SAMPLING VARIATION AND CONFIDENCE INTERVALS - LEARNING OUTCOMES Flashcards
What is the purpose of using random sampling?
Random sampling is the best way to ensure that the sample we are taking is representative of the whole population. This is because every individual in the population has an equal chance of being in the sample.
What is a sampling frame?
The list of people that you can choose or sample from is known as the sampling frame. For example for school children the sampling frame may be a collection of school registers.
What is systematic sampling?
Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point and a fixed, periodic interval.
You have to be careful with this sort of sampling because it is only valid if the order of subjects in the population is effectively random.
What is a simple random sample?
‘Simple Random Sample’ - A subset of a statistical population in which each member of the subset has an equal probability of being chosen. A simple random sample is meant to be an unbiased representation of a group.
How might you obtain a random sample for a group?
First you identify your sampling frame. You then need to select from the sampling frame. You can do this by numbering the list from 1 to N and using random number tables to decide who is in the random sample.
Alternatively, you can use a suitable computer programme, such as SPSS. If you have all the names listed in SPSS you can select a random sample of a certain size from among them.
List two types of random sampling.
- Simple random sampling
2. Systematic sampling
What is meant by the term ‘sampling error’?
Sampling error is defined as error in statistical analysis arising from the unrepresentativeness of the sample taken.
Why is it unlikely that for any given sample we are unlikely to obtain the true mean for the actual population from that sample?
Because our estimates are subject to sampling error.
What does the central limit theorem state?
The central limit theorem states that the sampling distribution of the mean approaches a normal distribution as the sample size increases.
What statistic do can we use to tell us how representative our sample is likely to be compared to the overall population?
This statistic is called the standard error of the mean, and it is simply the standard deviation of the sampling distribution.
SE = s / sqrt(N)
where s is the sample standard deviation, and N is the sample size.
What does a large value of standard error tell us?
A large value will tell us that the sample means can be quite different to each other, and therefore a particular sample may not be particularly representative of the population.
What does a small value of standard error tell us?
Small values for the standard error tell us that the sample means will be fairly similar, and therefore our particular sample is likely to be a fair reflection of the population.
Other than standard error, what other measures can we use to assess sampling error?
We could also use confidence intervals to define the limits between which we would expect most of the sample means to fall. Most studies will use 95% confidence intervals, although you may sometimes see 99% confidence intervals reported.
If the mean of your sample represents the data well what will the confidence intervals look like?
If the mean of your sample represents the data well, then the confidence intervals of that mean should be small (much like the standard error).
If the mean of your sample represents the data poorly what will the confidence intervals look like?
If the sample mean is a bad representation of the population, then the confidence interval will be wider, indicating that a different sample might produce a mean quite different to that from our original sample.
