Below is the data that I collected from The World Factbook’s website after I found the missing countries, sorted in alphabetical order:
Now that I have both the data for the countries population sizes and the amounts of medals awarded to them, I can test my theory in a pilot test.
I will select ten different samples from the finite population that I collected using stratified random sampling. By saying random, I mean that the out coming country cannot be predicted and is chosen without conscious decision.
There are many types of sampling that can be done including simple random sampling, stratified sampling, systematic sampling, cluster sampling, quota sampling, convenience sampling and opinion polls.
Simple Random Sampling – In this type of sampling, every sample unit within the population has an equal chance of being chosen.
Stratified Sampling – For this type of sampling, the population is divided into strata (categories) and then a random sample is chosen from each of the strata within the population. The size of each sample is in proportion to the size of each stratum (category) within the population.
Systematic Sampling – As the name suggests, systematic sampling is where a regular pattern is devised to choose the sample. Every item in the population is listed and a starting point is chosen at random, with every nth item being selected.
Cluster Sampling – For cluster sampling, the population is divided into groups, or like the name suggested clusters. A random sample of groups or clusters is chosen and every item in the chosen cluster is surveyed.
Quota Sampling – In quota sampling, instructions are given concerning the amount (quota) of each section of the population to be sampled.
Convenience Sampling – Convenience sampling is by far the easiest sampling to make as it is, as the name suggests, convenient. The most convenient sample is chosen which for thirty countries, could be the first thirty countries in the list.
Opinion Polls – Opinion polls, as the name suggests are large-scale opinion polls that often use a combination of cluster and quota sampling.
As you can see, stratified sampling is the most suited type of sampling that I can use. Stratification of sampling is necessary when the sampling frame is significantly non-homogeneous (which tends to be true of most human populations and I believe is true of this exercise). Some characteristics will be shared but most will be influenced by cultural, socio-economic, gender, religious and ethnic differences. For example, I believe that countries in the developing world (e.g. Zimbabwe, Malaysia), who do not have the benefit of the intense training that athletes in the developed world (e.g. England, Australia) endure, will not win as many medals.
Firstly, I will categorise each the population into stratum. I will do this by using the method in which the Commonwealth Games’ website used – separating each country into that country’s locality (Asia, Oceania, Europe, Caribbean and the Americas).
Below are the strata that I have made:
Now that I have made the strata, I can now take samples from them. Before I can do this, I must determine the number of samples that will be chosen from each stratum -
Samples to be taken from the Americas = ∑ (American Strata) x 50
∑ (Population)
= 6 x 50
72
= 0.083… x 50
= 4.16
= 4
To avoid any confusion, I ‘truncated’ the answer, which means that I simply ‘cut off’ the decimal. This will negate any rounding errors that may occur. I will do this for each of the other strata.
Now that I have determined the number of samples to be chosen from the Americas, I must use a way to decide which sample will be chosen. In order to do this, I will use the ‘random number generator’ on my calculator. The random number generator chooses, at random, a decimal number. Then I must simply multiply that number by the number of sample units that there are within that stratum. Since if you were to get a small decimal, when you multiplied it by any integer, the answer will be less that 1 so therefore, I will add 1 to the answer. Seeing that the random number generator will only give me a number, I will have to label each of the sample units within the strata. Below are the listings that I have created for the Americas –
Now that I have created a listing for each sample unit, I will use the random number generator in order to pick a unit at random. Now I must do this four different times.
1st sample unit to be chosen = (Random # x 6) + 1
= (0.81 x 6) + 1
= 4.86 + 1
= 5.86
= 5
2nd sample unit to be chosen = (Random # x 6) + 1
= (0.112 x 6) + 1
= 0.672 + 1
= 1.672
= 1
3rd sample unit to be chosen = (Random # x 6) + 1
= (0.381 x 6) + 1
= 2.286 + 1
= 3.286
= 3
4th sample unit to be chosen = (Random # x 6) + 1
= (0.785 x 6) + 1
= 4.71+ 1
= 5.71
= 5
As you can see, 5 has appeared once already, so I must try again –
4th sample unit to be chosen = (Random # x 6) + 1
= (0.638 x 6) + 1
= 3.828 + 1
= 4.428
= 4
Now that I have chosen the sample units to be chosen, which are 5,1,3,4, I can now translate those numbers to the countries, Guyana, Belize, Canada and Falkland Islands.
