Reasons for variability . Natural Variability (People come in different shapes and sizes and so we expect to get different forearm length measurements) . Measurement variability -> read the meter wrongly etc . Group variability ( we also find differences in our observations because the two groups, males and females, do tend to have different lengths. This is the variability we are really interested in) . Sampling Variability(What we would like to do is to use the averages we calculate in our study to say something about people in general. But if we did the study again then we might get different data which say something else!) Types of Variables A variable is a characteristic that can be recorded about the subjects or objects in a study. 1. Quantitative variables: they represent measurements such as height · Continuous Take any value over some range (Variable that is obtained by measuring) · Discrete Only have a small number of possibilities such as age measured in whole years (Variable that is obtained by counting) 2. Categorical variables: They represent a group of objects with a particular characteristic · Nominal Categorical variables with no order between them like gender · Ordinal Categorical variables that have an order like recording an age group because age can be put in an order Designing Studies Observational Studies: It has the same aims as an experiment but it is passive and usually works with existing data eg. medical records. However, it is hard to establish causation,, determine that the variable is the reason why the outcome was attained not because of other factors Randomisation Randomisation is important to help reduce bias and protect against other variables. Using random samples from populations allow us to make more representative conclusions The Language of Hypothesis Testing Null Hypothesis: The statement of no effect. It is denoted by Ho. It is rare for authors to specify the null hypothesis at all. P-value: The probability that the data could be derived by chance. . If the P-value is large, then the data observed were likely by chance and there is no reason to doubt the null hypothesis. . If the P-value is small, then there is evidence against the null hypothesis. Alternative hypothesis: Denoted by H1, the alternative hypothesis shows a possible outcome to be as unusual as the one actually observed.
Strong ¥ Moderate 0 0.01 0.05 Weak Inconclusive 0.1 1 Hypothesis testing has been used as a tool for decision making. For example: to do this, a threshold is chosen such as 0.05, and if we find a P-value which is less than 0.05 then we say that "the results were significant at the 5% level". This will also often be written in journal articles as "the results were found to be significant (< 0.05)". (This role is usually used for scientific research where there isn't usually a need for making binary decisions The cycle of making a hypothesis and testing its predictions is known as hypothetico-deductive method (since the