**9.10 Convenience sampling**

Convenience sampling appears to be a favorite sampling technique among students, as it is cheap and simple compared to other sampling techniques. It is collection of participants since they are often readily and conveniently available.

Convenience sampling is not the preferred form of sampling for successful research as samples are taken from a particular segment of the population, so the degree of generalizability is questionable (**Figure 9**) [38].

**Figure 8.** *Snowball sampling (source: https://cuttingedgepr.com/find-mobilize-unofficial-opinion-leaders/).*

## **10. Standard error of a sample mean**

Suppose we have taken a sample of n measurements of some continuous variate, such as blood pressure or hemoglobin level. The sample mean *x* may be different from the population mean because it is based on a sample. Different samples of the same size *n* would give different values of the mean. These differences are due to sampling error. The sample mean therefore has its own distribution.

If the distribution of *x* in the population has mean *μ* and standard deviation **σ** and a sample of size *n* is taken, then the *sampling distribution* of the sample mean *x* has the following properties:

1.The mean of the distribution of *x* is the same as that of the whole population, i.e.

**E**ð Þ¼ *x*̅ *μ* ð Þ *see Appendix for proof*

or the sample mean is an unbiased estimate of the population mean.

2.The standard deviation of *x* is equal to **σ/** √**n**. The standard deviation of an estimate is referred to as the standard error (SE). The standard error of the mean is therefore [39]

$$\mathbf{SE}\left(\overline{\mathfrak{x}}\right) = \mathfrak{o}/\mathfrak{n}$$

3.By the central limit theorem, *x* is approximately Normally distributed, i.e. the distribution of *x* tends to be Normal even if the distribution in the population is markedly non-Normal. The distribution of means becomes closer to the Normal distribution as *n* increases.

The standard error of the mean is a measure of the sampling error [40]. For example, consider the measurement of lung function, forced expiratory volume, measured in liters. This is known to have a standard deviation of 0.5 in a population. If we select various sample sizes from this population, we have:

$$n = 1\text{ SE}(\bar{\mathbf{x}}) - \mathbf{0.5}/\mathbf{1} = \mathbf{0.50}$$

$$n = 9\text{ SE}(\bar{\mathbf{x}}) - \mathbf{0.5}/\mathbf{3} = \mathbf{0.17}$$

$$n = 25\text{ SE}(\bar{\mathbf{x}}) = \mathbf{0.5}/\mathbf{5} = \mathbf{0.10}$$

$$n = 100\text{ SE}(\bar{\mathbf{x}}) = \mathbf{0.5}/10 = \mathbf{0.05}$$

The larger the sample size, the smaller the sampling error. The standard error of the mean is used when we want to indicate how precise our estimate of the mean is. The standard deviation s, on the other hand, is used to show how widely spread our measurements of *x* are.
