Design and Analysis of Experiments-Analysis of Covariance (ISS (Statistical Services) Statistics Paper IV): Questions 1 - 6 of 6
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Question number: 1
» Design and Analysis of Experiments » Analysis of Covariance
Appeared in Year: 2009
Describe in Detail
What is the use of analysis of covariance? Give the general procedure of analysis of covariance for a RBD, stating the necessary assumptions.
Explanation
Analysis of Covariance (ANCOVA) : Extension of ANOVA gives way of statistically controlling the (linear) effect of variables one does not want to examine and the extraneous variables are called covariates, or control Variables. It allows removing covariates from the list of possible explanations of variance in the dependent variable.
ANCOVA is us
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Question number: 2
» Design and Analysis of Experiments » Analysis of Covariance
Appeared in Year: 2010
Describe in Detail
Discuss the procedure for carrying out the analysis and testing procedure by means of ANOVA table for two-way classification.
Explanation
Two-way ANOVA technique is used when there are two factors, which may affect the variate values. For example, the agricultural output may be affected by difference in treatments on the basis of seeds and also on the different fertilizers used.
Let there be two factors A and B which affect the variate value. Let X_{ijk} (i = 1,2, . . p; j = 1,2, …, q
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Question number: 3
» Design and Analysis of Experiments » Analysis of Covariance
Describe in Detail
Using the following data, perform a one way analysis of variance using . Write up the results in APA format.
Explanation
Sample means for the groups:
Intermediate steps in calculating the group variances:
Sum of squared deviations from the mean (SS) for the groups:
Calcul
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Question number: 4
» Design and Analysis of Experiments » Analysis of Covariance
Describe in Detail
Using the following summary data, perform a one way analysis of variance using
Explanation
Calculating the remaining error (or within) terms for the ANOVA table:
Intermediate steps in calculating the variance of the sample means:
Grand mean
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Question number: 5
» Design and Analysis of Experiments » Analysis of Covariance
Describe in Detail
To compare the heights of Soprano, Alto, Tenor and Bass singers, data have been collected from the NY Choral Society in (singers). Determine whether these four groups have the same mean height. Use α=0.05.
Explanation
- We use ANOVA to answer this question as we have a response variable (heights) measured across a categorical variable (Singers) of more than two levels (Soprano, Alto, Tenor, and Bass)
- H_{o}: is that the mean heights of the four types of singers are equal. In statistical notation this is:
- H_{a}: is that at least one of these means differ
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Question number: 6
» Design and Analysis of Experiments » Analysis of Covariance
Describe in Detail
A clinical psychologist has run a between-subjects experiment comparing two treatments for depression (cognitive-behavioral therapy (CBT) and client-centered therapy (CCT) against a control condition. Subjects were randomly assigned to the experimental condition. After 12 weeks, the subject’s depression scores were measured using the CESD depression scale. The data are summarized as follows:
Use a one-way ANOVA with for the test
Explanation
Calculating the remaining error (or within) terms for the ANOVA table:
Intermediate steps in calculating the variance of the sample means:
Grand mean
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