Skills Flashcards
Cranedale aim
To investigate downstream changes in the river channel on the River Derwent to see if they fit Bradshaw’s model
Crandale hypothesis
Load particle size decreases with distance downstream
Helwath Beck
110m
3km from source
Drainage basin 10km2
2nd order stream
Jugger Howe Beck
100m
5km from source
Drainage basin 28km2
3rd order stream
Broxa
60m
12km from source
4th order stream
Cranedale location
North York Moors, W of Scarborough
9km stretch dropping 50m in height
High moorland plateaus in the north, coniferous forest in the east and grassland in the south
Deep V-shaped valleys
Very little human interference
Permeable sandstone overlain by impermeable peat
Drainage basin has a high rainfall - river flows all year round > large
Risk assessment > safe and accessible
Landowner’s permission to access
Can all be visited in one day
Graded profile shows…
How a river changes downstream
Height/distance from source
Bradshaw’s model
All rivers follow this model
Based on a few USA rivers
River variables in proportion > we are testing this
Bed load size decreases downstream and becomes more rounded due to erosion - abrasion and attrition
Velocity increases downstream as tributaries added and less friction with bed and banks - greater efficiency and reduced channel bed roughness
Data collection method and sampling
Sites chosen using satisfied sampling - situated progressively downstream from source > OS map used, stream orders
Cross-section sampled using systematic point sampling
1. Peg and line to work out width - 90 degrees and 30m tape measure
2. Width/10 to give 11 sample points across river (including bank)
3. Metre ruler placed down at each sample point and stone touching bottom of ruler picked up and measured along its B-axis using a mm ruler
4. Stone placed back - repeated at all three sites
Data collection strengths and weaknesses
STRENGTHS
Systematic point sampling - representative of entire channel so bias reduced
Easy to replicate (reproducible) so can be directly compared > greater accuracy, conclusions more reliable
Easy and quick - all 3 sites in one day
11 points - sufficient for Mann-Whitney U stat test
WEAKNESSES
Difficult to measure B-axis accurately with a rule > sides not straight
Easier to pick up larger stones that hit ruler - skew in favour of larger stones
Not representative of smaller stones underneath
Data presentation method
Pebble size at sample points bar chart
Mean pebbles size on bar chart
Located bar chart - on cross-section/wetted perimeter
Located proportional circles of velocity (radius)
Data presentation strengths and weaknesses and justification
STRENGTHS
All in one clear graph - patterns can be made out and links between different variables
Ease of comparison between each site
Too much data for scatter graph etc.
Valid conclusions can be drawn
Suggests link with pebble size/ velocity and cross section
WEAKNESSES
Difficult to extract data, especially circles
3 needed
Not comparing directly with different sites
Can’t compare values easily - objective
JUSTIFICATION
Relate to aim, graph shows, illustrates conclusion clearly
Better than a single graph - one axes/comparisons between variables
Better than a scatter/line graph as more than one data points per sample point
Better than a pie chart - only averages and 3 sites
Better than a dispersion graph as difficult to read and only shows one variable
Data analysis method
Mann Whitney U test
Null hypothesis and research hypothesis
Rank and calculate U values and critical value
U1 = 49.5
U2 = 71.5
CV = 30
If either U value higher than CV then reject RH and accept NH - no significant difference at 0.05 significance level
Less than 5% probability that this happened due to chance
Data analysis strengths, weaknesses and justification
STRENGTHS
Can be used on different sized data sets
Determines significant difference and chance
Quantifies a perceived relationship
WEAKNESSES
Calculation long - prone to human errors
Does not explain why difference occurred
Cannot be applied to categorised data
JUSTIFICATION
Determines whether two sets of data of the same variable are significantly different
Tests between medians - outliers not used
Test proved no significant difference as U values higher than CV
Subjective view on data
Adds statistical validity to my investigation
Appropriate as measured in mm - continuous - can be ranked
Cranedale Conclusions
No significant difference between stone size at Helwath Beck and Broxa
How could your results be of use to geographers?
