User:Tntigers2013/sandbox

One Way ANOVA

A superintendent of district X wants to test the relative efficacy of educational technology marketed to their schools. In particular, he wants to determine the effectiveness of classroom technology at improving student achievement. He asks for volunteer schools to participate in the study, and from the list of volunteer schools, he randomly selects classrooms and randomly assigns them to one of 3 groups. Group 1 received an on-site classroom technology support each day for 1 hour. Group 2 received a 15-minute on-site classroom technology support daily for 3 months, and Group 3 received a placebo daily for 3 months. For the placebo group, the classroom teachers are informed that the software update will improve the effectiveness of the technology at improving student achievement. In all groups, a software is installed on their classroom technology. Every classroom was required to keep a formative assessment log, linked to the targets of daily instruction. Prior to the analysis of the data, the superintendent tested to see if there were any differences among the 3 groups of classrooms in terms of teacher experience, technology literacy, instructional styles/methods, content areas, student background and additional educational resources. There were no differences on any of these variables. Subsequently, he analyzed to data with a One-way ANOVA. The attached printout shows the results of the analyses. Use α=.05 for all statistical tests.

1. What are the independent and dependent variables for this study? Independent variables are the number of hrs. of on-site classroom technology support each day. Dependent variable is the effectiveness of classroom technology at improving student achievement.

2. Why did the researcher randomly assign the subjects to the 3 groups? To account for internal validity.

3. Why did the researcher test to see if the 3 groups were the same in teacher experience, technology literacy, instructional styles/methods, content areas, student background and additional educational resources? The researcher wanted to ensure all groups were similar and also rule out any other outside influences.

'''4a. What are the assumptions underlying the analysis of variance?''' The normality assumption, the homogeneity of variance assumption, and the independence assumption

'''4b. Which assumption is tested on the printout?''' Homogeneity of variance is tested on the printout.

'''4c. Is the assumption met for these data?''' Yes, HDV was met.

'''4d. What specific information on the printout did you use to come to this conclusion?''' The Levene statistic 2.364 has a significance of .113>.05 alpha level, according to the Test of HOV chart.

'''5a. Is the average percent the same for the 3 groups?''' No, the average percent is different for the 3 groups.

'''5b. What specific information on the printout did you use to come to this conclusion?''' The Anova chart indicates an F sig. (.000) which is less than .05 alpha level. 6. What does this represent? The omega squared value of .662 indicates that 66.2% of the variance in the effectiveness of classroom technology can be explained/attributed to the differences between the 3 treatment groups.

7. According to the Tukey results on the attached printout, what pairs of groups differ? Pairwise Groups 1 and 3 (.000), Groups 2 and 3 (.000), Groups 2 and 1 (.011) differ according to the results.

8. What are your substantive conclusions relative to Group 1, Group 2, and Group 3 (the placebo group)? The groups are statistically significantly different from one another.

9. To whom, if anyone, can we generalize our findings? We can generalize the findings to the participants in the study.

10. Write a brief Results section describing the findings of this experiment based on the analyses presented here. A one-way ANOVA was used to test for differences among the 3 groups. The effectiveness of classroom technology at improving student achievement was statistically significant across groups, F (2, 27) = 30.385, p = .000. Tukey post-hoc comparisons of the three groups and homogeneous results indicated that the 3 groups were statistically significantly different from one another.

Multiple regression Coleman and his colleagues (1966) were the first to study the association between school inputs and student achievement using national probability samples of elementary and secondary students. In their pioneering work, Coleman et al. estimated education production functions in order to quantify the association between students’ academic performance in standardized tests and school and family input measures. One of the key findings of the Coleman report was that when the socioeconomic background of the students was held fixed, the differences among schools accounted ‘‘for only a small fraction of differences in pupil achievement.’’ In other words, variations in school characteristics were not closely associated with, and had hardly any effect on, variations in student achievement. Researcher X wanted to replicate Coleman's study using her own data. She gathered data on 200 high school students and that data was analyzed using multiple regression. The attached printout shows the results of her analysis. In that analysis, she regressed student achievement (ACHIEVE) on family background (SES), ethnicity (ethnic coded 0= White, 1=Hispanic), and several school measures: advanced placement courses, length of school year, pupil-teacher ratio, dropout rate, and students in college prep classes. Use the output and alpha level=.05 to answer the following questions. 1.(a)Does multicollinearity appear to be a problem in the analyses? (Goto the VIF in the Collinarity Stats. If the VIFs are less than 10 you do not have a problem.) No, multicollinearity does not appear to be a problem. (b)What specific information did you use to come to this conclusion? The VIFs in the coefficitents table are less than 10.

