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# Introduction to statistical terms

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Introduction to Statistical Terms

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### Introduction to statistical terms

1. 1. Introduction to Statistical Terms Dr Bryan Mills
2. 2. Contents <ul><li>Some key statistical terms </li></ul><ul><li>What makes useful output </li></ul><ul><li>Sampling </li></ul>
3. 3. <ul><li>Statistics – turn data into information </li></ul><ul><li>Inferential statistics – using a sample to talk about the whole population </li></ul><ul><li>Variables – things that can vary e.g. student grades, height, etc. </li></ul><ul><li>Empirical data – data collected from observation or measurement </li></ul>
4. 4. The Problem <ul><li>Measurements </li></ul><ul><li>The basis of both models and statistics is being able to measure a variable numerically (quantitatively). </li></ul><ul><li>Statistics </li></ul><ul><li>Usually describe either a set of data or the strength of a relationship. </li></ul><ul><li>Mathematical models </li></ul><ul><li>Something along the lines of &quot;this = that + something else * something other&quot; </li></ul><ul><li>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 </li></ul>
5. 5. Types of Data (Discrete ) <ul><li>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 ). </li></ul><ul><li>Ordinal - differences and magnitude - e.g. ratings in order, A, B, C grades, small- medium - large ( Non-parametric ). Use Mann-Whitney, Kruskal Wallis, Spearmans </li></ul>
6. 6. Types of Data (Continuous) <ul><li>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 ). </li></ul><ul><li>Ratio - differences, magnitude and equal intervals plus the ability to say this is twice that etc. MPH, size, Kelvin ( Parametric ). </li></ul>
7. 7. Type of analysis <ul><li>Between groups - between different groups (e.g. independent group t-test) </li></ul><ul><li>Within groups - repeated measures, before and after an experiment (e.g. related samples t-test) </li></ul>
8. 8. Number of Variables <ul><li>Univariate - 1 variable </li></ul><ul><li>Bivariate - 2 variables </li></ul><ul><li>Multivariate </li></ul>
9. 10. Meaningless Mean <ul><li>  Mean grade = 56% but 7 students out of the 10 are below this. </li></ul>
10. 12. A Reminder Often Low High Small and rich in data Qualitative Phenomenology High Often Low Represents a large population Both, but mostly quantitative Positivist Reliability Validity Sample Size Qualitative Quantitative
11. 13. What Makes Good Output <ul><li>There are 2 main points to consider: </li></ul><ul><li>Your audience </li></ul><ul><li>The data </li></ul>
12. 15. Sampling <ul><li>Statistics rely on having gathered enough data from a sample to be able to represent the population . </li></ul><ul><li>A sample is a subset of the main population . </li></ul>
13. 16. Stratification <ul><li>population stratification </li></ul><ul><ul><li>Age </li></ul></ul><ul><ul><li>Gender </li></ul></ul><ul><ul><li>Ethnicity </li></ul></ul><ul><ul><li>Other known characteristics </li></ul></ul>
14. 17. Ideal Response Size <ul><li>Sample size = Ideal Response Size </li></ul><ul><li>Estimated Response Rate (%) </li></ul>
15. 18. <ul><li>Where: </li></ul><ul><li>n = Number of usable questionnaires returned p = Proportion being estimated </li></ul><ul><li>Z = Confidence coefficient (1.96 by convention) E = Error in proportion (<5% by convention) </li></ul>
16. 21. Types of Sample (probability) <ul><li>Simple Random Sampling </li></ul><ul><li>Stratified Random Sampling </li></ul><ul><ul><li>proportional or quota </li></ul></ul><ul><ul><li>Divide into sub-groups and take random sample from each </li></ul></ul><ul><li>Cluster (Area) Random Sampling </li></ul><ul><ul><li>Narrow down to area (e,.g. Districts) </li></ul></ul>
17. 22. Types of Sample (non-probability) <ul><li>Convenience Sampling </li></ul><ul><li>Purposive Sampling </li></ul><ul><ul><li>Modal Instance Sampling </li></ul></ul><ul><ul><ul><li>Target ‘typical’ </li></ul></ul></ul><ul><ul><li>Expert Sampling (Delphi) </li></ul></ul><ul><ul><li>Quota Sampling (work to a quota) </li></ul></ul><ul><ul><li>Heterogeneity Sampling (diversity of views) </li></ul></ul><ul><ul><li>Snowball Sampling </li></ul></ul>