Suggests Bradshaw’s model is not applicable to this/British rivers
Derwent is glaciated/rejuvenated
Secondary data used
From previous fieldwork by other groups
Weather reports
OS maps
Bradshaw’s model
Evaluation: Improvements and extensions
Use callipers instead of a rule - more accurate measure of B-axis
More sites measured for more representative data = more reliable conclusions
More points along river width - reduce error margin = reliable
Measure A,B and C axes and work out VOLUME of each stone - more accurate
Power’s’ scale of Roughness to look at pebble shape downstream (chi squared)
Compare at different rivers or in different weather conditions/seasons for comparison/different order streams - same conclusions?
Other variables measured eg velocity
Land use compared
Cranedale success
Found no sig difference
May be due to rejuvenation of River Derwent or redirection after glaciation period
Other variables may influence
Understanding has further developed - links between variables etc
How accurate/reliable?
Scatter graph uses and examples
Used when investigating the relationship between 2 continuous variables
Used in combination with Spearman’s rank
Velocity/dist from source = positive
Pebble size/ dist from source = negative
Scatter graph advantages
Clearly show positive, negation or no correlation - line of best fit
Shows strength of correlation - distance from line
Useful when carrying out Spearman’s Rank - gives a more precise and objective expression of the strength and reliability of the relationship
Graph allows analysis on which conclusions can be based - line of best fit
Lots of points in a small space
Patterns identified quickly and easily and anomalies identified
Relatively easy to construct
Shows data spread clearly
Scatter graph disadvantages
Line of best fit is a subjective judgement and can give a subjective judgement
Only 2 variables can be displayed
Too few data points can produce skewed results - incorrect graph analysis
Impossible to label data points - hard to ascertain exact values
Too many data points can quickly make graph unreasonable
Bar graph uses and example
Used to display categoric or grouped data
Absolute values and contrasts between areas and places
Simple show a single series of data eg temp/month
Comparative show 2 or more sets of dad side by side eg temp/month different locations
Compound show how the total in each bar is divided up into a number of subtotals eg traffic - cars/vans/lorries
Divergent where data is spread on either side of x or y axis eg population pyramids (y axis)
Histograms show frequency of occurrence of data eg pebble sizes in a river/frequency
Pictographs show data in the form of pictures (key) eg world pop/yrs
Bar graph advantages
Relationships can be easily perceived and compared
Original data can be easily extracted
Many potential uses - versatile
Can show pos and neg values
Pictographs make it very easy to see data
Good visual representation of statistical data - general trend
Simple to construct and easy to understand
Clear to see anomalies
Bar graphs disadvantages
Histograms can be confusing as area of bar represents data - cacluclations needed
Pictogrpahs have no actual scale - not very accurate and only a limited amount of data can be dispalcyes
Only small data sets can be plotted or patterns can be missed
Wide range of data - loses impact/difficult to read
Graph categories can be reordered to emphasise certain effects
Use only with discrete data
Limited space for labelling with vertical bar graphs
Reading accurately can be difficult
Time consuming
Line graph uses and examples
Use continuous data
Simple show a single series of data eg rainfall
Comparative show 2 or more sets of data on the same graph using the same scale eg DTM
Compound have several different components eg worl d popn/ time split into continents
Line graph advantages
Can suggest trends and estimate future patterns eg 1941 no UK census, but using 1931 and 1951 popn data, 1941 popn can be estimated (interim data can be inferred)
Can be combined with bar graphs to show more info eg climate graphs, storm hydrographs
Log and semi log scales can be used
Can compare multiple continuous data sets easily
Line graph disadvantages
Too many lines can be confusing
Only continuous data
Triangular graph uses and examples
Scatter graphs showing 3 sets of variables to see interrelationships
3 variables that each total 100 eg employment structures where employment is divided into primary, secondary and tertiary sectors as a percentage of working population
Triangular graphs advantages
Varying proportions can be seen - relative importance
Dominant component can be identified
Shows clusters
Triangular graphs disadvantages
