Exam 12: Glm 1: Comparing Several Independent Means

What two assumptions must not be violated when running an ANOVA?a.By reviewing the standard error.

What is the F-statistic?

A teacher in a school was interested in examining the differences in children's maths scores across a year group,which consisted of three classes.She was particularly interested in whether the class the child was in had a possible influence on the child's maths score.She ran an ANOVA with the predictor variable 'class',which had three categories,'Yellow Class','Green Class' and 'Purple class'; the outcome variable was 'maths score'. Her ANOVA had an F-statistic of 4.23 (p 0.68).How would you interpret her findings?

When the between-groups variance is a lot larger than the within-groups variance,the F-value is ____ and the likelihood of such a result occurring because of sampling error is _____

The student welfare office was interested in trying to enhance students' exam performance by investigating the effects of various interventions.They took five groups of students before their statistics exams and gave them one of five interventions: (1)a control group just sat in a room contemplating the task ahead (Control); (2)the second group had a yoga class to relax them (Yoga); (3)the third group were told they would get monetary rewards contingent upon the grade they received in the exam (Bribes); (4)the fourth group were given beta-blockers to calm their nerves (Beta-Blockers); and (5)the fifth group were encouraged to sit around winding each other up about how much revision they had/hadn't done (You're all going to fail).The student welfare office made four predictions: (1)all interventions should be different from the control; (2)yoga,bribery and beta-blockers should lead to higher exam scores than panic; (3)yoga and bribery should have different effects than the beta-blocker drugs; and (4)yoga and bribery should also differ.Which of the following planned contrasts (with the appropriate group codings)are correct to test these hypotheses?

Robust ANOVA tests are able to work with which two data 'violations'?

If the differences between group means are large enough,then:

Of the tests below,which tests that the group means are a better fit of the data than the grand mean?

What are post hoc tests?

After an ANOVA you need more analysis to find out which groups differ.When you did not generate specific hypotheses before the experiment use:

The student welfare office was interested in trying to enhance students' exam performance by investigating the effects of various interventions.They took five groups of students before their statistics exams and gave them one of five interventions: (1)a control group just sat in a room contemplating the task ahead; (2)the second group had a yoga class to relax them; (3)the third group were told they would get monetary rewards contingent upon the grade they received in the exam; (4)the fourth group were given beta-blockers to calm their nerves; and (5)the fifth group were encouraged to sit around winding each other up about how much revision they had/hadn't done (a bit like what usually happens).The final percentage obtained in the exam was the dependent variable.Using the critical values for F,how would you report the result in the table below?

When conducting a one-way independent ANOVA with three levels on the independent variable,an F-ratio that is large enough to be statistically significant tells us:

What kind of trend does the following graph show?

Imagine we conduct a one-way independent ANOVA with four levels on our independent variable and obtain a significant result.Given that we had equal sample sizes,we did not make any predictions about which groups would differ before the experiment and we want guaranteed control over the Type I error rate,which would be the best test to investigate which groups differ?

Imagine you compare the effectiveness of four different types of stimulant to keep you awake while revising statistics using a one-way ANOVA.The null hypothesis would be that all four treatments have the same effect on the mean time kept awake.How would you interpret the alternative hypothesis?

A business analyst was interested in the variation of sales income across four shops in a retail chain.He ran an ANOVA with the predictor variable 'shop location',which had four categories,'High street','Outlet','Online' and 'Suburb'; the outcome variable was 'monthly sales income'. His ANOVA had an F-statistic of 98.12 (p 0.02).How would you interpret his findings?

Which of the following is not a rule for conducting orthogonal contrasts?

A health researcher was interested in the variation of patient recovery rates across four different treatment programmes.He was particularly interested in whether the treatment programme that the patient was in had a possible influence on the patient's recovery rate.He ran an ANOVA with the predictor variable 'treatment programme',which had three categories,'Placebo','Drug X' and 'Natural'; the outcome variable was 'Patient recovery rate'. His ANOVA had an F-statistic of 98.12 (p 0.02).How would you interpret his findings?

How can we decide whether our group means are significantly different in an ANOVA?

Subsequent to obtaining a significant result from an exploratory one-way independent ANOVA,a researcher decided to conduct three t-tests to investigate where the differences between groups lie. Which of the following statements is correct?