Drawing sampling grids by hand
Although there is available software that can generate grids easily on a map, we do not always have the luxury of having electronic or digitised type of maps or map data that can be used to generate the map itself on the computer. It is often the case that we just have printed maps to work with. Hence, Being able to draw appropriately sized grids on a map by hand is still an important skill in spatial sampling.

###### 1. Finding the right map

The ideal map for spatial sampling would be a large scale map of the area to be surveyed. This would be a map that shows as much detail (e.g., towns, villages, roads, water bodies, etc.) and shows the entire survey area. For very large areas, this would mean having a collection of large scale maps that when put together forms the entire survey area. The map scale is also an important feature to have in a map for spatial sampling as it allows us to make measurements on the map that are in proportion to the actual measurements in the real setting. Step 2 explains further how to make measurements on the map using the map scale.

Figure 1. Map showing cities and villages with a map scale

###### 2. Understanding the map scale

The map scale allows us to make measurements on the map that would be in proportion to measurements that we would want in the actual or real setting. The scales allow us to determine the right size of the grids to draw on the map that would match the size that we require in the actual or real setting. It is therefore important to learn how to interpret the map scale and how to use it to make measurements on the map.

Figure 2 is a zoomed in view of the bottom left corner of the map shown in Figure 1. Here you can see two types of map scales.

Figure 2. Two different types of map scales

The upper scale presents a ratio hence it is called a ratio scale. The ratio scale, as the name implies, is a ratio between 1 unit of measurement on the map and its equivalent number of units measurement in the actual setting. By default, unless stated otherwise in the map, the unit measurement is in centimetres (cm). The ratio scale in Figure 2 is 1:570,000. This is saying that for every 1 centimetre measurement in the map, it corresponds to 570,000 centimetres (or 5,700 metres or 5.7 kilometres) in the actual setting.

The lower scale presents a graphical scale. The graphical scale basically indicates that the length of the line graphic as measured on the map is equivalent to the measurement indicated when it comes to the actual setting. So, in the example in Figure 2, if we measure the length of the line in the graphical scale and it measures 2 centimetres, then the scale is telling us that every 2 centimetres on the map is equivalent to 20 kilometres in the actual setting. Compared to the ratio scale, the graphical scale requires you to measure the line first for you to come up with the ratio between the map and the actual setting.

###### 3. Making measurements on the map

Based on this understanding of map scales, we can now make measurements on the map that would help us draw grids.

Now, let’s say we want to draw square grid on the map shown in Figure 2 and we want give it a size of 10km by 10km. This means that we need to calculate based on the map scale the equivalent measurement of 10km on the map. For this, let us use the ratio scale of 1:570,000 as our reference.

To make things clearer and easier, let us convert the map scale into a unit that will match the unit of square grid that we are trying to create. Remember, the map scale indicates that every 1 centimetre

on the map is equivalent to 570,000 centimetres in real life or in the actual setting. We can convert 570,000 centimetres into kilometres so that we are working with the same units as the square grid we are trying to create. So, we first calculate how many centimetres there are in a kilometre:

$$\frac {100 \text { cm}}{1 \text { m}} \times \frac {1000 \text { m}}{1 \text { km}} = \frac {100000 \text { cm}}{1 \text { km}}$$

and then we calculate how many kilometres there are in 570,000 cm as follows:

$$\frac {x}{570000 \text { cm}} = \frac {1 \text { km}}{100000 \text { cm}}$$

$$x = 1 \text { km} \times {\frac {570000 \text { cm}}{100000 \text { cm}}} = 5.7 \text { km}$$

So, our converted map scale is 1 centimetre on the map is equivalent to 5.7 km in the real world. Using the ratio, we can now calculate how much centimetres on the map is equivalent to 10 km in the real world. We use the following calculations:

$$\frac {x}{10 \text { km}} = \frac {1 \text { cm}}{5.7 \text { km}}$$

$$x = 1 \text { cm} \times {\frac {10 \text { km}}{5.7 \text { km}} \approx 1.75 \text { cm}}$$

###### 4. Drawing the grid

Now that we know that 1.75 cm on the map is equivalent to 10 km in the real world, we can now draw the grids using this measurement.

We would need drawing materials such as pencils, rulers and erasers. Ideally, we would want to protect the maps as they are hard to come by and can be expensive to produce or have printed. So, if you decide to draw directly on the map, soft HB or No. 2 pencils would be ideal as they mark lightly on paper and can easily be erased. An alternative would be to use an clear acetate sheet that covers the whole map (or multiple sheets that when put together will cover the whole map) and draw on the acetate with special markers (either permanent or non-permanent or a combination of both) so as to preserve the paper map.

Using a ruler and starting from either west or east or north or south of the map, measure equal distances of 1.75 cm intervals up to the edge and even a little bit beyond the borders of the map. If you are drawing a rectangular grid, then the measurement of the intervals going west to east will be different from north to south (this is further discussed below on creating hexagonal grids).

Once you have marked these intervals, you can now draw straight lines going north to south and west to east. This will produce the square grids of 10 km by 10 km.

Figure 3 is an example of a map with a 10 km by 10 km grid. Figure 4 is an example of a map with a rectangular grid.

Figure 3. Map with 10 km by 10 km grid

Figure 4. Map with rectangular grid with 15km by 8.7km grid

###### 5. Drawing hexagonal grids on a map

Following is a step-by-step tutorial on stage 1 spatial sampling method using hexagonal grids.

