1. Numeracy & Quantitative Methods: Level 7 – Advanced Quantitative Analysis

2. 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) Non parametric tests: Nominal: Phi, Cramer’s V Ordinal: Spearman’s Rank Order Non parametric

3. Phi: used for tables of two dichotomous categorical variables. Cramer’s: used for tables where one or both variables has two or more categories. Phi and Cramer’s V are chi-square based measures of association. Phi & Cramer’s V

4. Size of the chi-square coefficient depends on the strength of the relationship and sample size. Phi eliminates sample size by dividing chi-square by n, the sample size, and taking the square root. Phi varies between -1 and 1. Close to 0 it shows little association between variables. Close to 1, it indicates a strong positive association. Close to -1 it shows a strong negative correlation. Phi Square root of the chi-square statistic (X 2 )divided by the sample size (N)

5. Cramer’s V varies between -1 and 1. Close to 0 it shows little association between variables. Close to 1, it indicates a strong positive association. Close to -1 it shows a strong negative correlation. Cramer’s V n = number of subjects & k = number of rows or columns

6. Pearson’s Correlation, r, describes the relationship between two variables that are scale (interval/ratio) and have many different data values. Where we have two ordinal variables (or one ordinal and one scale) with a large number of scores we can use Spearman’s rho. Spearman rho can be defined as the Pearson Correlation Coefficient between the ranked variables Spearman’s rank order correlation coefficient

7. Spearman’s rho Similar principles as Pearson’s r except that it is based on rank order of scores and not the score data. Raw scores may be ordinal but the rank scores are scale (interval/ratio) – transforming the relationship into a linear one by using the ranks of the items rather than their actual values Concerned with predicting the ranking of pairs of data from the independent and dependent variables

8. D = difference in the ranks given to the two variable values for each item of data n= sample size

9. Example (taken from Argyrous 2005: 180) A physiotherapist wishes to explore whether age affects the mobility of their patients. They have recorded the patients age (interval/ratio) They have devised a measurement tool for mobility based on multiple measures. The mobility score is ranked 1 to 15. The lower the mobility score the worse their mobility.

10. AgeRank on AgeMobilityRank on Mobility DD2D2 2311415-14196 2521516-14196 2831213-10100 304851 3551314-981 37610 -416 3871112-525 3988539 40910 1 411097.52.56.25 451110 11 501297.54.520.25 52137310100 551485981 60154114196 62166214196 ΣD2ΣD2 1225.5 Example (taken from Argyrous 2005: 180)

11. -0.8 = Strong negative correlation.

12. Argyrous, G. (2005) Statistics for Research: With a Guide to SPSS. 2nd edn. Sage, London. 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

13. 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 (http://creativecommons.org/licenses/by-nc-sa/2.0/uk/).http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ 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 – non parametric Date Created July 2011 Educational Level Postgraduate (Level 7) Keywords Parametric, non parametric, correlation coefficient, Spearman’s rank, phi and Cramer’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