1. Introduction to Statistical Terms Dr Bryan Mills

2. Contents Some key statistical terms What makes useful output Sampling

3. Statistics – turn data into information Inferential statistics – using a sample to talk about the whole population Variables – things that can vary e.g. student grades, height, etc. Empirical data – data collected from observation or measurement

4. The Problem Measurements The basis of both models and statistics is being able to measure a variable numerically (quantitatively). Statistics Usually describe either a set of data or the strength of a relationship. Mathematical models Something along the lines of "this = that + something else * something other" These are often expressed as x = f(a,b,c) or income = f(age, social class, qualifications) - in other words x is a function of other variables

5. Types of Data (Discrete ) Nominal - differences e.g. voting preference, Towns, types of beach (sandy, rocky, etc.), discrete categories, occupations, named groups. Uses cross-tabulation (contingency tables) and Chi 2 as a means of display/analysis (Non-parametric). Ordinal - differences and magnitude - e.g. ratings in order, A, B, C grades, small- medium - large (Non-parametric). Use Mann-Whitney, Kruskal Wallis, Spearmans

6. Types of Data (Continuous) Interval - differences, magnitude and equal intervals, centimetres above and below an average height, IQ - 125 is the same to 110 as 115 is to 100, but 120 is not twice 60, Centigrade, there can be no 0, however, so height from 0 would be a ratio scale (Parametric). Ratio - differences, magnitude and equal intervals plus the ability to say this is twice that etc. MPH, size, Kelvin (Parametric).

7. Type of analysis Between groups - between different groups (e.g. independent group t-test) Within groups - repeated measures, before and after an experiment (e.g. related samples t-test)

8. Number of Variables Univariate - 1 variable Bivariate - 2 variables Multivariate

10. Meaningless Mean Mean grade = 56% but 7 students out of the 10 are below this.

12. A Reminder Qualitative Quantitative Sample SizeValidityReliability PositivistBoth, but mostly quantitative Represents a large population Often Low High PhenomenologyQualitativeSmall and rich in data HighOften Low

13. What Makes Good Output There are 2 main points to consider: Your audience The data

15. Sampling Statistics rely on having gathered enough data from a sample to be able to represent the population. A sample is a subset of the main population.

16. Stratification population stratification –Age –Gender –Ethnicity –Other known characteristics

17. Ideal Response Size Sample size = Ideal Response Size Estimated Response Rate (%)

18. Where: n = Number of usable questionnaires returned p = Proportion being estimated Z = Confidence coefficient (1.96 by convention) E = Error in proportion (<5% by convention)

21. Types of Sample (probability) Simple Random Sampling Stratified Random Sampling –proportional or quota –Divide into sub-groups and take random sample from each Cluster (Area) Random Sampling –Narrow down to area (e,.g. Districts)

22. Types of Sample (non-probability) Convenience Sampling Purposive Sampling –Modal Instance Sampling Target ‘typical’ –Expert Sampling (Delphi) –Quota Sampling (work to a quota) –Heterogeneity Sampling (diversity of views) –Snowball Sampling