Since I have chosen the sample units that will be chosen from the Americas, I will now choose the sample units for Africa. But first, I will need to create a listing for Africa, much like I did for the Americas –
Now I will need to find out how many samples will need to be taken from this stratum –
Samples to be taken from the Africa = ∑ (Africa Strata) x 50
∑ (Population)
= 19 x 50
72
= 0.2638… x 50
= 13.19
= 13
Therefore, I will need to choose 13 different samples from the stratum –
1st sample unit to be chosen = (Random # x 19) + 1
= 13.319 + 1
= 14.319
= 14
2nd sample unit to be chosen = (Random # x 19) + 1
= 1.387 + 1
= 2.387
= 2
3rd sample unit to be chosen = (Random # x 19) + 1
= 18.131 + 1
= 19.131
= 19
4th sample unit to be chosen = (Random # x 19) + 1
= 10.051 + 1
= 11.051
= 11
5th sample unit to be chosen = (Random # x 19) + 1
= 8.018 + 1
= 9.018
= 9
6th sample unit to be chosen = (Random # x 19) + 1
= 15.884 + 1
= 16.884
= 16
7th sample unit to be chosen = (Random # x 19) + 1
= 16.562 + 1
= 17.562
= 17
8th sample unit to be chosen = (Random # x 19) + 1
= 0.114 + 1
= 1.114
= 1
9th sample unit to be chosen = (Random # x 19) + 1
= 2.66 + 1
= 3.66
= 3
10th sample unit to be chosen = (Random # x 19) + 1
= 4.218 + 1
= 5.218
= 5
11th sample unit to be chosen = (Random # x 19) + 1
= 11.628 + 1
= 12.628
= 12
12th sample unit to be chosen = (Random # x 19) + 1
= 17.043 + 1
= 18.043
= 18
13th sample unit to be chosen = (Random # x 19) + 1
= 12.065 + 1
= 13.065
= 13
As you can see, I have chosen the four different sample units to be chosen, which translates to the countries, South Africa, Cameroon, Tanzania, Nigeria, Mozambique, Uganda, Zimbabwe, Botswana, Gambia, Kenya, Seychelles, Zambia and Sierra Leone.
Now, like Africa and the Americas, I will label the different countries for Asia –
Samples to be taken from the Asia = ∑ (Asia Strata) x 50
∑ (Population)
= 8 x 50
72
= 0.111… x 50
= 5.555…
= 5
1st sample unit to be chosen = (Random # x 8) + 1
= 1.464 + 1
= 2.464
= 2
2nd sample unit to be chosen = (Random # x 8) + 1
= 2.416 + 1
= 3.416
= 3
3rd sample unit to be chosen = (Random # x 8) + 1
= 7.704 + 1
= 8.704
= 8
4th sample unit to be chosen = (Random # x 8) + 1
= 4.632 + 1
= 5.632
= 5
5th sample unit to be chosen = (Random # x 8) + 1
= 0.704 + 1
= 1.704
= 1
These numbers translate to the countries, Brunei, India, Sri Lanka, the Maldives and Bangladesh.
