Design Of Experiments

by Tomowsiak

1 508 played - 11 yrs ago

Questions about what we've learned so far.

30 QUESTIONS

51%

We can use use ANOVA to test the equality of two or more means.

True

False

Neither

Huh? . . what's ANOVA?

What is meant by a replication of an experiment?

A complete performance of the experiment. That is, every treatment possibility is applied.

Only some of the treatments are applied.

Neither

Does the picture below suggest that we have a significant result for differences between treatments.

True. . it's obvious one of the means must be different

False. . the means all seem to fall within the spread of the data. . it would be difficult to tell them apart.

In a completely randomized experiment all of the runs are made in random order.

True

False

Why randomize the application of treatments in the first place?

There is no reason to randomize. We do it because we're told to do it.

Randomization reduces bias by equalising other factors that have not been explicitly accounted for in the experimental design.

Sometimes factor that are unknown can play a role, and randomization breaks any dependence between these factors, so their effect is negligible.

1 and 2 options both.

In a fixed effect experiments, the treatments are chosen at random.

False

True

The basic anova identity is shown below.

False

True

Which is the correct value for the expected value of the mean square of the error?

If the F-statistic in a single-factor ANOVA is significant this indicates that all of the means being compared are different.

True

False

Neither

According to the data given below, what is the value of the F statistic?

10/50

50/10=5

Something else

In the picture below, does it seem that the results of the should be significant or not? That is, does it seem that at least one of the treatment means is different from the others?

Yes. . it seems so. .

No. . it doesn't seem so

I don't know. . how do I tell?

In the single-factor ANOVA model, the mean of treatment i is the sum of the grand mean and the ith treatment effect. Is the picture below correct?

Yes

In the picture below, what exactly is the factor and what are the treatment levels and the response?

The etch rate is the factor and the levels of etch rate are the response

The power is the factor and the settings of power are the treatment levels and the etch rate is the response

Neither of these is correct

In the picture below, we see one one replicate of the experiment highlited.

True. . one power setting. . several measurements

False. . only 1 power setting is used instead of all

In the picture below, we see one full replicate of the experiment highlited

True. . all the power setting are applied

False. . this picture doesn't show one full replicate

In the picture, how many runs are in the red box? How many deviations from this treatment mean? How many degrees of freedom for error under this treatment?

There is one mean to be calculated for this level . . 5 runs, so 4 degrees of freedom with respect to this treatment level mean

5 runs. . so four deviations from this treatment level mean. . and the 5th is forced

Both of the above are accurate

Neither of answers 1 or 2 works

In the picture on the left, we see 3 runs under level 1 of the factor. This means there is a mean and consequently 2 degrees of freedom for error with respect to this mean. We have 4 all together.

True

False

Something else

In the picture we see 6 data points, and 1 grand mean. This means we can calculate 5 deviations from this mean the 6 is forced by the values of the first 5. So we have only 5 degrees of freedom.

False

True

Is the picture shown on the left correct or incorrent?

Correct

Incorrect

In the table below, if I increase n, what happens to the number of dots in a scatter diagram at every treatment level? Do the dots increase in number vertically or horizontally?

It goes down vertically

The dots increase in number. . more appear at every level vertically

Nothing happens. . there is no connection between scatter points and n

If I increase a in the table below, what will happen to the number of dots in a scatter diagram? Will the increase come from adding dots vertically at every level or horizontally WITH new levels?

Nothing

It will go down

It will go up as we add levels. . horizontally

Which picture, the left or right, shows the correct groupings in terms of the definition of a replicate of an experiment?

Left

Right

Neither

If in the table below, I increase n, will the degrees of freedom for error increase or decrease? Is the total variabiilty in the data affected? Are the degrees of freedom for treatments affected?

No clue

Freedom degrees for error increase, treatment degrees go down, total variability stays the same

Freedom degrees increaes, treatment degrees are constant, total variability increases

In the table below, if we change the number of dots in the scatter diagram per level from let's, say, 3 to 5, which of the following will happen?

Treatment means will change. . so SSTreatment will change. . and so will the MStreatment. . and so will the F ratio. . total variability will change

Nothing will happen. .

Most of the change will be in the error

Some but not of all the things in the first option will happen

If in the picture below, I change the number of levels from, let's say 2 to 3, what will happen ?

Df for treatments will increase, the grand mean will change, the SStreatments will change, the MSsquaretreatments will change and the F test will chan

Nothing will happen. .

Some of the things in option 1 will occur

Something else will happen