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Chapter 17: Statistical Analysis

Chapter 17: Statistical Analysis. CONTENTS. The statistics approach Statistical tests Types of data and appropriate tests Chi-square Comparing two means: the t-test A number of means: one-way analysis of variance A table of means: factorial analysis of variance Correlation

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Chapter 17: Statistical Analysis

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  1. Chapter 17: Statistical Analysis

  2. CONTENTS • The statistics approach • Statistical tests • Types of data and appropriate tests • Chi-square • Comparing two means: the t-test • A number of means: one-way analysis of variance • A table of means: factorial analysis of variance • Correlation • Linear regression • Multiple regression • Factor and cluster analysis

  3. The statistics approach • Probabilistic statements • The normal distribution • Probabilistic statement formats • Significance • The null hypothesis • Dependent and independent variables. A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  4. Probabilistic statements • descriptive: e.g. : 10% of adults play tennis • comparative:e.g. : 10% play tennis, but 12% play golf • relational:e.g. 15% of people with high incomes play tennis but only 7% of people with low incomes do so: there is a positive relationship between tennis-playing and income. • However: when based on a samples, the above must be made using a probabilistic format A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  5. Probabilistic statements contd • We can be 95% confident that the proportion of adults that plays tennis is between 9% and 11% • The proportion of golf players is significantly higher than the proportion of tennis players (at the 95% level of probability) • There is a positive relationship between level of income and level of tennis playing (at the 95% level) • (See discussion of Confidence intervals: Chapt 13). A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  6. Probabilistic statement formats • 95% probability • sometimes expressed as 5% • sometimes as 0.05 • 99% probability is also used • also expressed 1% or 0.01 A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  7. Normal distribution (Fig. 17.1): a. Drawing repeated samples (theory) A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  8. Normal distribution contd b. Normal distribution/curve A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  9. Normal curve (Fig. 13.1) A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  10. Significance • Statistically significant: unlikely to have happened by chance (highly probable) • Level of significance is affected by sample size (not by population size) • Probability of finding happening by chance related to normal curve and similar theoretical distributions. • But NB: small differences or weak relationships may not be socially or managerially significant – even when they are statistically significant A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  11. Null hypothesis • H0 – Null hypothesis: there is no significant difference or relationship • H1 – Alternative hypothesis: there is a significant difference or relationship • eg. • H0tennis and golf participation levels are the same; • H1tennis and golf participation levels are significantly different. A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  12. Dependent and independent variables Independent variable 1 Independent variable 2 Dependent variable Independent variable 3 A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  13. Statistical tests A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  14. Statistical tests contd A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  15. Statistical tests contd A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  16. Data • Extended version of Campus Sporting Life survey with • additional variables • additional cases • See Appendix 17.2 • SPSS used, as in Chapt. 16 A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  17. Chi-square(X2) • Testing the relationship between two variables presented in a frequency crosstabulation. • Null/alternative hypotheses: • H0 - there is no relationship between student status and gender in the population • H1 - there is a relationship between status and gender in the population • Findings (Fig. 17.5): • Value of Chi-square: 6.522 • Significance: 0.011 • Less that 0.05 (5%) • Conclusion: H0 rejected, H1 accepted: there is a relationship A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  18. Comparing two means: t-test • Paired samples: whole sample: comparing means for two variables • Independent samples: sample divided into two groups (eg. males and females) and comparing means for one variable A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  19. Comparing 2 means: t-test : Paired samples (Fig. 17.9) • Example 1: Compare average times played sport in last 3 months (12.2) with average times visited national parks (9.8) • Difference is 2.4 • value of t is 1.245 • Significance is 0.219, which is larger than 0.05 • Null hypothesis is accepted: difference is not significant A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  20. Comparing 2 means: t-test : Paired samples (Fig. 17.10) • Compare course costs for males ($110.00 pa) and females ($136.60) • Difference is $28.60 • value of t is -1.245 • significance is 0.219 • Null hypothesis is accepted: difference is not significant A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  21. One-way analysis of variance (ANOVA)(Fig. 17.11, 13) • Means of one variable for groups defined by another variable • F-test rather than r-test • eg. Means of times played sport by student status: • F/T student/no paid work: mean = 9.7 times in 3 months • F/T student/paid work: 9.6 times • P/T student – F/T job: 19.1 times • P/T student – Other: 12.2 times • Value of F: 2.485, Significance 0.072, which is greater than 0.05 • Null hypothesis accepted: no relationship between status and sport • But for ‘going out for a meal’: F = 6.64 and Sig. = 0.001, which is less than 0.05, so null hypothesis rejected: there is a significant relationship A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  22. Factorial analysis of variance (Fig. 17.14, 15) • A table of means: two variables and means of a third • eg. Mean visits to theatre by gender by student status • Status not significant and gender not significant • But for status x gender: F = 3.681, Sig. = 0.019, which is <0.05, so null hypothesis rejected: there is a significant relationship. A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  23. Correlation (Fig. 17.16) Watched sport by income: weak positive: r = .46 A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  24. Correlation (Fig. 7.16) Played sport by income: weak negative: r = -0.44 A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  25. Correlation (Fig. 7.16) Sport exp. by income: strong positive: r= 0.91 A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  26. Correlation (Fig. 17.18) • Correlation coefficient (r) expresses the relationship numerically • No relationship: r =0 • Exact relationship: r = 1 (positive) -1 (negative) • Correlation matrix shows correlations between a number of variables A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  27. Correlation matrix (simplified Fig. 17.18) * = significant at the 0.05 level ** = significant at the 0.01 level A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  28. Regression Fits best fit ‘regression line’ to scatterplot: Fig. 17.21 A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  29. Regression: best fit may be a curve (Fig. 17.22) A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

  30. Multi-variate analysis • Multiple regression has one dependent variable and a number of independent, influencing, variables • One development: Structural Equation Modelling explores inter-relationships between a number of variables • Cluster and factor analysis: combine large numbers of variables into groups – eg. lifestyle or personality groups A. J. Veal & S. Darcy (2014) Research Methods for Sport Studies and Sport Management: A practical guide. London: Routledge

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