Only work with a limited range of data - 3 variables in % form
Can be difficult to read and construct
Can be wrongly interpreted
Kite graphs uses and examples
Used to display changing characteristics of flora/fauna across and area eg different species across a dune transect - changes over a distance
Kites represent presence or absence or individual species along line of transect
Thickness of kite shows number of % of each
Represents number or percentage surface of each species
Kite graphs advantages
Can be interpreted to reveal relationships between the organisms and the physical character of the surface
Dune zones can be identifies by characteristic species
Often plotted with height and gradient of surface. This allows explanations to be attempted for any interrelationships between species or between species and surface characteristics
Width of kite, representing a single species, enables a visual comparison to be made of a distribution of vegetation at any point on section
Sees trends in statistics in a visual way
Visually effective - changes between species over distance easily identified
Any species/combinations - distinguish one from another - competition
Quick and specific % read off
Sections for large scale
Density shown
Kite diagrams disadvantages
Only works with a limited range of data Visually subjective Dominant species over estimated Scale = some species not shown Data discrete but lines show continuity Can be tricky to construct and analyse correctly Time consuming
Radial diagrams uses and example
Used to plot data in a circular fashion around a central point
Used to show orientations as given by the points on a compass eg wind rose
Used to show continuous cycles related to change over time of change in direction - polar graphs eg daily/annual progressions of temp/traffic flows
Good when one variable is a directional feature
Radial diagrams advantages
Allow you to display several independent variables
Visual
Compare multiple data sets
Radial diagrams disadvantages
Only useful with a limited type of data - scale must be continuous around the edge
Polar graphs slightly distort higher values - difficult to interpret
Anomalies difficult to spot
Scaling difficult
Pie charts and proportional divided circles uses and examples
Show how data is split (total) into separate components
Proportional circles used when size of 2 or more totals is being compared
Area of circle represents totals - can also be split eg energy sources
Useful for %s and statistical data
Pie charts and proportional divided circles advantages
Clear visual comparison of relative proportions of components and statistical data - general trend
Comparisons between charts - show changes in distribution or total
Simple to construct and easy to understand
Clear anomalies
Cumulative/discrete - many purposes
Easy to draw
Shows % of each segment
Can represent a wide range of statistical data and are visually very effective - contribution to each section is easy to see
Comparison between percentage components
Pie charts and proportional divided circles disadvantages
Very difficult to extract original data unless stated
If the amount of data is complex, the interpretation of patterns is challenging
Best used with a wide range of values within categories - difficult for smaller values
Too few/many categories is simplistic and difficult to interpret
Scales difficult for proportional circles
Calculation of amounts is difficult
Only 1 point at a time
Accuracy in drawing
Overlapping issues - maps
Dispersion diagrams and box and whisker plots uses and examples
Visual investigation of spread of data
Show a range of values in a data set
Data in one column - variable on vertical
Dispersion diagrams and box and whisker plots advantages
Range becomes apparent and clustering identified
Box and whisker analyse further - remove extreme values and focus on IQR
Dispersion diagrams of more than one data set can be constructed and compared - same scale
Skewing becomes evident eg pebble size at different sample site on a river
Often used with statistical techniques such as standard deviation
Visual representation of dispersion in a data set
Useful for making comparisons between ahead or at the same location over a period of time
Shows spread from mean
Indication of reliability
Mean, range, mode etc can be calculated
Anomalies seen
Dispersion diagrams and box and whisker plots disadvantages
Usually only display one data set
Time consuming to compare many
Data must be in a form which can be placed along a number line
Works better with lots of data
Sketch maps uses and examples
Display certain features of an area for a clearer understanding
- rough map of study site
eg follow a river along its course
