By using random sampling, the likelihood of bias is reduced.
Simple Random Sampling
Simple random sampling is the basic sampling technique where we select a group of subjects (a sample) for study from a larger group (a population). Each individual is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. Every possible sample of a given size has the same chance of selection; i.e. each member of the population is equally likely to be chosen at any stage in the sampling process.
Stratified Sampling
There may often be factors which divide up the population into sub-populations (groups / strata) and we may expect the measurement of interest to vary among the different sub-populations. This has to be accounted for when we select a sample from the population in order that we obtain a sample that is representative of the population. This is achieved by stratified sampling.
A stratified sample is obtained by taking samples from each stratum or sub-group of a population.
When we sample a population with several strata, we generally require that the proportion of each stratum in the sample should be the same as in the population.
Stratified sampling techniques are generally used when the population is heterogeneous, or dissimilar, where certain homogeneous, or similar, sub-populations can be isolated (strata). Simple random sampling is most appropriate when the entire population from which the sample is taken is homogeneous. Some reasons for using stratified sampling over simple random sampling are:
- the cost per observation in the survey may be reduced;
- estimates of the population parameters may be wanted for each sub-population;
- increased accuracy at given cost.
Example
Suppose a farmer wishes to work out the average milk yield of each cow type in his herd which consists of Ayrshire, Friesian, Galloway and Jersey cows. He could divide up his herd into the four sub-groups and take samples from these.
Quota Sampling
Quota sampling is a method of sampling widely used in opinion polling and market research. Interviewers are each given a quota of subjects of specified type to attempt to recruit for example, an interviewer might be told to go out and select 20 adult men and 20 adult women, 10 teenage girls and 10 teenage boys so that they could interview them about their television viewing.
It suffers from a number of practical flaws, the most basic of which is that the sample is not a random sample and therefore the sampling distributions of any statistics are unknown
Below is a graph showing the comparisons of prices, new and second hand for the first 20 cars.
You can see the comparison of the prices new and second hand. Obviously the second hand prices are less, but if you look carefully the prices vary more for the new ones than the second hand. You can see the new cars go up and down in price, ranging from 20,000 down to 7,000. This showed me there was something that really affects the price, because even the Mercedes which is the most expensive new car, was in the range of the fords and Nissans.
Below is a tally chart showing the colour of the cars in tally, and how frequent they are in the first 20 cars
You can see the most frequency colours in the first 20 cars were black, white and blue, which does not prove that it affects the cars pricing because, when looking at the prices on the previous page, you can see all cars vary between colours and prices. I will now represent the data on the left on a pie chart, to give a more easier view.
Below is a pie chart expressing the colours of the cars
You can see a much easier view of the colours, and how they vary, less than half of the data is taken up by the black white and blue cars, as you can see it is very popular. But this still does not prove that it affects the price
Below is a line graph showing the first 20 cars and their make along with the price it is second hand.
The results have helped support my hypothesis incredibly, when looking at the graph you can see that that, the second dot, the Mercedes, is way above the rest, as we know Mercedes is a very well known make, so looking at this helps us identify that the better the make, the more you will have to pay.
This is a look at how the amount of owners can affect the price
In my hypothesis I stated that the amount of owners would affect the price, the more owners, the less the price will be. When looking at the chart above, you can see that the cars with 3 owners, the two fiats are very low in price, but comparing this to the others that have one, they are more. However, as I look at the mitsubushi, it is only a couple of hundred pounds more and it as only had one owner, this has confused me and my hypothesis is on 50% correct. I will need to research more into the data if I want to get a more clearer and accurate result.
Below is another chart which shows the mileage of the cars, and the make, this shows what cars have been driven more. You can see that the Mercedes car has a low mileage even though it is very expensive. The cheaper cars however have got a higher mileage, so this may encourage the price to go lower because I has been used more.
This is a look at how the engine can affect the price of the car
To prove that the engine affects the price of the car, you will have to compare two of the cars with the same make. Example, looking at the rover, it has a 2.3 engine at 6999. But looking at the other rover, it has a size of 1.6, but is only 4995, this could mean that the engine size does affect the price of the car.
BELOW IS A GRAPH COMPARING THE LAST 30 CARS AND THEIR SECOND HAND PRICES
You can see from the chart above that, the expensive make MERCEDES has the highest price ranging from 15000-20000 and this gives an idea that the the better the make, the more expensive the car. So my hypothesis was correct.
You can notice that, the mileage is more between the cheaper cars, and less between the expensive cars. This could mean, the better the make, the less mileage, the more expensive car.
Below is a chart showing the mileage vs second hand price.
You can see from the chart above that, the more the mileage, the cheaper the price, because you can see from the first car, the mileage is very low, and the price is more. But looking at the 12th to 14th car, you can see the car price is very low.
Below are a series of charts which represent the prices of 3 makes, Ford, Vauxhall and Rover.
FORD
VAUXHALL
ROVER
Now I will use simple random sampling to represent my data, this means I will pick out random data and interpret them.
Below I have randomly selected 4 cars, with their price when new and second hand, this is simply to show how the much the price of the second hand car is different to when new.
If you look at the graph, you can see that the price when new is almost more than double the second hand price, but with the Mercedes, a high class make, the prices are not that spread out, this could help me prove that the make could affect the price. And this information will be used when I decide to group my data and to prove my hypothesis is correct.
Above is another graph showing the prices second hand and new for 5 random cars which are of an equal class. As you can now see, the new prices are now more than doubled, which has helped me prove my hypothesis that the make does effect the price.
BELOW IS A SERIES OF TALLY CHARTS SHOWING THE COLOURS OF THE CARS AND SHOWING THE MOST POPULAR COLOUR.
First 20 cars
Black, white and blue seem to be the most popular colour in the first 20 cars.
Next 20 cars
The most popular colour in the next 20 cars is the red colour.
I Will now use more accurate methods of finding results, I will use stratified sampling by categorising my data.
I will take 3 makes with their models and then I will compare the new prices with the second hand prices, and then compare the prices with the other make prices.
VAUXHALL
Above you can see that the prices of the 5 Vauxhall cars when new were in the same price range, but looking at the second hand prices, the prices have decreased by a huge margin, this may prove that the lower class cars prices decrease larger than the more high class cars.
MERCEDES
Now from the picture on the previous page, you can notice that the Mercedes is a very expensive make, and the second hand price have decreased from the new prices, but there is a less amount decreased. With the Vauxhall cars, you saw that the second hand priced halved, when you look at the Mercedes, you will see it has not halved, but it has decreased by a small amount. This can prove that the MAKE does indeed express the second hand price. So my hypothesis is correct.
FORD
Now you can see another change, the ford make is a highly used car but not considered to be at a high class, so this proved my hypothesis that the better the make,
I will now compare other makes and their prices to get a greater look at the comparison between prices.
Above you can see a great deal of difference, the better make Mercedes has a high second hand price than the ford, rover and Volkswagen when new, so this does prove my hypothesis again that make affects the price of a car.