Now I must repeat the procedure for the Caribbean –
Samples to be taken from the Caribbean = ∑ (Caribbean Strata) x 50
∑ (Population)
= 15 x 50
72
= 0.208… x 50
= 10.416…
= 10
1st sample unit to be chosen = (Random # x 15) + 1
= 5.025 + 1
= 6.025
= 6
2nd sample unit to be chosen = (Random # x 15) + 1
= 10.845 + 1
= 11.845
= 11
3rd sample unit to be chosen = (Random # x 15) + 1
= 8.94 + 1
= 9.94
= 9
4th sample unit to be chosen = (Random # x 15) + 1
= 11.715 + 1
= 12.715
= 12
5th sample unit to be chosen = (Random # x 15) + 1
= 0.39 + 1
= 4.39
= 4
6th sample unit to be chosen = (Random # x 15) + 1
= 9.135 + 1
= 10.135
= 10
7th sample unit to be chosen = (Random # x 15) + 1
= 0.315 + 1
= 1.315
= 1
8th sample unit to be chosen = (Random # x 15) + 1
= 7.485 + 1
= 8.485
= 8
9th sample unit to be chosen = (Random # x 15) + 1
= 14.685 + 1
= 15.685
= 15
10th sample unit to be chosen = (Random # x 15) + 1
= 13.425 + 1
= 14.425
= 14
These numbers translate to the countries, Cayman Islands, St Kitts, Montserrat, St Lucia, Barbados, Jamaica, Anguilla, Grenada, Turks & Calcos and Trinidad & Tobago
Now I will do the same for Europe –
Samples to be taken from Europe = ∑ (Europe Strata) x 50
∑ (Population)
= 10 x 50
72
= 0.138… x 50
= 6.944…
= 6
1st sample unit to be chosen = (Random # x 10) + 1
= 9.83 + 1
= 10.83
= 10
2nd sample unit to be chosen = (Random # x 10) + 1
= 6.26 + 1
= 7.26
= 7
3rd sample unit to be chosen = (Random # x 10) + 1
= 4.18 + 1
= 5.18
= 5
4th sample unit to be chosen = (Random # x 10) + 1
= 2.2 + 1
= 3.2
= 3
5th sample unit to be chosen = (Random # x 10) + 1
= 5.83 + 1
= 6.83
= 6
6th sample unit to be chosen = (Random # x 10) + 1
= 7.21 + 1
= 8.21
= 8
These numbers translate to the countries, Wales, Malta, the Isle of Man and Gibraltar, Jersey and Northern Ireland.
I must now repeat the procedure once more for the region of Oceania –
Samples to be taken from Oceania = ∑ (Oceania Strata) x 50
∑ (Population)
= 14 x 50
72
= 0.194… x 50
= 9.722…
= 9
1st sample unit to be chosen = (Random # x 14) + 1
= 1.064 + 1
= 2.064
= 2
2nd sample unit to be chosen = (Random # x 14) + 1
= 7.938 + 1
= 8.938
= 8
3rd sample unit to be chosen = (Random # x 14) + 1
= 6.384 + 1
= 7.384
= 7
4th sample unit to be chosen = (Random # x 14) + 1
= 13.636 + 1
= 14.636
= 14
5th sample unit to be chosen = (Random # x 14) + 1
= 5.936 + 1
= 6.936
= 6
6th sample unit to be chosen = (Random # x 14) + 1
= 10.64 + 1
= 11.64
= 11
7th sample unit to be chosen = (Random # x 14) + 1
= 4.86 + 1
= 5.86
= 5
8th sample unit to be chosen = (Random # x 14) + 1
= 12.838 + 1
= 13.838
= 13
9th sample unit to be chosen = (Random # x 14) + 1
= 2.428 + 1
= 3.428
= 3
These numbers translate to the countries, the Cook Islands, Norfolk Islands, Niue, Vanuata, New Zealand, the Solomon Islands, Nauru, Tuvalu and Fiji.
I have now collected all of the samples that I will be using. Below is the complete listing of the countries that I have chosen through the random number generator and through stratified sampling –
NOTE: There are 47 countries here instead of the originally intended 50. This is because of errors in truncating the number of samples to be taken.
Now I shall compare each country’s population with their amount of total number of medals awarded –
Now I must compare this data. In order to this, I will do a scatter graph.