12 Statistical Analysis 1 n SPSS Statistical Package

12. Statistical Analysis 1

n SPSS: Statistical Package for the Social Sciences 2

The Statistics Approach n 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% 3

The Statistics Approach (continued) n The normal distribution: Figure 12. 1. Page 335. n n Significance The null hypothesis (H 0) H 0 (null hypothesis): - there is no significant difference or relationship 4

The Statistics Approach (continued) H 1 (alternative hypothesis): - there is significant difference - there is significant relationship Researcher is interested in H 1; Deductive approach; The hypothesis is set up in advance of the analysis, possibly within a theoretical framework. 5

The Statistics Approach (continued) Example: Study of leisure participation pattern; Sample is 1000 adults; The study focuses on relative popularity of golf and tennis. H 0: tennis and golf participation levels are the same. H 1: tennis and golf participation levels are significant different. 6

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

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

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 9

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 10

SPSS And Regression n 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 11

SPSS And Regression (continued) n - R 2 (r 2) - F Test - t Test - ANOVA (Analysis Of Variance) 12

SPSS And Regression (continued) Example 1: Figure 12. 20 Page 360 Income (independent) by holiday expenditure (dependent) Model R R Square Adj. R Square Std Error Est 1 0. 915 0. 836 0. 833 104. 51 13

SPSS And Regression (continued) Anova Model 1 SS df Reg 2, 679, 971. 336 1 Res 524, 283. 164 48 Total 3, 204, 254. 500 49 MS F Sig 2, 679, 971. 336 245. 361 0. 000 10922. 566 14

SPSS And Regression (continued) Coefficient Model B 1. Stand Error Constant -323. 493 49. 890 Income 52. 563 3. 356 t -6. 484 15. 664 Sig 0. 000 Holiday Expenditure = -323. 493 + 52. 563 Income Y = -323. 493 + 52. 563 X 15

SPSS And Regression (continued) Example 2: Figure 12. 23 Page 364 Model R R Square Adj. R Square Std Error Est 1 0. 580 0. 336 0. 308 1. 87 16

SPSS And Regression (continued) Anova Model 1 SS Reg 83. 023 Res 163. 857 Total 246. 880 df MS 2 47 49 41. 512 3. 486 F Sig 11. 907 0. 000 17

SPSS And Regression (continued) Coefficient Model B 1. Constant -3. 493 Income 0. 056 Age 0. 227 Stand Error 1. 316 0. 084 0. 076 t -2. 654 0. 662 2. 969 Sig 0. 011 0. 511 0. 005 Reg Line? 18