluvioglacial landforms Proglacial landforms: sandurs, varves and kettle holes Glacial landscape suites and change over time Periglacial ground ice and permafrost features Periglacial weathering, mass movement, water and wind Glacial landscapes and human activity

Changing Places

Topic overview Place characteristics and the home place A contrasting place: profiles compared Flows, connections and the shaping of place Global connections and MNC fast food chains Place meaning, attachment and identity in the Lake District Representing places through advertising and promotion Birmingham Grand Central and the marketed place Formal, media and popular images compared Structural employment change and the Clark Fisher model External forces driving economic restructuring Decline of primary employment in rural places Deindustrialisation, deprivation and social exclusion Government policy in deindustrialised places Retail, commercial and entertainment change in central areas Gentrification and re-urbanisation Knowledge economy clusters and their locational factors Rural rebranding and the post-productive countryside Rural management, counter-urbanisation and second homes Urban rebranding: flagship developments and cultural quarters Urban management, conflict and the Covid-19 legacy

Water and Carbon Cycles

Topic overview Systems, mass balance and the water balance Global water stores, their size and residence times Changing stores: sea level change and cryospheric processes The drainage basin as an open system Precipitation inputs and interception Infiltration, overland flow and throughflow Percolation, groundwater flow, channel flow and basin outputs River regimes and the factors that control them The storm hydrograph: components and shape Climatic factors influencing storm hydrographs Catchment factors influencing storm hydrographs Cloud formation and theories of precipitation Excess runoff: natural and human causes Deficit in the water cycle and aquifer recharge The global carbon cycle: stores, fluxes and mass balance Fast carbon pathways between land and atmosphere Ocean and atmosphere exchange and the slow carbon cycle Carbon stores in tropical rainforest and temperate grassland Land-use change and the carbon store Peatlands and the changing carbon store Rising atmospheric carbon, the energy budget and its impacts Feedback, thresholds and permafrost thaw

Global Migration

Topic overview Globalisation, global systems and global flows Classifying migrants and mapping global migration patterns A shrinking world: transport, communication and media representation Poverty, primary commodity prices and access to markets Diasporas, colonial and Commonwealth links and freedom of movement Superpowers, global hubs and the competition for migrants Remittances and the brain drain Interdependency of host and source countries Migration policies and contested views on cultural change Causes of refugee movements and internal displacement Consequences of refugee movements for refugees and host states Managing refugee crises: UNHCR, national governments and NGOs Rural push factors, land grabs and indigenous displacement Urban pull factors, export processing zones and megacity growth

Global Governance of the Oceans

Topic overview Supranational institutions and the law of the sea Maritime zones from the baseline to the high seas Chokepoints, canals and piracy in maritime trade Britain's maritime past and the Commonwealth Container shipping, oil tankers and shipping regulation Smuggling and people trafficking at sea Seafloor data cables: growth, patterns and uses Risks to seafloor cables and international protection Ownership of ocean resources and contested sovereignty Unequal access: landlocked states and indigenous coastal peoples The Global Commons and over-exploitation of marine ecosystems Sustainable management: quotas, no-catch zones and conservation zones Sources and consequences of ocean pollution Managing marine waste and the scales of ocean governance

Tectonic Hazards

Topic overview Earth's internal structure and plate movement Divergent plate margins Convergent margins, subduction and collision Conservative margins and hot spots Global distribution of tectonic hazards The hazard profile and magnitude scales Types of volcano and styles of eruption Primary volcanic hazards Secondary volcanic hazards Impacts of volcanic activity at local, regional and global scales Contrasting volcanic eruptions Earthquake characteristics and seismic waves Ground shaking, liquefaction and landslides Tsunami generation and impacts Impacts of earthquakes in contrasting contexts Human factors affecting risk and vulnerability Monitoring, prediction and warning Mitigation and the hazard management cycle

EcosystemsContemporary theme

Topic overview The value of ecosystems: goods and services Global distribution of biomes and its climatic controls The ecosystem concept, energy flow and trophic levels Nutrient cycling and the Gersmehl model Contrasting nutrient cycles: tropical rainforest and taiga Net primary productivity and limiting factors Measuring biodiversity Threats to biodiversity from local to global scale Tropical rainforests and coral reefs at risk Wetlands at risk Conserving biodiversity: strategies, priorities and funding Succession, seres and the climatic climax Sub-climax and plagioclimax communities The Arctic tundra: climate, soils, plants and animals Impacts of climate change on the Arctic tundra Sustainable use and management of the Arctic tundra