2.(a)Does the set of independent variables explain a significant proportion of variance in students achievement? (Goto the ANOVA chart. Look at Sig. If p<sig(0.05) then yes.) Yes, the set of independent variables explains a significant proportion of variance in       students achievement. (b) What information on the printout did you use to come to answer this question? By looking at the sig in the ANOVA chart.

3.'''(a)What proportion of variance in student achievement is explained by the set of independent variables?''' (Look at the Correlations table and at R square.) 45.4% of the variance in student achievement is explained by the set of independent variables. (b) What did you use to determine your answer? The adjusted R square adjusts for the number of explanatory terms in a model.

4.(a)Which of the independent variables have a significant influence on student achievement? (Look at the sig values on the coefficients chart. Must be <sig(0.05).      We are explaining a significant influence on student achievement: 1)ethnic 2)ses 3)ap courses 4) length 5)dropout (b) What particular information on the printout did you use to answer this question? We used the significance column under the coefficients table to determine degree of       influence of the independent variables on a dependent variable. If given significance level is 0.05, then the coefficient is statistically significant to zero. The following variables are significant at the 0.05 alpha level:ethnic,ses,ap_courses,length,dropout.

5.(a)What is the relative importance of the independent variables in their influence on student achievement? (Look at the Standardized Coefficients Beta chart. Rank by highest to lowest.) In the presence of the other variables in the model,the following standardized coefficients are used for comparing the effects of independent variables:dropout(.346),apcourses(.266), length(.207),ses(.188),ethnic(.186),pt-ratio(.003).

(b) What particular information on the printout did you use to answer this question? In the coefficient model the values for standardized coefficients Beta column indicate the relative importance of the significant independent variable.

6.'''(a)Are school characteristics more important than family background? Why or not not?''' Yes, school characteristics are more important than family background because the Beta explains the power of that variable. 7.'''How do you substantively interpret the coefficient for ethnic? Be specific.''' (Look at the code: 0=white, 1=Hispanic (0is the same as #2, Reference group is always 0.)      Controlling for all other explanatory variables in the model, the unstandized coefficient Beta    value(.186) indicates that HIspanic population scored 1.86 points higher than whites on student    achievement.

Part 3 1.A researcher in the field of Higher Education believes that there would be differences in students' ratings of the quality of the instruction within liberal arts institutions, comprehensive institutions, and research institutions. ONE WAY ANOVA

2.An early childhood educator believes that children taught utilizing a directive approach will score higher on a readiness for first grade assessment than children taught using a non-directive approach. INDEPENDENT SAMPLES T TEST

3.The Associate Vice-President for Assessment of an institution believes that measures of students effort exerted in their studies would have greater unique effects on their academic performance than measures of their background characteristics. MULTIPLE REGRESSION

4.An evaluator of a Learning Communities project believes that student will score higher on their intention to graduate after participating int he Learning Community than they scored prior to taking part in the Learning Community. PAIRED SAMPLES T TEST

5.A researcher believes that there is no relationship between students assessment of the quality of teaching in their class and the grade they anticipate receiving for that class. CORRELATION

ONE WAY ANOVA - Differences,GROUPS(Freshmen,sophmores,juniors & scores)

COORELATION-relationship (2 relationships that go together,two test scores)

Multiple Regression - Relative Influences (Multiple Relationship,more than 2 variables then MR)

Independent T Test - One outcome two groups(One is better than the other)"perception of counselor's expertise"

Paired Sample T Test - (Pre&Post tests)