Exam 14: Analysis of Variance

You are doing a one-way ANOVA and the sample results are consistent with the research hypothesis. On the basis of the following output, your results _____ significant and you _____ proceed to discuss the post-hoc multiple comparisons. ANOVA KIDSBEST Sum of Squares Mean Square Sig. Between Groups 1.523 2 .761 .741 .478 Within Groups 213.586 208 1.027 Total 215.109 210

What is a main effect?

You are doing a one-way ANOVA and the sample results are consistent with the research hypothesis. On the basis of the following output, your results _____ significant and you _____ proceed to discuss the post-hoc multiple comparisons. ANOVA EDUC Sum of Squares Mean Square Sig. Between Groups 203.047 2 101.523 9.209 .000 Within Groups 2348.171 213 11.024 Total 2551.218 215

Your research hypothesis is "In the population, college graduates have a higher average self-confidence than those same persons had when they were just high school graduates." What type of hypothesis test should be used?

You want to know if, on average, participants weigh significantly less at the end of a weight-loss program than they did at the start of the program. Which would be an appropriate procedure to use?

Your research hypothesis is that there is a difference between Protestants, Catholics, and Jews in average reported ideal number of children (KIDSBEST) for a family. Your sample results are consistent with the _____ and you should proceed to _____. Descriptives KIDSBEST Mean Std. Deviation Std. Error 1 Protestant 147 2.71 1.034 .085 2 Catholic 44 2.59 .996 .150 3 Jewish 20 2.45 .887 .198 Total 211 2.66 1.012 .070

Your research hypothesis is "In the population, there is a difference in the average self-confidence among the following groups: Protestants, Catholics, Jews, other religionists, and atheists." What type of hypothesis test should be used?

Your research hypothesis is "In the population, the effect of occupation on number of work days per year lost due to injury varies by sex." What type of hypothesis test should be used?

You are doing a one-way ANOVA. Your research hypothesis is that there is a difference in the mean knowledge about the Bible between Baptists, Catholics, and Methodists. What is your null hypothesis?

Answer the questions that follow this SPSS output: Descriptive Statistics Dependent Variable: AGEKDBRN R'S AGE WHEN 1ST CHILD BORN CLASS SUEJECTIVE SEX Mesn Std. Deviation 1 LOWER CLASS 0 MALE 23.89 5.593 18 1 FEMALE 19.55 3.336 40 Total 20.90 4.587 58 2 WORKING CLASS 0 MALE 23.30 4.285 159 1 FEMALE 22.23 4.904 278 Total 22.62 4.712 437 3 MIDDLE CLASS 0 MALE 26.48 5.454 172 1 FEMALE 23.68 5.380 299 Total 24.70 5.553 471 4 UPPER CLASS 0 MALE 27.07 5.830 27 1 FEMALE 23.80 6.488 20 Total 25.80 6.285 47 Total 0 MALE 25.05 5.258 376 1 FEMALE 22.78 5.202 637 Total 23.82 5.334 1013 Tests of Between-Subjects Effects Dependent Variable: AGEKDBRN R'S AGE WHEN $1 S T$ CHILD BORN Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 2929.60 7 418.516 16.286 .000 Intercept 192981.648 1 192981.648 7500.420 .000 CLASS 1451.486 3 483.829 18.804 .000 SEX 729.105 1 729.105 28.337 .000 CLASS -SEX 239.362 3 79.787 3.101 .026 Error 25858.093 1005 25.729 Total 594131.000 1013 Corrected Total 28787.702 1012 $\text { a. } R \text { Squared }=.102 \text { (Adiusted R Squared }=.098 \text { ) }$ You have done a two-way analysis of variance with age at birth of first child (AGEKDBRN) as the dependent variable and CLASS and SEX as the factor variables. A) Is the overall model statistically significant? (yes / no) B) Is the interaction effect statistically significant? (yes / no / skipped) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.) C) Is the main effect of CLASS statistically significant? (yes / no / skipped) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.) D) Is the main effect of SEX statistically significant? (yes / no / skipped) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)

