Analysis and Interpretation - Statistics Project Example

Statistical assumptions Researchers generally seek to generalize their results from the available data to some larger context by generalizing a sample to a population. Statistical assumptions are important aspect of empirical studies. This study, just like any other study, applies some statistical assumptions in order to achieve at the desired results. The statistical assumptions are: The mean difference is zero The data is normally distributed The variance of the two variables are equal (homoscedasticity) The observations are independent of each other Linearity of graded responses to quantitative stimuli The independent variable of the study is “attending religious services” while the dependent variable is “political views”. The study mainly duels on correlation and regression for data analysis. Correlation coefficient is important in showing whether and how strongly religious service attendance and political views are related. Because the study is linear in nature, Pearson product-moment correlation coefficient is necessary to measure the direction and strength of the linear relationship between religious service attendance and political views. The value of Pearson’s correlation coefficient is influenced by the distribution of the independent (attending religious services) variable in the sample. Hypothesis statement The null hypothesis for the study is described below: Ho: the error variance of the dependent variable is equal across groups Ha: the error variance of the dependent variable is not equal across groups Results Tests of Between-Subjects Effects Dependent Variable: THINK OF SELF AS LIBERAL OR CONSERVATIVE Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared Corrected Model 98.521a 8 12.315 6.646 .000 .071 Intercept 10576.996 1 10576.996 5707.657 .000 .892 ATTEND 98.521 8 12.315 6.646 .000 .071 Error 1286.068 694 1.853 Total 13705.000 703 Corrected Total 1384.589 702 a. R Squared = .071 (Adjusted R Squared = .060) Dependent Variable: THINK OF SELF AS LIBERAL OR CONSERVATIVE F df1 df2 Sig. 3.455 8 694 .001 Descriptive Statistics Dependent Variable: THINK OF SELF AS LIBERAL OR CONSERVATIVE HOW OFTEN R ATTENDS RELIGIOUS SERVICES Mean Std. Deviation N NEVER 3.68 1.407 110 LT ONCE A YEAR 3.65 1.205 55 ONCE A YEAR 4.09 1.244 98 SEVRL TIMES A YR 4.08 1.342 89 ONCE A MONTH 4.32 .913 50 2-3X A MONTH 4.03 1.470 63 NRLY EVERY WEEK 4.47 1.298 36 EVERY WEEK 4.60 1.482 134 MORE THN ONCE WK 4.79 1.531 68 Total 4.19 1.404 703 Multiple Comparisons Dependent Variable: THINK OF SELF AS LIBERAL OR CONSERVATIVE (I) HOW OFTEN R ATTENDS RELIGIOUS SERVICES (J) HOW OFTEN R ATTENDS RELIGIOUS SERVICES Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound Tukey HSD NEVER LT ONCE A YEAR .03 .225 1.000 -.67 .73 ONCE A YEAR -.41 .189 .428 -1.00 .18 SEVRL TIMES A YR -.40 .194 .513 -1.00 .21 ONCE A MONTH -.64 .232 .133 -1.36 .08 2-3X A MONTH -.35 .215 .790 -1.02 .32 NRLY EVERY WEEK -.79 .261 .064 -1.60 .02 EVERY WEEK -.92* .175 .000 -1.46 -.37 MORE THN ONCE WK -1.11* .210 .000 -1.77 -.46 LT ONCE A YEAR NEVER -.03 .225 1.000 -.73 .67 ONCE A YEAR -.44 .229 .609 -1.15 .28 SEVRL TIMES A YR -.42 .233 .671 -1.15 .30 ONCE A MONTH -.67 .266 .233 -1.49 .16 2-3X A MONTH -.38 .251 .855 -1.16 .40 NRLY EVERY WEEK -.82 .292 .117 -1.73 .09 EVERY WEEK -.94* .218 .001 -1.62 -.26 MORE THN ONCE WK -1.14* .247 .000 -1.91 -.37 ONCE A YEAR NEVER .41 .189 .428 -.18 1.00 LT ONCE A YEAR .44 .229 .609 -.28 1.15 SEVRL TIMES A YR .01 .199 1.000 -.61 .63 ONCE A MONTH -.23 .237 .989 -.96 .51 2-3X A MONTH .06 .220 1.000 -.62 .74 NRLY EVERY WEEK -.38 .265 .885 -1.21 .45 EVERY WEEK -.51 .181 .120 -1.07 .06 MORE THN ONCE WK -.70* .215 .031 -1.37 -.03 SEVRL TIMES A YR NEVER .40 .194 .513 -.21 1.00 LT ONCE A YEAR .42 .233 .671 -.30 1.15 ONCE A YEAR -.01 .199 1.000 -.63 .61 ONCE A MONTH -.24 .241 .986 -.99 .51 2-3X A MONTH .05 .224 1.000 -.65 .74 NRLY EVERY WEEK -.39 .269 .872 -1.23 .44 EVERY WEEK -.52 .186 .122 -1.10 .06 MORE THN ONCE WK -.72* .219 .032 -1.40 -.03 ONCE A MONTH NEVER .64 .232 .133 -.08 1.36 LT ONCE A YEAR .67 .266 .233 -.16 1.49 ONCE A YEAR .23 .237 .989 -.51 .96 SEVRL TIMES A YR .24 .241 .986 -.51 .99 2-3X A MONTH .29 .258 .971 -.51 1.09 NRLY EVERY WEEK -.15 .298 1.000 -1.08 .77 EVERY WEEK -.28 .226 .950 -.98 .42 MORE THN ONCE WK -.47 .254 .635 -1.26 .31 2-3X A MONTH NEVER .35 .215 .790 -.32 1.02 LT ONCE A YEAR .38 .251 .855 -.40 1.16 ONCE A YEAR -.06 .220 1.000 -.74 .62 SEVRL TIMES A YR -.05 .224 1.000 -.74 .65 ONCE A MONTH -.29 .258 .971 -1.09 .51 NRLY EVERY WEEK -.44 .284 .832 -1.33 .44 EVERY WEEK -.57 .208 .143 -1.21 .08 MORE THN ONCE WK -.76* .238 .038 -1.50 -.02 NRLY EVERY WEEK NEVER .79 .261 .064 -.02 1.60 LT ONCE A YEAR .82 .292 .117 -.09 1.73 ONCE A YEAR .38 .265 .885 -.45 1.21 SEVRL TIMES A YR .39 .269 .872 -.44 1.23 ONCE A MONTH .15 .298 1.000 -.77 1.08 2-3X A MONTH .44 .284 .832 -.44 1.33 EVERY WEEK -.12 .256 1.000 -.92 .67 MORE THN ONCE WK -.32 .281 .967 -1.19 .55 EVERY WEEK NEVER .92* .175 .000 .37 1.46 LT ONCE A YEAR .94* .218 .001 .26 1.62 ONCE A YEAR .51 .181 .120 -.06 1.07 SEVRL TIMES A YR .52 .186 .122 -.06 1.10 ONCE A MONTH .28 .226 .950 -.42 .98 2-3X A MONTH .57 .208 .143 -.08 1.21 NRLY EVERY WEEK .12 .256 1.000 -.67 .92 MORE THN ONCE WK -.20 .203 .988 -.83 .43 MORE THN ONCE WK NEVER 1.11* .210 .000 .46 1.77 LT ONCE A YEAR 1.14* .247 .000 .37 1.91 ONCE A YEAR .70* .215 .031 .03 1.37 SEVRL TIMES A YR .72* .219 .032 .03 1.40 ONCE A MONTH .47 .254 .635 -.31 1.26 2-3X A MONTH .76* .238 .038 .02 1.50 NRLY EVERY WEEK .32 .281 .967 -.55 1.19 EVERY WEEK .20 .203 .988 -.43 .83 LSD NEVER LT ONCE A YEAR .03 .225 .903 -.41 .47 ONCE A YEAR -.41* .189 .030 -.78 -.04 SEVRL TIMES A YR -.40* .194 .041 -.78 -.02 ONCE A MONTH -.64* .232 .006 -1.09 -.18 2-3X A MONTH -.35 .215 .104 -.77 .07 NRLY EVERY WEEK -.79* .261 .003 -1.30 -.28 EVERY WEEK -.92* .175 .000 -1.26 -.57 MORE THN ONCE WK -1.11* .210 .000 -1.52 -.70 LT ONCE A YEAR NEVER -.03 .225 .903 -.47 .41 ONCE A YEAR -.44 .229 .057 -.89 .01 SEVRL TIMES A YR -.42 .233 .070 -.88 .03 ONCE A MONTH -.67* .266 .013 -1.19 -.14 2-3X A MONTH -.38 .251 .134 -.87 .12 NRLY EVERY WEEK -.82* .292 .005 -1.39 -.24 EVERY WEEK -.94* .218 .000 -1.37 -.51 MORE THN ONCE WK -1.14* .247 .000 -1.62 -.65 ONCE A YEAR NEVER .41* .189 .030 .04 .78 LT ONCE A YEAR .44 .229 .057 -.01 .89 SEVRL TIMES A YR .01 .199 .947 -.38 .40 ONCE A MONTH -.23 .237 .335 -.69 .24 2-3X A MONTH .06 .220 .785 -.37 .49 NRLY EVERY WEEK -.38 .265 .152 -.90 .14 EVERY WEEK -.51* .181 .005 -.86 -.15 MORE THN ONCE WK -.70* .215 .001 -1.12 -.28 SEVRL TIMES A YR NEVER .40* .194 .041 .02 .78 LT ONCE A YEAR .42 .233 .070 -.03 .88 ONCE A YEAR -.01 .199 .947 -.40 .38 ONCE A MONTH -.24 .241 .316 -.71 .23 2-3X A MONTH .05 .224 .834 -.39 .49 NRLY EVERY WEEK -.39 .269 .144 -.92 .13 EVERY WEEK -.52* .186 .006 -.88 -.15 MORE THN ONCE WK -.72* .219 .001 -1.15 -.28 ONCE A MONTH NEVER .64* .232 .006 .18 1.09 LT ONCE A YEAR .67* .266 .013 .14 1.19 ONCE A YEAR .23 .237 .335 -.24 .69 SEVRL TIMES A YR .24 .241 .316 -.23 .71 2-3X A MONTH .29 .258 .264 -.22 .79 NRLY EVERY WEEK -.15 .298 .609 -.74 .43 EVERY WEEK -.28 .226 .220 -.72 .17 MORE THN ONCE WK -.47 .254 .062 -.97 .02 2-3X A MONTH NEVER .35 .215 .104 -.07 .77 LT ONCE A YEAR .38 .251 .134 -.12 .87 ONCE A YEAR -.06 .220 .785 -.49 .37 SEVRL TIMES A YR -.05 .224 .834 -.49 .39 ONCE A MONTH -.29 .258 .264 -.79 .22 NRLY EVERY WEEK -.44 .284 .122 -1.00 .12 EVERY WEEK -.57* .208 .007 -.97 -.16 MORE THN ONCE WK -.76* .238 .001 -1.23 -.29 NRLY EVERY WEEK NEVER .79* .261 .003 .28 1.30 LT ONCE A YEAR .82* .292 .005 .24 1.39 ONCE A YEAR .38 .265 .152 -.14 .90 SEVRL TIMES A YR .39 .269 .144 -.13 .92 ONCE A MONTH .15 .298 .609 -.43 .74 2-3X A MONTH .44 .284 .122 -.12 1.00 EVERY WEEK -.12 .256 .625 -.63 .38 MORE THN ONCE WK -.32 .281 .252 -.87 .23 EVERY WEEK NEVER .92* .175 .000 .57 1.26 LT ONCE A YEAR .94* .218 .000 .51 1.37 ONCE A YEAR .51* .181 .005 .15 .86 SEVRL TIMES A YR .52* .186 .006 .15 .88 ONCE A MONTH .28 .226 .220 -.17 .72 2-3X A MONTH .57* .208 .007 .16 .97 NRLY EVERY WEEK .12 .256 .625 -.38 .63 MORE THN ONCE WK -.20 .203 .331 -.60 .20 MORE THN ONCE WK NEVER 1.11* .210 .000 .70 1.52 LT ONCE A YEAR 1.14* .247 .000 .65 1.62 ONCE A YEAR .70* .215 .001 .28 1.12 SEVRL TIMES A YR .72* .219 .001 .28 1.15 ONCE A MONTH .47 .254 .062 -.02 .97 2-3X A MONTH .76* .238 .001 .29 1.23 NRLY EVERY WEEK .32 .281 .252 -.23 .87 EVERY WEEK .20 .203 .331 -.20 .60 Based on observed means. The error term is Mean Square(Error) = 1.853. *. The mean difference is significant at the .05 level. Homogeneous Subsets THINK OF SELF AS LIBERAL OR CONSERVATIVE HOW OFTEN R ATTENDS RELIGIOUS SERVICES N Subset 1 2 3 TukeyHSDa,b,c LT ONCE A YEAR 55 3.65 NEVER 110 3.68 2-3X A MONTH 63 4.03 4.03 SEVRL TIMES A YR 89 4.08 4.08 4.08 ONCE A YEAR 98 4.09 4.09 4.09 ONCE A MONTH 50 4.32 4.32 4.32 NRLY EVERY WEEK 36 4.47 4.47 EVERY WEEK 134 4.60 4.60 MORE THN ONCE WK 68 4.79 Sig. .109 .285 .062 Means for groups in homogeneous subsets are displayed. Based on observed means. The error term is Mean Square(Error) = 1.853. a. Uses Harmonic Mean Sample Size = 66.899. b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed. c. Alpha = .05. Profile Plots Interpretation The descriptive results show that the mean and the standard deviation of the study are 4.19 and 1.404 respectively. The sample size for the study is 703. Taking 95% confidence interval, DF1 and DF2 are 8 and 694 respectively. This shows the difference of means between the groups with a significant level of 0.05. The p-value is the probability of obtaining a test statistic at least extreme as the one that was actually observed (Cronk, 2008). The p-value of the study is 0.01 at 95% confidence interval. The error term of the study is the mean square=1.853 with the harmonic mean sample size of 66.899. The harmonic mean is used in the study because the group sizes are not equal. The harmonic mean result shows that 66 out of 703 of the people interviewed attend religious services several times in a year. The confidence interval of the study is 95%. This shows that there is 95% confidence that the real value is within the calculated interval (mean). The Pearson correlation coefficient is 1. This means that there is a strong positive correlation between religious services and political views. The correlation coefficients across all the age groups also show positive results. The positive sign shows that both attending religious services and political views changes towards a similar direction. Most of the people (134) interviewed attend religious services every week while 36 people who gave their opinions attend religious nearly every week. Hypothesis testing The one way Anova gives a p-value of 0.01. The study uses 95% confidence interval that means the significance level is 0.05. Therefore, the P-value (0.01) < significance level (0.05) and as a result we reject the null hypothesis and accept the alternative hypothesis (Cronk, 2008). We conclude therefore that the error variance of the dependent variable is not equal across groups. Conclusion From the statistical results of the study, it is clear that political views are affected by how often an individual attend religious services. Most people who gave their views regarding his/her political position attend religious services regularly. This statement is emphasized by the results from the profile graph. The graph shows a rather interesting trend whereby the mean increases with an increase in the religious service attendance. Those who had never attended religious services had the least mean while those who attend religious services more than once a week have the highest mean. However, the error variance of the political views is not the same across all the groups. For that reason, we use the harmonic mean instead of arithmetic mean. This is a representation of a real world where people tend to related to a political party or ideology based on his/her religious experience. Nevertheless, it should be noted that religion is just one of the factors that influence choice on political party affiliation. References Cronk, B. C. (2008). How to use SPSS: A step-by-step guide to analysis and interpretation. Glendale, CA: Pyrczak Pub. Read More