Week 5 Theory Questions Flashcards

1
Q

How is randomized block design different from completely randomized design?

A

Instead of completely randomly assigning subjects into different treatment groups (as in completely randomized design), in randomized block design subjects are first divided into homogeneous blocks of size equal to the number of treatment groups. Then within each block, each subject is randomly assigned to one treatment group and each subject is assigned to a different treatment group.

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2
Q

Why may we consider doing RMD?

A

Doing this is to control for the impacts of any nuisance factors related to the blocking criteria on the outcome variable, so that the focal difference on outcome variable due to the factor of interest is less likely to be masked or hidden due to the noise introduced by those nuisance factors (i.e., reducing the probability of making a Type II error).

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3
Q

On the conceptual level, how is one-way ANOVA with completely randomized design different from ANOVA with randomized block design?

A

In one-way ANOVA with CRD, total variation in the outcome variable is partitioned into two parts: variation due to treatment and variation due to error. The subsequent test is essentially comparing variation due to treatment against variation due to error. In ANOVA with RBD, total variation is partitioned into three parts: variation due to treatment, variation due to block, and variation due to error. In other words, variation due to block is separately estimated, which otherwise would be included in the variation due to error. The subsequent test is still comparing variation due to treatment against variation due to error.

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4
Q

Compared to two separate one-way ANOVA tests, what unique aspect can be tested in two-factor ANOVA?

A

The interaction effect between the two factors on the outcome variable can be tested in two-factor ANOVA, which is not possible with two separate one-way ANOVA tests. In other words, two-factor ANOVA test can inform us whether the differences in population means between different levels of one factor are contingent on the level of the other factor.

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5
Q

Explain the rationale underlying the two χ^2 goodness-of-fit tests discussed in the lecture.

A

Both χ^2 goodness-of-fit tests (test for dependence between two categorial variables and test for normality) build on comparing the observed frequencies in the sample against the expected frequencies under the null hypothesis. If observed frequencies are sufficiently close to expected frequencies, we take this as evidence consistent with the null hypothesis and thus do not reject the null hypothesis. Otherwise, we reject the null hypothesis.

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6
Q

Explain the rationale of ordinal least squares (OLS) method.

A

OLS produces estimates for linear regression model by making the fitted or predicted values of y from the linear regression model come closest to the observed values of y on average. More precisely, it minimizes the sum of squared differences between fitted values of y and observed values of y over all data points in the sample.

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7
Q

Can you do a test at 5% significance level to see if the randomized block design is worthy?

A

Yes, we just test for the block effect. If the block effect is significant, meaning the randomized block design is worthy to control for the significant impacts from the blocking variable on the outcome variable; otherwise, the randomized block design is not worthy because the blocking variable does not significantly affect the outcome variable.

–> Just do the F test and if we reject Ho it means that at least two blocks differ. It’s indeed worthy to conduct the one-way ANOVA for randomized block design instead of completely randomized design.

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