User:Hawkeyelion/sandbox

One Way ANOVA The police commissioner of a large city wants to institute a training course for policemen related to improving human relations skills.He has the option of offering a 5-hour course,a 10-hour course, or a 15-hour course. He decides to run a pilot course to determine the optimal length of the class necessary to enhance human relations skills. He randomly selects 45 policemen and randomly assigns 15 to each length of course. At the end of the course, the human relations skills of the policemen are assessed and a OneWay Anova is used to test for differences in the mean level of human relation skills for the policemen taking the three classes. The results of this analysis are given in the attached printout. Use alpha=0.05 for all statistical tests.

1. What are the independent and dependent variables for this study? Independent variables length of each course (5hour, 10hour, 15hour) Dependent variable is the human relations skills.

2. Why did the researcher randomly select the 45 policemen? To account for external validity. 3. Why did the researcher randomly assign the subjects to the 3 groups? To account for internal validity.

4a. What are the assumptions underlying the analysis of variance? The normality assumption=the data are normally distributed in each group. The homogeneity of variance assumption=The variance is the same in each group, and the independence assumption=the data are independent.

4b. Which assumption is tested on the printout? Homogeneity of variance is tested on the printout, the means across the groups are equal.

4c. Is the assumption met for these data? Look At the sig level from the test of Homogeneity of Variances,if it is larger than the α level then Yes, HDV was met.

4d. What specific information on the printout did you use to come to this conclusion? The Levene statistic table tells us there is no difference across the 4 groups. On the printout, the test of homogeneity of variance is met for these data. We looked at the SIG portion of the table, where the significance of .302 is greater than the given alpha level of .05.

5a. Is the average percent the same for the 3 groups? No, the average percent is different for the 3 groups. OR The sig = .000 < alpha = 0.05, therefor we reject.

5b. What specific information on the printout did you use to come to this conclusion? The Anova table indicates an F sig. (.000) which is less than .05 alpha level.

6. What does Omega Square this represent? This represents the proportion of the dependent variable that can be attributed for by the independent variable. Thus,25.8% of the variance in human relations skills can explained/attributed for by the training courses.

7. According to the Tukey results on the attached printout, what pairs of groups differ? The poplulation means for a 5hour course and a 15 hour course are statistically different (p<0.01). However, a 10 hour course does not differ from a 5 hour course and 15 hour course (p=.075>.05 ad p=.137>0.05, repsectively, fail to reject the null hypothesis.)

8. The Cohen d for hte man differences for hte 5 hour course and the 15 hour course is 1.53. What does this Codhen d represent? The Cohen's d represent the two tail effect size.

Null Hypothesis is True-Ho       Alternative is True-Ha Ho  Null Hypothesis is true              Accurate                       Type 2 Error Ha  Null Hypothesis is false           Type I Error                        Accurate

9. 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.

10. To whom, if anyone, can we generalize our findings? We can generalize the findings to the participants in the study. OR Assuming the researcher fulfilled both random assignment and random selection the results of the findings can go to sample population. (OR if the participants are VOLUNTEERS: Given the samples were volunteers participants research may comprise external valitiy.) The findings however show that there are significant differences in the means of the groups.

11. Write a brief Results section describing the findings of this experiment based on the analyses presented here. We would write the F ratio as: The one-way, between subjects analysis of variance revealed a statistically significant difference in the mean level of human relations skills for hte policemen taking the three classes, F(2,42) = 8.815, p=.001, alpha = .05. The 2 is the betweek groups degrees of freedom, 42 is the within groups degrees of freedom, 8.815 is the F ratio fromt eh F column, .001 is the value in the Sig column (the p value) and 87.540 is the within groups mean square estimate of variance. The population means for a 5hour course and a 15hour course are statistically different (p<0.001). However, a 10 hour course does not differ from a 5hour course and a 15 hour course (p=.075>0.05 and p=.137>0.05, respectively, fail to reject the null hypothesis.) IF THERE IS NOT A DIFFERENCE: Teh one way anova failed to reveal a significant effect of other majors on GPA. F(3,41)= .781, p=.511, alpha=0.05, therefore we failed to reject the HO.

Multiple regression

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. The set of independent variables explains a significant proportion of variance in students SAT scores. b. What information on the printout did you use to come to answer this question? Because the sig (p) value of .000 on the ANOVA table is less than the given alpha level of .05, it is significantly different from zero.

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. R2 = 0.34. It means that 34% of variation is explained by the model. The adjusted R2=0.329 adjusts for the number of explanatory terms (independent variables) in a model and increases only if the new independent variable(s) improve(s) the model more than would be expected by chance.

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 SAT mathematics performance? Look at the sig values on the coefficients chart. Must be <sig(0.05). The following variables have statistically significant unique influence on SAT mathematics performance: 1) sex, 2) grades in math courses, 3)number of years of math taken, 4) high school rank, 5) self-rating of math abilities.

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.

5.a.What is the relative importance of the independent variables in their influence on student achievement? The following variables are significant at the .001 level: sex, self-rating of math abilities. The following variables are significant at the .05 level: grades in math courses, number of years in math taken, and high school rank.

b. What particular information on the printout did you use to answer this question? Look at the Standardized Coefficients Beta chart. Rank by highest to lowest. In the coefficient model the values for standardized coefficients Beta column indicate the relative importance of the significant independent variable. 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).

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. OR 7a. to answer the researcher's other question, are there differences between males and females in their SAT mathmatics performance after controlling for the other variables in the model? YES 7b. Why or why not? Because the associated significance level is >0.05, the coefficient of the variable "sex" is statistiacally significant from zero.

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

EXPLAIN: Associated with, influence, relationship, predict

CORRELATIONS-Relationship -2 variables, 1 Criteria, 1 Predictor (2 relationships that go together,two test scores)

MULTIPLE REGRESSION-(more complex),1 Criteria,>1 Predictor (Relative Influences)

GROUP: Difference, Cause, Experimental

INDEPENDENT TTEST - Simple - 1 dep. variable, 1 Ind Variable, (2 groups) One outcome,two groups(One is better than the other)

ANOVA - More complex - More complex-1 dep variable,1 Ind Variable, (>2 groups) Differences,GROUPS(Freshmen,sophmores,juniors & scores)

Paired Sample T Test - (Pre&Post tests)

How important is the homo of assumption? Very important. To see if there is variance within each group.

Can you use the Test of Homo of Variance if the outcome variance is not continuous? (Example: Dead/Alive, Graduated/Not Graduated) No.

What is the Welch Test? Opposite of Homo = hetro If homo assumption is violated it is hetrostadastic.

The Cohen's D represents the 2 tale effects size.

What is the Omega 2? The proportion of the variance of the independent variable by the dependent variable.

Where is the Global Comparison of the Group Means? The F in the ANOVA table.

What is the p value? A measure of how much evidence we have against the null hypothesis.

Tukey/Scheffe's test: The effects size is significantly greater for schedffe's test. Why use ANOVA instead of several ttests? ANOVA is appropriate to use because its greater than 2 groups.

What is confidence interval? The CV in this case is 95% due to the alpha level being 0.05.

When the null is true, you reject the null.

Type I - Not innocent, you let go. Type II - Innocent, you convict.