Sketch maps advantages
Good memory tool - accompanied with detailed annotations
Sketch maps disadvantages
May not be accurate
OS base maps uses and examples
Show direction, distance, relief, routeways and recognisable features of lank marks eg car parks
eg useful when understanding why river channel variables are different at different parts of a river > stream orders
OS base maps advantages
Universally recognised
Proportional and accurate
OS base maps disadvantages
Too much data
Maps with located proportional symbols uses and examples
Used to investigate spatial patterns and compare characteristics of different places
Located symbol maps eg location of river study sites
Located proportional bars eg world population current/future
Proportional divided circles eg showing proportion of work force in P/S/T industry
eg show spatial patterns well - earthquake maps show plate boundaries well
Anomalies can be identified and begin to explain (hot spots)
Maps with located proportional symbols advantages
Located proportional bars easy to read Good visual representation of data Large ranges Not dependent on size Adds data/location
Maps with located proportional symbols disadvantages
Show only a limited number of points Large range looks messy/cluttered Small range makes patterns hard to identify Wide range of extreme values - scale? Scale needs to be right so scale fits Difficult to produces Can't extract data Overlap = confusing
Maps showing movement: flow, desire and trip line maps uses and examples
Flow line represent movement along a given route - variable width along a given route. Width of arrow is proportional eg traffic
Desire lines show movement of a population from one place top another eg migration
Trip lines show where people have visited - central point eg supermarket
Maps showing movement: flow, desire and trip line maps advantages
Good to show direction and size of movement (flow)
Good visual impression of movement (flow)
Clear sense of direction
Location compared
Only concentrate on origin and destination and number on route - generalised (desire)
Possible to identify sphere of influence (trip)
Maps showing movement: flow, desire and trip line maps disadvantages
Best used on large scale maps - % or rate plotted (trip)
Must use same scale (trip)
Ignores actual route taken (desire)
Non-density (trip)
Maps lack precise interpretation unless statistical data is added - overlap (flow)
Desire and trip lines only interested in source and destination areas
Hard to draw
Difficult to show meeting point (lots of lines)
Chloropleth maps uses and examples
Show spatial distributions, using shadings of different densities to represent different densities of population or different %s of land of a particular crop etc.
Chloropleth maps advantages
Very effective at displaying distribution and spotting patterns
Easy to read
Show which areas have similar/different densities - compare
Visually effective
Shows density
General trend and anomalies identified
Chloropleth maps disadvantages
Do not show total values of distribution they represent
Suggests abrupt changes, but usually more gradual
Consistent values implied by shading - don’t reflect densities
Size of administrative area affects size
Only applied where clear boundaries exist
Hides variation within each zone - actual data at a point not shown
Class intervals chosen carefully to see patterns
Can’t extract data from a point
Large variation = lots of colours and confusing
Measures of central tendency uses and examples
Calculate ‘average’ > representative of all data - midpoint = typical
Mean, median and mode
Stone sizes
Measures of central tendency advantages
Can compare with other averages
MEAN: useful in small ranges
MEDIAN: not affected by extreme values
MODE: shows skewing (highest frequency)
Measures of central tendency disadvantages
MEAN: heavily influenced by extreme values
MEDIAN: not based on figures, but rankings; not arithmetically sound
MODE: not useful with data with no representative figures; useful with only large data sets
Measures of dispersion uses and examples
Analyse spread of data
Stone sizes
IQR: rank order; median is accompanying central tendency
STANDARD DEVIATION: shows how the data is spread about a mean value if there are fixed independent variables and a frequency of these variables eg pebble size at one site in a river - often shown in a histogram with IV on horizontal axis and frequency on vertical axis. Higher value = more spread out from mean. Parametric test as it assumes normal distribution pattern - bell shaped curve
Measures of dispersion advantages
IQR: removes outliers
STANDARD DEVIATION: average amount by which the values in a data set vary from the mean - low = few extreme values and a more reliable representation of mean
