Stage 4- Present the data collected in appropriate forms

Types of data

• Discrete, ordinal, continuous, areal, time-series, period
• qualitative versus quantitative

Aspects of presentation to be considered

• type of presentation should fit type of data
• use of colour or shading
• size of diagram or symbol- scale is crucial
• ease of comparability
• annotation- location, detail etc
• lettering- font, spacing, size
• located on a map or not
• add a key, scale, title and north if using a map
• logical organisation to help analysis

Non-spatial displays

• Tables- simple and effective way of displayingraw data
• Charts- bar, pie, rose, proportional symbols
• Graphs- line, scatter, triangular, compound, positive and negative

Spatial displays

• Maps- think scale, projection
• Isopleths- think interval, interpolation, curve
• Choropleths- think boundaries, shading, class interval
• Others- trend surfaces, topological
• Located symbols, e.g. dots, proportional circles- think of scale/size, location and key

Movement

• Flow lines, trip lines- width, direction, arrows and subdivisions

• Types (landscape, oblique, aerial, satellite) think scale, direction; remember they capture an instant of reality
• Maps show static long-term features
• Always include scale (e.g. person, building, etc) time of day/year taken, title
• Annotate- arrows to selected items of interest and minimal text

When selecting method of presentation, consider:

• The data type
• The purpose of the diagram
• How accurate the plotting must be
• The range of values in the data set
• The space available for the diagram
• The visual impact desired
• Labelling and annotating
• The time available
• Calculations required
• Use of ICT

Common problems- scale, size of diagram, data interval, data class division, use of colours or shades, labelling

When looking at a diagram check: title and figure number/letter, sensible scale or key, note of its location and appropriate shading or colouring

• A large number of values may be generalised and represented as tables
• Tabulating data usually involves putting values into groups or classes either nominally or numerically
• Frequncy distribution tables show values grouped in numerical classes- requires two key decisions
  • The number of classes needed
  • The size of the internal between classes
  • Two few classes mean that data become excessively generalised and important detail is lost, however, too many classes fragment the data and obscure the overall picture

• Used for most types of data but especially discrete or time series data
• Can be horizontal or vertical. length of bar is proportional to its value
• Advantages
  • Quick and easy
  • Very visual as provides instant visual impression
• Disadvantages
  • Should only be used for interval data
  • Width of bar can mislead over the value represented by the bar
  • Gaps should be left between the bars otherwise it is known as a histogram

• Used to show constituents of a whole
• Must keep the divisions in the same order if they are being compared
• Disadvantages
  • Cannot have to many sections
  • Difficult to use colours
  • Not always easy to compare

• The stepped appearance of a histogram is determined artificially by the choice of class intervals, so a more meaningful way to show the data is to replace the bars with a smooth frequency distribution curve
• A normal distribution is approximately symmetrical and bell shaped and can vary in their degree of sharpness or flatness- property known as kurtosis
• Many data sets are asymmetricaol or skewed
  • Positively skewed distributions are where the 'tail' of the distribution extends to the right occur widely
  • Negatively skewed distributions where the 'tail' extends to the left are less common
• Frequency distributions are sometimes plotted as cumulative frequency curves- they show the proportion of a data set above or below particular thresholds

• Used with percentage data to show the constituent parts of a whole
• Advantages 
  • Very visual
  • Easy to compare
• Disadvantages
  • Must use percentage data
  • Too many divisions confuse the eye
  • Need to standardise order of segments
  • Everyone uses them
  • Difficult to label so that all the sectors can be easily read

• Used to show directions
• Length of bar usually reflects frequency and width or some other aspect
• Disadvantages- time consuming to draw and takes time to read as three aspects shown

• The area of the symbol is proportional to cube root of data value
• Advantages- copes with large numbers and provides good visual appearance
• DIsadvantages
  • Time consuming to calculate and draw
  • Not easy to compare accurately
  • Scale even more complex to draw

• Advantages- good at showing trends or patterns (and anomalies)
• Disadvantages- should only be used for continous variables which are rare

