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In a research of this magnitude there is always the question of the sample size and whether this is done properly to have precision in the survey results. The answer is not straight forward as there is involvement of the time and cost factors (Bryman and Bell, 2015). Even though a large sample cannot guarantee precision when there is increase of its size that means that the chances of a likely better precision sample are increased. This can be interpreted as: size increase, sampling error decreases.

The necessary size of the sample is determined by two important aspects: 1. The grade of accuracy that is required for the sample

2. The amount to which variation exist in the targeted population in respect with the major study characteristics

A decision has to be made into how much error tolerance has to be accepted and how much certainty exists to the generalisation level of the sample.

Through the two statistical approaches of “sampling error” and “confidence intervals” there is assistance to state first the grade of accuracy (through the “sampling error”) and second the amount of confidence that exist into the generalisation level of the sample (through the “confidence interval”).

There has to be a calculation of the error margins in the sample. De Vaus (2013) provides a good example of how this can be achieved. He hypothetically suggests that in a forthcoming election a sample of voters found to be 48 per cent towards party A. The question posed is how close this 48 per cent figure to the real population figure is.

Probability theory gives the answer. If there is taken a large proportion of random samples of the population in most cases the percentage estimates will be close to the real ones and only a few will be high deviated from the expected. In such a case the sample represents an approximate “normal” distribution (shown in Figure 3.2).

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There is an issue here that is related with the number of random samples. If there is only one random sample selection how can somebody be certain of this being representative of the true population percentage? To estimate this there is usage of the statistical approach called “standard error” through the following formula:

SB = √𝑃𝑄/𝑁

Where

SB= standard error for the binomial distribution

P= per cent in the category of interest of the variable Q= per cent in the remaining category (ies) of the variable N= number of cases in the sample

The sample that De Vaus (2013) uses initially estimated a 48 per cent vote for party A. This will be the value of P. Therefore the rest 52 per cent will vote other parties except A, and so this figure represents the value of Q. The sample size found to be for De Vaus example 1644 people and that will be the value of N. By putting all this values into the above equation there can estimation as to within what range the sample estimate of 48 per cent will be:

Y axis 500 400 300 200 100 N u mbe r o f sa mples True population of party A vote = 50% Distribution of sample estimates 45% 50% 55% Party A sample voters = 48%

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SB = √𝑃𝑄/𝑁= √48 ∗ 52/1644 = SB = √2496/1644 = SB = √1.52 = 1.23

The equation shows a standard error of 1.23 and through the use of probability theory there can be an estimation within which the population percentage is likely to be. This range is called the confidence interval and the certainty that the sample will be 48 per cent is called confidence level.

Now probability theory says that in 95 per cent of samples the percentage of the population will lie within +_ two standard error units of the sample percentage.

In this case the standard error of 1.23 and two standard errors make it 2 x 1.23 = 2.46 per cent and the initial sample percentage of 48 per cent indicates that there is a 95 per cent chance that the population intention is to vote party A for 48 per cent +_2.46 per cent. That is the true population percentage indicating that people’s vote for party A is likely to be somewhere between 45.54 per cent and 50.46 per cent.

The size of the standard error is a function of sample size. In order to estimate the population percentage with even less margin of error (e.g. small confidence interval) there has to be reducing in the standard error. For doing this the sample size has to be increased and there has to be substantially increase: quadrupling the sample size halves the standard error (De Vaus, 2013).

De Vaus however raises quite high the sample size, he says that for further accuracy that has to go to 2000 (De Vaus, 2002). That is because as the confidence intervals increases so does the confidence level of the sample accuracy. By this way the bigger the sample size gets, the bigger becomes the accuracy levels of it (Veal, 2011). There is a point however whereas the sample accuracy cannot go beyond it, it is irrelevant. For some like Lewin (2011) the limit is 1000 and others like De Vaus (2002) put this to 2000. The latter also argues that the sample confidence level is influenced by the population variance whereas in the case of a homogeneous sample the chances are the sample error to be smaller in contrast with a non- homogeneous one.

In this survey the confidence interval was remained to 5% as this is considered representative. In order to calculate the sample size the formula that was used was:

ME = 𝑧√(𝑝(1 − 𝑝)/𝑛 Where:

ME = Margin of desired error (here is 5%)

z = confidence coefficient (for 95% confidence interval the value is 1.96 - Saunders et al., 2007; Gilbert et al., 2009)

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p = standard deviation (value is 0.5 in order to provide maximum variability) n = sample size

The formula after putting the values is as follows:

0.05 = 1.96√(0.5(1 − 0.5)/𝑛 =>

0.05*0.05 = 1.96*1.96 (0.5 *0.5)/n =>

0.0025 = 3.8416 * 0.25/n =>

n = 3.8416 * 0.25/0.0025 =>

n = 384.16 which is round up to 385

Therefore the minimum amount of participants would be 384 for a considered 5% confidence interval. Based on that figure principle the researcher went to collect data from at least 400 participants. He managed to collect 650 but due to the fact that 250 participants answered partly the questionnaire put the researcher in the unpleasant position to discard them and carried on the survey with a sample of 400 which is representative.