2. Why do we usually sample? <ul><li>Is it possible to measure all the pebbles on a beach to work out the average pebble size? </li></ul><ul><li>Chances are the answer is no- therefore as geographers we can sample a number of the population to gain an insight into the patterns. </li></ul><ul><li>We can also sample in human geography as well. </li></ul>
3. Why is sampling desirable? <ul><li>It is quicker than measuring every item. </li></ul><ul><li>It is cheaper </li></ul><ul><li>Often it is impossible to measure everything. </li></ul><ul><li>It is unnecessary to measure the whole population because a carefully chosen sample can give you a result which is close to the figure you would obtain even if you measured every pebble. </li></ul>
4. Why is sampling desirable? <ul><li>We may wish to take a snapshot of the population at one moment in time- for example meteorological readings are taken simultaneously at only a limited number of sample sites in the UK and sent to the met office. </li></ul><ul><li>It is sometimes impossible to gain access to the complete population </li></ul><ul><ul><li>For example if we asked a questionnaire to everybody in Plymouth about their shopping habits some could be quite in their rights to say no. </li></ul></ul>
5. Why is sampling desirable? <ul><li>We may not know the population size or location and therefore we would be forced to sample. </li></ul>
6. Avoiding Bias <ul><li>Bias can arise for many reasons. </li></ul><ul><li>The data from which the sample is taken is biased- For example why would selecting the addresses of 100 people from a telephone directory be biased? </li></ul><ul><li>Insufficient care in the choice of sample may result in an unrepresentative data set- for example asking a spread of young and old people is better than only asking young or only old. </li></ul>
7. Avoiding Bias <ul><li>4. The time the sample was taken may produce bias- Why would asking a street questionnaire at 10:00 on a weekday be biased? </li></ul>
8. Sampling Methods. <ul><li>Before selecting a sample it is necessary to decide on the sampling method. </li></ul><ul><li>When selecting samples from an area on the ground or from a map there is one decision to be made </li></ul><ul><ul><li>Are you looking for points, lines or quadrats- these are known as the three spatial sampling methods </li></ul></ul>
9. Point sampling <ul><li>This involves choosing individual points and sampling those points, such as specific houses down a street or crop types on a land use map. </li></ul>
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11. Line sampling <ul><li>This involves taking measurements along a line- for example to sample vegetation across a series of sand dunes and note the dominant vegetation type along each part of the line. </li></ul>
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13. Quadrat sampling. <ul><li>Also known as area sampling </li></ul><ul><li>This involves marking a square on the ground and noting the occurrence of the feature you are interested in within the square. </li></ul>
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15. How do we decide what to do? <ul><li>There are three commonly used methods. </li></ul><ul><li>Random Sampling. </li></ul><ul><ul><li>Decide how many sample points you want. </li></ul></ul><ul><ul><li>Obtain random numbers- either from a published sheet or from a calculator which generates random numbers. </li></ul></ul><ul><ul><li>Overlay a map of the area with grid lines and number them. </li></ul></ul><ul><ul><li>Use random numbers to read off grid references. </li></ul></ul><ul><ul><li>Find out the land use at each points chosen by visiting the places on the ground or from a land use map. </li></ul></ul>
16. Random sampling. <ul><li>Can be used for most types of sampling </li></ul><ul><li>The provide a means by which we can select samples in the knowledge that no human bias is involved. </li></ul><ul><li>The disadvantage is that if the sample size is small we might obtain an unrepresentative result. </li></ul>
17. 2. Stratified sampling <ul><li>With this type of sampling we start by asking the question Are there subsets of the pattern being measured that must be included within our sample? </li></ul><ul><li>For example- we might think older people shop differently to young- therefore our sample must contain old and young people. </li></ul><ul><li>These subsets are known as strata. </li></ul>
18. 2. Stratified sampling <ul><li>In order to sample this way you plot the points on a map as in random sampling but do not allow more than the allotted number of points to fall on each area of study </li></ul><ul><ul><li>you then ignore an excess points which are chosen by random numbers. </li></ul></ul>
19. 2. Stratified sampling <ul><li>This has the great advantage in that it helps to reduce any bias which might possibly arise if samples were chosen completely at random. </li></ul><ul><li>The only problem with the method is identifying what the strata should be. </li></ul><ul><li>The difficulty is knowing for certain that the strata are relevant and how many strata to create within each- how many age division for example. </li></ul>
20. 3. Systematic sampling. <ul><li>In this method the sample is chosen according to some agreed interval- i.e we visit every 5 th house or measure every tenth pebble. </li></ul><ul><li>The advantages of this method are great </li></ul><ul><ul><li>It ensures complete coverage of the map. </li></ul></ul><ul><ul><li>It is simple to do. </li></ul></ul><ul><li>The danger is that the systematic sample might inadvertently pick up some underlying regularity. </li></ul>
21. Sample size. <ul><li>The size of the sample will usually be dictated by the time available. </li></ul><ul><li>The larger the sample the better the quality of the results. </li></ul><ul><li>Also your capacity to handle the data collected influences the size of the sample- for example computers now allow us to collect more data and produce accurate analysis and graphs. </li></ul>
22. Required sample size. <ul><li>There is a way to calculate the best possible sample size- known as the required sample size. </li></ul><ul><li>We will use measuring pebbles on a beach to calculate this. </li></ul>
23. Required sample size. <ul><li>Collect a pilot sample of 30 pebbles- Measure their lengths. </li></ul><ul><li>Calculate the standard deviation of the results- this is how far the results are away from the mean- another lesson for this. </li></ul><ul><li>Decide on a tolerable margin of error- how close you wish to be to the result you would obtain if you measured all the pebbles- e.g 0.5 cm </li></ul><ul><li>Decide on the level of certainty you wish to achieve- e.g 90% sure that the average length of the pebbles measured lies in the 0.5 cm margin or error. </li></ul><ul><li>Calculate using this formula </li></ul><ul><ul><li>zs </li></ul></ul><ul><ul><li>n= d </li></ul></ul>2 N= required sample size. Z= z score (a different table you aquire as a table of numbers) S =standard deviation. d= Tolerable margin of error.
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