# Probability vs nonprobability sampling

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breed [households household] patches-own [ psize ] households-own [ income ] globals [ average-estimate average-100-estimates n ] to setup clear-all set-default-shape households "house" ask patches [set pcolor green] ask n-of No-of-settlements patches [ set psize random-normal Average-settlement-size Std-dev-settlement-size sprout-households psize [ set size 0.5 set income psize * 2 + random-float 3 set color white left random-float 360 jump random-normal 0 psize / 10000 ] ] reset-ticks end to random-sample let pom 0 ask households [set color white] ask n-of Sample-size households [ set color red set pom pom + income ] set average-estimate pom / Sample-size end to hundred-random-samples set average-100-estimates 0 let pom 0 set n 0 clear-plot repeat 100 [ set n n + 1 random-sample set pom pom + abs (average-estimate - mean [income] of households) * 100 / mean [income] of households tick ] set average-100-estimates pom / 100 end to convenience-sample let pom 0 ask households [set color white] ask one-of patches with [((count turtles-here + count turtles-on neighbors) >= Sample-size) and (count turtles-here > 0)] [ ask one-of households-here [ set color red ask n-of Sample-size households in-radius 7 [ set color red set pom pom + income ] set average-estimate pom / Sample-size ] ] end to hundred-convenience-samples set average-100-estimates 0 let pom 0 set n 0 clear-plot repeat 100 [ set n n + 1 convenience-sample set pom pom + abs (average-estimate - mean [income] of households) * 100 / mean [income] of households tick ] set average-100-estimates pom / 100 end

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## Attached files

File | Type | Description | Last updated | |
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Probability vs nonprobability sampling.png | preview | Preview for 'Probability vs nonprobability sampling' | almost 10 years ago, by Viktor Vojtko | Download |

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Viktor Vojtko

## Model description

## WHAT IS IT? This model should help students in understanding of basic research sampling concepts and methods - simple random (probability) sampling and convenience (nonprobability) sampling. It also shows differences in estimates that these methods provide. ## HOW IT WORKS Research population of households is being generated and then it is possible to virtually survey samples from this population about their income. Data from these surveys are being used for calculating estimates of average income for the whole population. Two sampling methods are available. Simple random sampling randomly chooses selected amount of households to survey. Convenience sampling randomly generates the first household and then chooses other households in its neighborhood. ## HOW TO USE IT At first, population for sampling has to be generated using Setup button. It is possible to define some basic parameters for the population to be generated - number of settlements, average settlement size and standard deviation of the settlement size. After the first step, an average income and distribution of income of the generated population is being shown. Estimates that are calculated from samples being surveyed by different methods and with different sizes then can be easily compared to the known population characteristics (average income). Then 2 decisions about sampling have to be made: 1) Sample size - can be set up by the appropriate slider 2) Sampling method - can be chosen by clicking the appropriate button It is also possible to repeat sampling 100 times which shows a more general pattern of differences between estimates and the real value of average income. ## THINGS TO NOTICE Simple random sampling (SRS) gives better and with increasing sample size also more precise results (i.e. with smaller estimate error). It is due to the way how the probability laws are being involved. It is also quite clear that a meaningful statistical error may be calculated for SRS - which can be vizualized on the chart with 100 samples (for 95 % confidence level it is possible to find and show the lowest error value with 5 occurences, i.e. 5 % of 100). Convenience sampling and estimates based on that typically gives very confounding results and there is no clear relationship between the sample size and errors in estimates. This shows, how for instance sampling based on Facebook friends network or geographical closeness may be very problematic for further generalization to the whole population. ## THINGS TO TRY It is possible to explore the relationship between sampling methods, sample size and errors in estimates. E.g. to try 100 samples for 5 different sample sizes (30, 100, 200, 500, 1000) and compare results. ## EXTENDING THE MODEL The income is being generated based on settlement size and the final distribution is not statistically normal which could be changed. ## CREDITS AND REFERENCES (c) 2014 Viktor Vojtko, Faculty of Economics, University of South Bohemia. All rights reserved. Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed: a) this copyright notice is included. b) this model will not be redistributed for profit without permission from Viktor Vojtko, Faculty of Economics, University of South Bohemia. Contact the author for appropriate licenses for redistribution for profit.

## Posted almost 10 years ago