Shows how much data is clustered around a mean value; gives a better idea how the data is distributed
Measures of dispersion disadvantages
SD: doesn’t give you the full range of the data; it can be hard to calculate; only used with data which can be plotted on a histogram so where an independent variable is plotted against the frequency of it; it can be affected by outliers in data; assumes a normal distribution pattern
Spearman’s rank correlation test uses and examples
Measures correlation (linear relationship) between the similarity of 2 different variables
Scatter graph drawn first to test relationship
-1 > 1 -ve > 0 > +ve
Check against table/graph critical values
eg distance downstream and speed of flow of river
Assumes no distribution pattern in the data so is non-parametric
Degrees of freedom = number of paired measurements
Reject NH if value calculated is higher than value of CV
Spearman’s rank correlation test advantages
Shows the significance of the data (or due to chance)
Proves/disproves correlation
Allows for further analysis
Doesn’t assume normal distribution
Tests strength of relationship
Does not imply a causal relationship ie change in 1 variables leads to change in other
Spearman’s rank correlation test disadvantages
Not reliable with fewer than 10 pairs of data
More than 30 pairs is difficult
Compares ranks not actual data
Can be difficult to work out
Quite a complicated formula
Can be misinterpreted
Need two sets of variable data so the test can be performed
Chi-squared test uses and examples
Examines spatial distributions
Compares data that have been collected (O) against a theoretical random distribution of those data (E)
Compares means
How dissimilar to expected?
eg provision of GP services in a city evenly spread? or concentrated in wards with high average incomes?
eg Spread of ethnic groups within wars of a city
Degrees of freedom = n-1
Calculated value higher than CV then reject NH
Chi-squared test advantages
Can test association between variables
Identifies difference between observed and expected
Objective statistical significant results
Chi-squared test disadvantages
Can’t use percentages
Data must be numerical
Categories of 2 are not good to compare
The number of observations must be 20+
The test becomes invalid if expected values are below 5
Quite complicated to get right - difficult formula
Large data sets - categoric
Comparison of O/E is a preliminary analysis
More complicated when O data evenly spread
Mann-Whitney U test uses and examples
Do 2 sets of data come from the same or different populations?
Assumes distribution for same population data
If lowest U value is less than CV (found in table), NH rejected
Assesses degree of overlap between 2 distributions more than would be expected by chance
Median values compared to see if there is any correlation
5-20 points best used
Mann-Whitney U test advantages
Shows the median between 2 sets of data
Good with dealing skewed data so data doesn’t need to be normally distributed
You can divide the boundaries of 2 groups
Only needs one variable in a set of data
Distribution can be uneven ie unpaired
Rid of outliers/not swayed by anomalies
Compares 2 data sets not normally distributed - data capable of being ranked
Point-dispersal graph used
Non-parametric
Mann-Whitney U test disadvantages
Best used with 5-20 small samples (less accurate)
More appropriate when data sets are independent of each other
More appropriate when both sets of data have the same shape distribution
Have to have equal sample sizes
What do statistics do?
Interpret and analyse data collected in fieldwork investigations
Aids improved understanding of geographical phenomena under investigation
Bigger sample size = more reliable conclusions
Hypothesis/null hypothesis established
Results tested for significance levels against tables - 5%/1% exceeded significant and null hypothesis
Therefore reliable and can be explained and justified to increase understanding
If results not significant, further geographical explanations sought
Can be used with presentation techniques to further develop understanding
Allows you to quantify a perceived relationship
How do maps improve understanding?
Aid interpretation and analysis of data to aid improved understanding of phenomenon under investigation
Basic tool of a geographer
Show spatial patterns - identified
How do graphs improve understanding?
Show data in continuous form
Give a clear visual representation of data so that patterns can be identified and anomalies found
Often used before stat tests to see if there is a relationship as often test relationships or allow a visual comparison between variables
