One way anova is a comparison of means test across a factor. Dependent variable is age ANOVA Q1. Age Between Groups Within Groups Total Sum of Squares 14489.903 10626193.940 10640683.840 df 4 50311 50315 Mean Square 3622.476 F 17.151 Sig. .000 F 17.151 Sig. .000 211.210 Test of Homogeneity of Variances Q1. Age Levene Statistic 7.959 df1 4 df2 50311 Sig. .000 ANOVA Q1. Age Between Groups Within Groups Total Sum of Squares 14489.903 10626193.940 10640683.840 df 4 50311 50315 Mean Square 3622.476 211.210 Post Hoc Tests Multiple Comparisons Dependent Variable: Q1. Age Bonferroni (I) Q3a. Country's present economic condition Very Bad Fairly bad (J) Q3a. Country's present economic condition Fairly bad Neither good nor bad Fairly good Very good Very Bad Neither good nor bad Fairly good Very good 95% Confidence Interval Mean Difference (I-J) .781* 1.265* Std. Error .174 .205 Sig. .000 .000 Lower Bound .29 .69 Upper Bound 1.27 1.84 1.397* .880 -.781* .485 .183 .330 .174 .201 .000 .077 .000 .160 .88 -.05 -1.27 -.08 1.91 1.81 -.29 1.05 .616* .099 .179 .327 .006 1.000 .11 -.82 1.12 1.02 Neither good nor bad Fairly good Very good Games-Howell Very Bad Fairly bad Neither good nor bad Fairly good Very good *. The mean difference is significant at the 0.05 level. Very Bad Fairly bad Fairly good Very good Very Bad Fairly bad Neither good nor bad Very good Very Bad Fairly bad Neither good nor bad Fairly good Fairly bad Neither good nor bad Fairly good Very good Very Bad Neither good nor bad Fairly good Very good Very Bad Fairly bad Fairly good Very good Very Bad Fairly bad Neither good nor bad Very good Very Bad Fairly bad Neither good nor bad Fairly good -1.265* -.485 .132 -.386 -1.397* -.616* -.132 .205 .201 .209 .345 .183 .179 .209 .000 .160 1.000 1.000 .000 .006 1.000 -1.84 -1.05 -.46 -1.35 -1.91 -1.12 -.72 -.69 .08 .72 .58 -.88 -.11 .46 -.517 -.880 -.099 .386 .332 .330 .327 .345 1.000 .077 1.000 1.000 -1.45 -1.81 -1.02 -.58 .42 .05 .82 1.35 .517 .781* 1.265* .332 .173 .206 1.000 .000 .000 -.42 .31 .70 1.45 1.25 1.83 1.397* .880 -.781* .485 .184 .348 .173 .201 .000 .084 .000 .111 .90 -.07 -1.25 -.06 1.90 1.83 -.31 1.03 .616* .099 -1.265* -.485 .132 -.386 -1.397* -.616* -.132 .178 .345 .206 .201 .210 .362 .184 .178 .210 .005 .999 .000 .111 .971 .825 .000 .005 .971 .13 -.84 -1.83 -1.03 -.44 -1.37 -1.90 -1.10 -.70 1.10 1.04 -.70 .06 .70 .60 -.90 -.13 .44 -.517 -.880 -.099 .386 .350 .348 .345 .362 .578 .084 .999 .825 -1.47 -1.83 -1.04 -.60 .44 .07 .84 1.37 .517 .350 .578 -.44 1.47 Running head: TESTING FOR ONE-WAY ANOVA Testing for One-Way ANOVA – Week 7 Assignment 1 Walden University 1 TESTING FOR ONE-WAY ANOVA 2 Testing for One-Way ANOVA – Week 7 Assignment 1 Example Research Question, One-Way ANOVA, and Analysis The following will examine an example research question from the High School Longitudinal Study 2009 Dataset: Is there a relationship between school locale and the number of AP Courses offered to their respective students? This research question would align with a quantitative method as it is strictly looking at data (whether or not there is a relationship/differences) and does not seek to address any reasons as to why differences is exist, if they should, or aim to implement new policies at this time. A One-Way ANOVA was conducted (Figure 3) using the two variables of “school locale” and “number of AP courses offered” as the independent and dependent variables, respectively, with school locale being a nominal measurement and number of AP courses being a ratio measurement (FrankfortNachmias & Leon-Guerrero, 2015; Laureate Education, 2016h; Wagner, 2016). The null hypothesis is that there are no significant statistical differences in the number of AP courses offered based on the school’s locale. The null hypothesis was rejected as statistical significance was found at p = 0.000, below the typical alpha threshold of 0.05 (Frankfort-Nachmias & Leon-Guerrero, 2015; Laureate Education, 2016h; Wagner, 2016). The F critical value was found at 2.61, calculated by SPSS to be 632.698, again supporting a strong level of statistical significance and safely rejecting the null hypothesis. A test of homogeneity was conducted (Figure 2) and significance was found at 0.000; therefore, equal variances were not assumed and a Games-Howell Post-Hoc (Figure 4) was used to address the levels of statistical significance between and within groups. In viewing the Post-Hoc, there are significant statistical differences among and between each of the four groups (city, suburb, town, rural) as statistical significance was found at 0.00 across the board. TESTING FOR ONE-WAY ANOVA 3 In addressing the descriptive data (Figure 1), schools located in a suburb offer the highest amount of AP courses followed by city, rural, and town locales in order of highest to lowest. In addressing the real world practicality and meaningfulness, effect size was calculated using the eta square (Frankfort-Nachmias & Leon-Guerrero, 2015; Laureate Education, 2016h; Wagner, 2016). Taking the between groups variance (64688.889) and dividing it by the total group variance (650745.306) the effect size came to 0.099, a small effect size indicating approximately 9.9% of the variance among the number of AP courses offered is attributable to school locale. This small effect size, in the light of a strong statistical significance being found, indicates that there are other variables which may more strongly account for the statistical differences regarding the number of AP courses offered in their respective locales. Implications for social change may include a better understanding of why these differences exist in an attempt to further equal the opportunities for students across all locales. Please see Figures 1-4 for further clarification and visual displays of the data. TESTING FOR ONE-WAY ANOVA 4 TESTING FOR ONE-WAY ANOVA 5 References Frankfort-Nachmias, C., & Leon-Guerrero, A. (2015). Social statistics for a diverse society (7th ed.). Thousand Oaks, CA: Sage Publications. High School Longitudinal Study 2009 Dataset. (2009). (dataset file) Laureate Education (Producer). (2016h). One-way ANOVA demonstration [Video file]. Baltimore, MD: Author. Wagner, W. E. (2016). Using IBM® SPSS® statistics for research methods and social science statistics (6th ed.). Thousand Oaks, CA: Sage Publications.
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