STAT1201 Semester 2, 2020. Online Learning Notes Module 1.1: Variability Error Variability: - Encompasses natural variability (variation as dictated by nature e.g. height) - and measurement variability (variability based on measurement techniques and discrepancies e.g. measurement error = variability in data) - Presence of Error variability makes it necessary to replicate our experiments Group Variability: - Variability caused by differences between groups (e.g. height differs between genders) - A standard statistical approach to seeing if there is a difference between the groups is to see if the group variability is larger than the error variability Sampling Variability: - Sampling variability is how much an estimate varies between samples - i.e. One group of males may have different heights than a second group of males What is a variable? - A variable is a characteristic that we can record about the subjects or objects in a study. These can be measurements we make, like a forearm length or blood pressure, or can be attributes, like sex or age. It is important to classify variables as being either quantitative or categorical. These two types will require different tools for exploration and analysis. Variable Types: Quantitative: - Quantitative variables ff represent measurements, such as the height of a person or the temperature of an environment. These can be: - Continuous variables ff taking any value over some range. Continuous variables capture the idea that measurements can always be made more precisely. - Discrete variables ff have only a small number of possibilities, such as a count of some outcomes or an age measured in whole years. Categorical: - Categorical variables ff represent groups of objects with a particular characteristic. For example, recording the sex of subjects is essentially the same as making a group of males and a group of females. - Variables like sex are called Nominal variables because they are arbitrary categories with no order between them. - Ordinal variables ff are those whose categories do have an order. A common example of this is in recording the age group someone falls into. We can put these groups in order because we can put ages in order. In this section we learned that: - The need for data analysis comes from the variability present in data. - Separating the differences between groups from background variability is a fundamental task of statistical analysis.
Online Learning Notes Semester 2, 2020. STAT1201 - It is important to be able to identify the types of variables recorded in a study. Data from quantitative and categorical variables will be described and analysed in different ways. Module 1.2: Designing studies Comparative Study: - A comparative study splits its subjects into two groups, one for the control and one for the treatment - Randomization is an effective way to reduce bias in measuring the effect of the treatment (this randomly assigns participants to either group). Subjects Caffeine No Caffeine Figure 1: Structure of a Comparative study Block Design: - With a randomized block design, the experimenter divides subjects