Question

ANOVAs by Hand - Show your work for all problems (use the back of the page if you need more space) 1. A psychologist wants to know whether there are any significant differences in the quality of mental health care available for different levels of prison security. Quality of health care for the prisons is based on ratings from an independent observer on a scale of 1-10 (with 10 being highest). For the data presented below, conduct the One-Way Between-Subjects ANOVA and fill in the appropriate values for the Source Table. Use .05 for the c-level. (20 points) Medium Security Maximum Security Minimum Security X 8 X2 X 5 2 9 7 T - NAW 7 8 I Sums: Source Table Source SS df MS For Ferit la = .05) Significant? (Yes/No) Between Within Total

Answer 1

2 25 36 49 X 64 81 = 255 x3 7 25 49 36 3664>X X234 = 210 4 16 2 1 From the given information,N 15, Grand total } X = 35+32+12 79 Raw sum of squares X2 499 (Σx) 2 correction factor(CF)= N ctor(CF)- 2x}_ (79 416.0667 15 ΣχΣη) Σχ' 2 SS 499-416.0667 82.9333 Total 2 352 322 122 SST -416.0667 62.5333 N 5 5 5 SSE SS SST 82.9333- 62.5333 20.4 Total ANOVA table DF Sig. Source SS MS obs cri 62.5333 31.2667 -=31.2667 2 Between groups 3-1 2 62.5333 Yes -=18.3922 3.89 1.7 20.4 -1.7 12 Within groups(Error) 15-3 =12 20.4000 Total 15-1 14 82.9333 Null hypothesis H0 4 = 2 f43 Alternative hypothesis H/:Not all the means are equal P-value 0.000 less than the level of signficance a = 0.05, we reject the null hypothesis The critical value is F(2,12) 3.89 at 5%level of significance The value of the test statistic F 18.3922 greater than the critical F(2,12)