Title: Hypothesis formulation and testing in random samples - A summary
Course: UGQuants (SSPS) > Section: Inference

Hypothesis formulation and testing in random samples - A summary

Let us summarise how we use quantitative data to make statements about a population when we can only gather information about a sample of it:

1 | We find a sampling frame for the population (that is an accurate and comprehensive list of all its members).
2 | From this we draw a random sample (one in which every member of the population has an equal chance of being selected).
3 | We measure the characteristics of this sample as a set of variables (e.g. by collecting published information about them, asking them to respond to a questionnaire or interview etc.).
4 | We enter the values for each of the variables for each case in a dataset. In what we refer to as secondary analysis (using already existing data), steps 1 to 4 have already been undertaken. For example, the European Social Survey Round 5 dataset contains information from a random sample of adults living in Britain in 2010.
5 | We decide what level of Type I error is appropriate for the kind of research we are undertaking. In essence, we decide what probability we are prepared to accept of mistaking a pattern thrown up by random chance for the existence of a real pattern in the population we’re studying. We must bear in mind, however, that if we set this level too low, we might interpret as random chance a pattern in our data that was in fact the product of a real pattern in the population.
6 | This level is known as statistical significance. It is often represented by the letter p (since it represents the probability of committing a type I error of rejecting a null hypothesis that is in fact true) or by the abbreviation sig. Conventionally this level is set at 5% or 1%, but it can actually be set at any level we think is appropriate.
7 | We formulate relevant null hypotheses about relationships between variables or the characteristics of the variables in our population. A null hypothesis is usually the hypothesis that no relationship exists between two or more variables of interest.
8 | If we set a null hypothesis of no relationship between two variables but find empirically that there is a low chance of there being no relationship in our sample (determined by the kind of test we are doing and the sample size), we can reject the null hypothesis in favour of the alternative hypothesis.
9 | We decide to accept or reject our null hypotheses on the basis of the results we obtain from our sample and the significance level we choose. Where we reject our null hypothesis, we provisionally accept our alternative hypothesis about the characteristics of our population.