• Used to plot 2 variables, x and y
• Variable x, the independent variable, which causes change in y, the dependent variable, is plotted on the horizontal axis
• The dependent variable (y) occupies the vertical axis 
• Scatter charts provide a visual impression of the relationship between variables: the closer the scatter of points to a straight line, the stronger the relationship
• Of the points on a scatter chart trend from bottom left to top right, the relationship is positive
• An inverse or negative relationship trends from top left to bottom right and shows that an increase in x produces a corresponding decrease in y

• Describes the inequality in a distribution
• Both variables are plotted as cumulative frequencies arranged by the rank order
• The more the Lorenz curve deviates from the diagonal the greater the unevenness of the population distribution
• The Gini coefficient provides a more precise measure of inequality
  • It is the ratio of the area between the diagonal and the Lorenz curve, to the total area below the diagonal
  • The ratio is usually multiplied by 100 and expressed as a percentage
  • The higher the value of the coefficient the more uneven the distribution is

Dispersion diagrams

• Are single-axis charts which show the distribution of values in small data sets

Triangular charts

• Used to plot 3 percentage values whose sum is 100%
• Can provide a visual comparison of differences between places, as well as changes at a place and time

Scatter charts

• Used to plot 2 variables, x and y
• Variable x is the independent variable causing changes in the dependent variable, y
• The closer the scatter of points approximates a straight line, the stronger the relationship 

• Maps are an important means of presenting statistical information
• They have particular value because they:
  • Make it easier to relate data to specific locations
  • Help to identify geographic trends and patterns more effectively than data tables and charts
• Statistical maps show the spatial distribution of quantitative data
• However to some extent all statistical maps compromise to achieve visual impact and clarity there is inevitably some loss of detail and accuracy
• Effective statistical maps show spatial information clearly and store statistical data that can be retrieved at least in general form without difficulty
• Looking at 5 types of statistical maps:
  • Dot maps
  • Choropleth maps
  • Proportional symbols maps
  • Isoline maps
  • Flow maps

• Show the location of a given quantity of a variable with a dot of constant size
• Advantages 
  • Simple
  • Shows clear location of values
  • Provide information on the distribution of phenomena within areal units
  • Visual impression of geographical distributions and densities
  • Spatial pattern is not interrupted artificially by the boundaries of areal units
• Disadvantages
  • Difficult to see/count
  • Exact location not always known
  • Time consuming to draw partly because a good deal of prior information is needed about the factors that control geographical distribution
  • They can also give a misleading impression of accuracy and precision
  • In high-density areas where the dots begin to merge, recovering accurate information may be difficult
  • In low-density areas they provide minimal details about the actual distribution

• 1. Source a base map, showing the geographical areal units of which data are aggregated
• 2. Decide on the number of items represented by each dot. Dot values should be small enough to allocated at least a few dots to the areal units of lowest denisty
• 3. Decide on the size of dots. Dot size will depend partle on the dot value and partly on the scale of the map. dots must be consistent in shape and size
• 4. Allocate the appropriate number of dots to each areal unit and plot on the map. the placement of dots must be guided by prior knowledge of the factors that affect the distribution.
  • Care should be taken to place some dots in boundary zones between statistical areas
  • within high density areas the dots should be placed randomly
  • in low density areas the dots should be allocated to areas of known importance
• Add a key, title, scale and direction to the map

• Show spatial variations in values between areas by colour or shading
• Use standardised data such as ratios, percentages and averages
• Advantages
  • Quick and easy to construct 
  • Very visual
  • Useful when data is published in bundles for areal units such as super output areas, wards and parishes
• Disadvantages
  • Interval size is critical
  • Treats area as a whole
  • Shading issues
  • Provide no information about the internal distribution of values within real units, this becomes a major limitation where units are large and distributions are irregular
  • Areal units often vary in size, large units can have a dominating effect on the appearance of the map
  • The boundaries of areal units often create sudden discontinuties in spatial patterns that are not present in reality