Answer the questions that follow this SPSS output: Descriptives RINCDOL Respondent's income; ranges recoded to midpoints Mean Std. Deviation Std. Error Less than high school 58 22043.10 19115.137 2509.940 High school 223 34060.54 21343.362 1429.257 Junior college or more 173 48882.95 29731.887 2260.474 Total 454 38173.46 26273.624 1233.082 ANOVA RINCDOL Respondent's income; ranges recoded to midpoints Sum of Squares df Mean Square Sig. Between Groups 3.87+10 2 1.935+10 31.854 .000 Within Groups 2.74+11 451 607543829.7 Total 3.13+11 453 Multiple Comparisons Dependent Variable: RINCDOL Respondent's income; ranges recoded to midpoints Bonferroni (l) NDEGREE Degree (J) NDEGREE Degree Mean Difference (-) Std. Error Sig. Less than high school High school -12017.4 3633.085 .003 Junior college or more -26839.8 3739.881 .000 High school Less than high school 12017.4 3633.085 .003 Junior college or more -14822.4 2497.244 .000 Junior college or more Less than high school 26839.8 3739.881 .000 High school 14822.4 2497.244 .000 *. The mean difference is significant at the .05 level. Your research hypothesis is "In the population, there is a difference in the average income among the following groups: those with less than a high school degree, those with just a high school degree, and those with at least a junior college degree." A) What is your null hypothesis? B) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research) C) What is the probability of getting the sample results you got if the null hypothesis is true? (If this step in hypothesis testing can be skipped, write the word "SKIP".) D) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?) E) Are your results statistically significant? (yes / no) F) Is it appropriate to discuss the results of the post hoc multiple comparisons tests? (yes / no) G) If it is appropriate to discuss the post hoc multiple comparison tests, which pairs of groups are probably different from one another in the population? If it is not appropriate, explain why it is not appropriate.

You are doing a one-way ANOVA. What level of measurement is required on the two variables you are using? (Circle the letter of the correct answer.)

Answer the questions that follow this SPSS output:   You have done a two-way analysis of variance with number of children (CHILDS) as the dependent variable and SEX and CLASS as the factor variables. A) Is the overall model statistically significant? (yes / no) B) Is the interaction effect statistically significant? (yes / no ) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.) C) Is the main effect of SEX statistically significant? (yes / no) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.) D) Is the main effect of CLASS statistically significant? (yes / no) (If this step was skipped because of earlier conclusions, write the word "skipped" as your answer.)

On the basis of this output, which of the following is true? Tests of Between-Subjects Effects Dependent Variable:INCOME Source Type III Sum of Squares df Mean Square Sig. Corrected Model 1.81010 5 3.6199 4.303 .001 Intercept 9.91110 1 9.91110 117.844 .000 MARRIED 6.674 2 3.337 3.967 .021 SEX 4.128 1 4.1289 4.908 .028 MARRIED * SEX 1.3089 2 6.5408 .778 .461 Error 1.35411 161 8.4108 Total 3.15611 167 Corrected Total 1.53511 166 a. R Squared $= .118 ($ Adjusted R Squared $= .090 )$

Your research hypothesis is "In the population, the effect of type of school attended on SAT score varies by social class." What type of hypothesis test should be used?

Your research hypothesis is "In the population, the average number of days unauthorized immigrants stay in the United States is less than 450." What type of hypothesis test should be used?

You want to know if there are any significant differences between the means of three groups, and, if so, between which groups. Which would be an appropriate procedure to use?

There is almost always an interaction effect present in the sample data, so why isn't there almost always a significant interaction effect?

Which of the following is NOT a possible stopping point in a two-way ANOVA problem?

The F ratio for a one-way ANOVA is reported to have 5 and 171 degrees of freedom. That means _____ groups were being compared and there were _____ cases included in the analysis.