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12. Statistical Analysis

12. Statistical Analysis. SPSS: Statistical Package for the Social Sciences. The Statistics Approach. Probabilistic statements: - make probabilistic statements about a population on the basis of information available from a sample drawn.

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12. Statistical Analysis

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  1. 12. Statistical Analysis

  2. SPSS: Statistical Package for the Social Sciences

  3. The Statistics Approach • Probabilistic statements: - make probabilistic statements about a population on the basis of information available from a sample drawn. Example: 10% of adults play tennis, can be 95% confident that the proportion of adults that play tennis is between 9% and 11%

  4. The Statistics Approach (continued) • The normal distribution: Figure 12.1. Page 335. • Significance • The null hypothesis (H0) H0 (null hypothesis): - there is no significant difference - there is no significant difference or relationship

  5. The Statistics Approach (continued) H1 (alternative hypothesis): - there is significant difference - there is significant relationship Researcher is interested in H1; Deductive approach; The hypothesis is set up in advance of the analysis, possibly within a theoretical framework.

  6. The Statistics Approach (continued) Example: Study of leisure participation pattern; Sample is 1000 adults; The study focuses on relative popularity of golf and tennis. H0: tennis and golf participation levels are the same. H1: tennis and golf participation levels are significant different.

  7. The Statistics Approach (continued) • Dependent And Independent Variables: - the independent variable influences the dependent variable? - one variable can be dependent on a number of independent variables

  8. Linear Regression • Quantitative analysis • If the correlation between 2 variables is consistent enough, one variable can be used to predict the other

  9. Linear Regression (continued) Example 1: Days Participation = a + b Age Y = a + b X a = intercept b = slope Y = dependent variable = Days Participation X = independent variable = Age

  10. Linear Regression (continued) Example 2: Trips = a + b Income Y = a + b X Y = dependent variable = Trips X = independent variable = Income a = intercept b = slope

  11. SPSS And Regression • Interested: - value of the regression coefficient - R (r) = correlation coefficient r = 0 = no relationship between two variables r = +1 = perfect positive correlation between two variables r = - 1 = perfect negative correlation between two variables 0 < r < +1 : some positive correlation -1 < r < 0 : some negative correlation

  12. SPSS And Regression (continued) • - R2 (r2) - F Test - t Test - ANOVA (Analysis Of Variance)

  13. SPSS And Regression (continued) Example 1: Figure 12.20 Page 360 Income (independent) by holiday expenditure (dependent) Model R R Square AdjR Square Std Error Est 1 0.915 0.836 0.833 104.51

  14. SPSS And Regression (continued) Anova Model SS df MS F Sig 1 Reg 2,679,971.336 1 2,679,971.336 245.361 0.000 Res 524,283.164 48 10922.566 Total 3,204,254.500 49

  15. SPSS And Regression (continued) Coefficient Model B Stand Error t Sig 1. Constant -323.493 49.890 -6.484 0.000 Income 52.563 3.356 15.664 0.000 Holiday Expenditure = -323.493 + 52.563 Income Y = -323.493 + 52.563 X

  16. SPSS And Regression (continued) Example 2: Figure 12.23 Page 364 Model R R Square AdjR Square Std Error Est 1 0.580 0.336 0.308 1.87

  17. SPSS And Regression (continued) Anova Model SS df MS F Sig 1 Reg 83.023 2 41.512 11.907 0.000 Res 163.857 47 3.486 Total 246.880 49

  18. SPSS And Regression (continued) Coefficient Model B Stand Error t Sig 1. Constant -3.493 1.316 -2.654 0.011 Income 0.056 0.084 0.662 0.511 Age 0.227 0.076 2.969 0.005 Reg Line?

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