Economic Growth and Challenge: IndiaContemporary theme

Topic overview Relief and drainage patterns of India India's climate and the monsoon Water availability and water stress Population distribution, growth and structure Governance, health, education and welfare Caste, gender and cultural influences Resources, relief and climate as opportunity and constraint Droughts, floods and climate variability Economic activity, democracy and the role of government The changing size and structure of India's economy Global shift, outsourcing and offshoring India's soft power and global governance Environmental pressures of economic growth Water, food and energy security and urban pressures Sustainable development strategies in India

Economic Growth and Challenge: ChinaContemporary theme

Topic overview Relief and drainage patterns of China China's climate and the monsoon Water availability and the north-south imbalance Population distribution, growth and structure Governance, health, education and welfare Gender and minority groups in China Resources, relief and climate as opportunity and constraint Droughts, floods and climate variability Economic activity, modified communism and the role of government The changing size and structure of China's economy Global shift, offshoring and the workshop of the world China's soft power and global governance Environmental pressures of economic growth Water, food and energy security and urban pressures Sustainable development strategies in China

Development in an African ContextContemporary theme

Topic overview Changing definitions of development Simple, composite and qualitative measures of development The development gap and the development continuum Regional, ethnic and gender variation within countries The resource base: minerals and energy Soils, relief, climate and water availability Climate variability, drought and flood Free trade, trade blocs and protectionism The resource curse and conflict minerals MNCs, foreign direct investment and offshoring Tourism and fair trade Colonialism, neo-colonialism, governance and corruption Education, health, welfare and the position of women The environmental costs of development Desertification in the Sahel Strategies to promote development

Energy Challenges and DilemmasContemporary theme

Topic overview Classifying energy resources Fossil fuel stocks, reserves and their global distribution Geological factors in energy supply Insolation, wind strength and reliability Relief, dam sites and hydroelectric power Waves, tides and biofuels: favourable locations Changing global patterns of energy demand Economic and technological influences on energy demand Transfers, storage and the pricing of oil and gas OPEC, national governments and the oil and gas companies Environmental problems of energy extraction, transport and use Political, economic and technological problems of energy Appropriate technology and micro-generation in developing countries National energy mixes and world energy prices Demand reduction and energy efficiency policies Clean fossil fuel technologies and the sustainability of alternatives

Weather and ClimateContemporary theme

Topic overview Structure of the atmosphere The atmospheric heat budget Global atmospheric circulation and the tricellular model Pressure belts and planetary surface winds Oceanic circulation, continentality and altitude The world's major climate types The ITCZ and seasonal migration The monsoon climate The climate of the UK Air masses affecting the UK The jet stream and UK weather ENSO and short-term climate change Vulnerability, resilience and adaptive capacity Hazards of low- and high-pressure systems and their management Urban climates and air quality Climate change: shifting belts, tipping points and response

Geographical Skills

Topic overview Grid references, coordinates and locating a place Distance, area, direction and scale Sampling and sources of error Percentages, ratios, densities and frequencies Measures of central tendency Measures of dispersion Concentration, ratios and development indices Correlation and Spearman Rank Chi-square and significance testing Mapping techniques Graphs and diagrams Digital and qualitative field techniques

Geographical Skills

Chi-square and significance testing

3 things to know
All three components

Overview

Chi-square formula and null hypothesis.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What does the chi-square test compare?

Key term

State the chi-square formula.

Numbers

For observed values of 30 and 20 against expected values of 25 and 25, calculate chi-square.

Questions from this subtopic

Each one with the model answer underneath.

1
What does the chi-square test compare?
Model answer
Chi-square compares observed frequencies with the frequencies expected if there were no pattern. The test shows whether the difference is greater than chance would produce.
2
State the chi-square formula.
Model answer
Chi-square is the sum of the squared difference between observed and expected, divided by expected, for every category.
3
For observed values of 30 and 20 against expected values of 25 and 25, calculate chi-square.
Model answer
Each category contributes 25 divided by 25, which is 1. The total chi-square value is 2.
4
How are degrees of freedom found for a chi-square goodness-of-fit test?
Model answer
Degrees of freedom equal the number of categories minus one. Two categories therefore give one degree of freedom.
5
With one degree of freedom, what is the critical chi-square value at the 0.05 level?
Model answer
The critical value is 3.84. A calculated value below that is not significant at the 95% level.
6
Is a calculated chi-square of 2 with one degree of freedom significant at the 0.05 level?
Model answer
A value of 2 falls below the critical value of 3.84, so the result is not significant. The difference from the expected pattern could reasonably have arisen by chance.

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