5.1 Find a map
The first step is to find a map of the assessment area. A map showing the locations of all town and villages in the assessment area is essential. For assessments over a large area such as a whole country or regions of a country, it will be practical and useful to have instead:

• A small-scale map of the entire large area. A small-scale map shows the entire large area but with less detail and geographic features. As such, the small-scale map does not need to show the location of all towns and villages in the assessment area. Example of small-scale map is shown in Figure 1 above.
• A collection of large-scale maps that together form the whole large area. Large-scale maps show only a small portion of the entire area being assessed but they have lots of details and features included. Large scale maps are useful in creating the sampling grids, selecting sampling points and locating the precise location of sampling villages. Examples of large-scale maps are shown in Figure 5 below.

Figure 5. Example of collection of large scale maps

The small scale map will be useful for identifying initial sampling locations. The large scale maps will be useful for identifying the precise location of sampling points and for selecting the communities to be sampled.

5.2 Decide the area to be represented by each sampling point

The easiest way of thinking about this is as a function of the intended maximum distance d of any village / community from the nearest sampling point.

If you are surveying the coverage of a programme treating a rare condition (e.g. SAM) then it is a good idea to select a small value for d. This helps to ensure that large areas are not represented by very few distant sampling points just because some sampling points yield no cases. The alternative to choosing a small value for d is to sample more intensively at or around each sampling point (i.e. taking a bigger sample from each community and / or sampling in more communities). A value for d of 10 km will probably be small enough in most circumstances.

For MAM on the other hand, we can expect more cases to be found in each village / community to be sampled. Also, because our case-finding approach is a house-to-house sampling with verbal census, we are sampling intensely in each sampling point with the expectation that we are finding all (or nearly all) MAM cases in each sampling village / community. For this reason, we can look into the possibility of having a d value higher than 10 km.

5.3 Draw a grid over the map
The next step is to draw a grid over the map. The size of the grid is determined by the distance d that you decided in section 5.2 above.

The grid is rectangular rather than square. The width of the grid in the east-west (x) direction is different from the height of the grid in the north-south (y) direction.

The width of the grid in the east-west (x) direction is calculated using:

$$x = \frac {3d}{2}$$

where d is the distance value that you decided in section 5.2.

The height of the grid in the north-south (y) direction can be calculated using:

$$y = \frac {\sqrt {3}d}{2}$$

where d is the distance value that you decided in Step 2.

For example, if $d = 10 \text { km}$ then:

$$x = \frac {3d}{2} = \frac {3 \times 10}{2} = \frac {30}{2} = 15 \text { km}$$

$$y = \frac {\sqrt {3}d}{2} = \frac {1.73 \times 10}{2} = \frac {17.3}{2} \approx 8.7 \text { km}$$

Figure 3 above is an example of the grid on a map at $d = 10 \text { km}$.

Table 1 below shows the grid sizes for different values of d:

Table 1: Grid sizes for different values of $d$

$d$ $x$ $y$
5 7.5 4.3
6 9.0 5.2
7 10.5 6.1
8 12.0 6.9
9 13.5 7.8
10 15.0 8.7
11 16.5 9.5
12 18.0 10.4
$d$ $x$ $y$
13 19.5 11.3
14 21.0 12.1
15 22.5 13.0
16 24.0 13.9
17 25.5 14.7
18 27.0 15.6
19 28.5 16.5
20 30.0 17.3

When drawing the grid make sure that it covers the entire survey area.

It is usually best to draw a grid that covers an area that is a little larger than the entire survey area. This helps to ensure that the survey will sample the entire survey area.

If you are drawing the grid directly onto the map then use a soft pencil (e.g. a 2B or #1 pencil). A soft pencil will not damage the surface of the map and is easy to erase should you make a mistake or need to draw a different grid.

5.4 Create an even spread of sampling points
Sampling points are located at the intersections of the rectangular grid in a staggered fashion. Make sure that your sample points go right to the edge (or even over the edge) of the survey area. This helps to ensure that the survey will sample the entire survey area.

Figure 6. Map with alternating sampling points

5.5 Select the communities to sample
Select the community (or communities) closest to the sampling points identified in section 5.4.

If you are investigating the coverage of a selective program for a rare condition (e.g. SAM) then you will need to select several communities in order to be confident of finding cases.

If you are investigating the coverage of a universal program with a limited age-range (e.g. EPI or GMP programs) or are investigating the prevalence of a condition or a behaviour then you should select a sufficient number of communities to give you a sample size of about twenty (20) or more from each sampling point.

The position of the sampling point is moved to the position of the selected community. This is shown in Figure 7 below.

Figure 7. Map with selected villages for sampling

If more than one community is selected then the position of the sampling point is moved to the middle of the selected communities. This is shown in Figure 8 below.

Figure 8. Map with selected multiple villages for sampling

You may drop sampling points if you find that many sampling points are clustered closely together. You may move or add sampling points if you find that there are populated areas that do not contain sampling points. The aim is to create an even spread of sampling points over the entire survey area.

5.6 Label each sampling point
Give each sampling point a unique identifying label:

• The label may be a number or a name.
• The label must be unique.
• The label is used to identify which community belongs to which sampling point.

The label is used when collecting, organising, and analysing data. Figure 9 is an example of a map with sampling villages labelled.

Figure 9. Map with selected sampling villages labelled

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