Numeracy & Quantitative Methods: Level 7 – Advanced Quantitative Analysis

So far.... Principles of hypotheses Testing the significance of relationships (hypothesis testing) Measuring the strength of the association. Introduction

Test used will depend on data type (nominal, ordinal, scale) Tests classified as: Parametric (scale and normally distributed data) Non parametric (nominal/ordinal and/or break assumptions of normal distribution) Routes to analysis: collect data summarise variables and explore (univariate and bivariate) measures of association inferential statistics Parametric

Parametric measures: Pearson’s r Non parametric phi Cramer’s V Measures of association

5 Linear relationships Pearson’s r assumes a linear relationship Use a scatter plot to visualise the relationship first. Strongly positive relationship

Linear relationships

Pearson’s r To determine the strength of any relationship found between two variables (parametric) – Pearson’s r. A correlation (theoretical or empirical) of 0 (zero) implies no linear dependence of the variables. A correlation of + or 1 implies a perfect linear dependence between the variables. Degree to which X and Y vary together Degree to which X and Y vary separately

Positive Correlation (0 to +1)Negative Correlation (-1 to 0) 8 Strength: 0=No association; =Trivial; =Low to Moderate; Moderate to Substantial; =Substantial to Very strong; =Very strong; Near perfect. 1=Perfect (Source: De Vaus (2002) Analysing Social Science Data. Sage: London p. 272) Interpreting Pearson’s r

Measures of association for non parametric data. Next...

David, M. and Sutton, C. (2011) Social Research : An Introduction. 2nd ed. London: Sage. De Vaus (2002) Analysing Social Science Data. Sage: London Fielding, J. and Gilbert, N. (2006) Understanding social statistics. 2 nd ed. London: Sage. References

This resource was created by the University of Plymouth, Learning from WOeRk project. This project is funded by HEFCE as part of the HEA/JISC OER release programme.Learning from WOeRk This resource is licensed under the terms of the Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales license ( The resource, where specified below, contains other 3 rd party materials under their own licenses. The licenses and attributions are outlined below: 1.The name of the University of Plymouth and its logos are unregistered trade marks of the University. The University reserves all rights to these items beyond their inclusion in these CC resources. 2.The JISC logo, the and the logo of the Higher Education Academy are licensed under the terms of the Creative Commons Attribution -non-commercial-No Derivative Works 2.0 UK England & Wales license. All reproductions must comply with the terms of that license. Author Laura Lake InstituteUniversity of Plymouth Title Advanced Quantitative Analysis Description Measures of association - parametric Date Created July 2011 Educational Level Postgraduate (Level 7) Keywords Parametric, non parametric, linear, correlation coefficient, Pearson’s r, UKOER, LFWOER, CPD, Learning from WOeRK, UOPCPDRM, Continuous professional development, HEA, JISC, HEFCE Back page originally developed by the OER phase 1 C-Change project ©University of Plymouth, 2010, some rights reserved