• 1. Calculate standardised values for area units, record them on a base map which shows the units for which data are available
• 2. Divide the data set into classes or groups. A balance between excessive generalisation and too much detail is needed
  • Too many classes will overcomplicated the map and make it difficult to recognise differences in colour or shading
• 3. Decide on class intervals. three methods are available depending on the type of information being mapped
  • (1) Fixed intervals where a data set has meaningful threholds
  • (2) Intervals designed to reflect the natural breaks in the data sets
  • (3) Fixed intervals based on mathematical relationships
  • At the simplest level, arithmetic classes are obtained by dividing the range of values by the number of classes- this method has problems if the data is skewed- it is important that no single class should occupy too large an area
• 4. Choose a logical system of colouring or shading. Monochrome maps use gradation of tones from light (low) to dark (high) and if colours are used softer clours (greens and yellows) represent lower values and stiking colours (red) represent higher values
• 5. Add a key, title, scale and direction to the map

• The symbols used are circles, squares, triangles and bars
• The area of the symbol is proportional to the value it represents
• Advantages
  • Can cope with large numbers
  • Show absolute values
  • Impact is clear and immediate
  • Visual impression
• Disadvantages
  • Time consuming to calculate and draw
  • Not easy to compare accurately
  • Tendency to underestimate the values represented by larger symbols, for example, doubling the sides of a square or radius of a circle increases the area four times, not twice
  • Causes problems when several symbols are concentrated within a small area- outcome may be overcrowding, with excessive overlap of symbols making interpretation difficult
  • They convey no information on the spatial distribution of values within geographic units

• 1. Choose a symbol- circle, square, triangle or bar
• 2. Choose a scale. The largest symbols should not obscure the symbols in adjacent areal units. Overlapping symbols are acceptable in high-density areas, providing their radii are visible to allow estimates of values.
• 3. Calculate the area of each symbol
• 4. Plot the symbol centrally within areal units
• 5. Add a key, title, scale and direction to map

• Isolines are lines on maps that join places of equal values
• Although derived from point measurements they represent distributions that have a continuous surface therefore are not appropriate for representing geographically discrete phenomena such as population
• Advantages
  • Helps to show or identify patterns from individually located values
  • Overview of spatial patterns
• Disadvantages 
  • Interval size is vital
  • Interpolation is dubious or guesswork
  • Shape is guesswork
  • More subjective that most other statistical maps
  • Assumptions of interpolation are rarely tenable and may be misleading when distributions are highly irregular

• 1. The point locations for data sources, or the areal units for data aggregation need to be identified on a base map
• 2. Values are plotted as points on the base map
• 3. Decide on the number of isolines and their values.
  • 5 or 6 is likely to be sufficient. Larger numbers make drawing impractical
  • The fewer the points on the map, the fewer the isolines
  • It is conventional to use regualar intervals between isolines
  • The allocation of values to isolines is similar to the procedure for defining class boundaries on choropleth maps
• 4. Fit the isolines by interpolation. Interpolation assumes a constant gradient of change between data point values. When drawing isolines they must never cross
• 5. Isolines should be numbered and if required, the areas betwen them layered or shaded
• 6. Add a key, title, scale and direction to the map

• Flow maps show the movement of people, vehicular traffic, goods and information between places
• Movements are represented as lines proportional in thickness to the volume of flow
• Flow paths can either be non routed or routed
• Advantages
  • Shows movement along routes, direction, volume and distance
  • Can be subdivided to show characteristics
  • Effective for showing the general pattern of movement and interaction between places
• Disadvantages
  • Following exact route can be over complex, 
  • Can mislead if it doesn't follow exact route
  • Highly generalised
  • Abrupt changes of flow often occur at count points which may not reflect actual changes on the ground

• 1. A base map is needed showing either the point location where flows are recorded or the areal units for data aggregation
• 2. Decide on the number of flow classes and the interval between classes
  • Usually 5 or 6 classes are sufficient
  • Class intervals may be arithmetic or geometric, butmust cover all values
• 3. Select a suitable scale for line widths, line width will depend on the scale of the map and the flow values. Widths will be proportional to the flow volumes. On non-routed maps the need to avoid flows which overlap may also influence widths
• 4. Draw the flows to scale and shade with a single colour to emphasises the flows. on computer drawn maps, base map may be muted
• 5. Add a key, title, scale and direction to the map