which of the following method should we use when dealing with experiments with more than one factor?
which of the following is not a common experimental strategy?
which of the following strategy can make the best use of experimental data?
which of the following can be achieved by using blocking principle?
during the following potential design factors, whose effect are relatively all?
by randomization, we can compensate for the effect of nuisance factors.
the fractional factorial experiment interprets the most straightforwardly.
replication reflects sources of variability only within runs.
experiments are used to study the performance of a process or system.
what are the basic principles of experimental design?
what are the advantages of repeated measurement?
what are the disadvantages of the best-guess approach?
when the degree of freedom k is greater than what, the t distribution has mean value μ = 0, and variance σ2 = k/(k-2)?
in the paired t test, there are n observations for each sample, by blocking or pairing we have effectively "lost" ( ) degrees of freedom.
which of the following distributions are symmetric?
experimental noise is generally controllable and avoidable.
the variability or dispersion can be measured by the variance.
the sample mean is an unbiased estimator of the population mean.
why does blocking serve as a noise reduction design technique?
why is blocking not always the best design strategy?
for unknown and uncontrollable nuisance factors, ( ) can be used to eliminate its effect.
what does “randomization” mean in a randomized complete block design（rcbd）?
when period becomes a factor in an experiment, ( ) can be chosen to perform?
in a graeco-latin square design, if there are four factors each with p levels, how many experiments need to be done?
in a randomized complete block design, we have treatments to compare and blocks with significant level α, and the test statistic is . when ( ), reject the null hypothesis that the treatment means are equal.
in a latin square designs, if a standard 5×5 latin square is used, the quantity of standard latin squares is ( )
in an experiment, what can be possible nuisance factors?
in a complete randomized block design, the total sum of squares can be written as the sum of the following ( )
in a randomized complete block design, block represents a randomization constraint, so is not a meaningful statistic in comparing blocks.
in a randomized complete block design, “complete” means each block (sample) contains all treatments.
briefly describe the differences among rcbd, latin square design and graeco-latin square design.
it is possible to have a main effect without an interaction, but it is impossible to have an interaction without a main effect.
the existence of interaction will affect the test of the main effect of a factor.
how do you deal with heteroscedasticity in model adequacy checking?
please list two other multiple comparison methods in addition to tukey's test and describe them.
in a two-level factorial design, the signs of the main effect a is “- - - - ”, and the signs of the main effect b is “-- -- ”. then the sign of the interaction ab is ________
analysis methods for a single replicate of two-level factorial design include ()
the variance of n duplicate measurements at the same level is greater than that of n replicates at the same level.
briefly explain why the normal probability plot can be used to detect significant effects in a single replicate of two-level factorial design.
an article in the at&t technical journal (march/april 1986, vol. 65, pp. 39–50) describes the application of two-level factorial designs to integrated circuit manufacturing. a basic processing step is to grow an epitaxial layer on polished silicon wafers. the wafers mounted on a susceptor are positioned inside a bell jar, and chemical vapors are introduced. the susceptor is rotated, and heat is applied until the epitaxial layer is thick enough. an experiment was run using two factors: arsenic flow rate (a) and deposition time (b). four replicates were run, and the epitaxial layer thickness was measured (). the data are shown in the table below. factor replicate factor levels i ii iii iv low（-） high（ ） 14.037 16.165 13.972 13.907 55% 59% 13.880 13.860 14.032 13.914 14.821 14.757 14.843 14.878 short （10 min） long （15 min） 14.888 14.921 14.415 14.932 (1) estimate the main effects and interactions of all factors. (2) conduct an ysis of variance. which factors are important? (3) write down a regression equation that could be used to predict epitaxial layer thickness over the region of arsenic flow rate and deposition time used in this experiment. (4) analyze the residuals. are there any residuals that should cause concern?
which of the following statement describes correctly the purpose of ysis of the variance?
does the experimental sequence need to be randomized?
what's the difference between a fixed effects model and a random effects model?
in an experiment, we can use blocking to deal with ( )
what's the main contribution of genichi taguchi?
if y obeys n(μ,σ2), then the random variable z=(y-μ)/σ follows ( ).
which of the following hypothesis is not true about single-factor ysis of variance model?
in the one-way anova model, when all the treatments are viewed as a random sample from a larger population of treatments, it is called
plotting the residuals in time order could be used to detect the following except
which of the following transformation should we use if the observations follow the binomial distribution?
in a contrast, or a linear combination, the contrast coefficients sum up to ( ).
which of the following method can be used to compare any and all possible contrasts between treatment means?
in the random-effects model of the single-factor experiment, factor a has four levels and each factor level is replicated 4 times. if sstreatment=6 and sse=4, then the statistic f is?
the f-statistic of anova is the basis of decision-making. generally,
which of the following statement is not ture about a random effect model with one factor?
when there are two interference factors, we may consider using
for known but uncontrollable nuisance factors, which of the following method can we use for processing and ysis.
how many nuisance factors can exist at most in the graeco-latin square design?
in a randomized complete block design, , then the degrees of freedom of is ( ).
in a two-factor factorial design, suppose factor a has a levels and factor b has b levels. what are the degrees of freedom for factor a, factor b, and the interaction between factor a and b?
what test method is used in the ysis of variance?
in a factorial experiment with two factors, namely factor a and factor b, each at two levels. when factor a and factor b are both at the low level, the response (y) is 15; when factor a at the high level and b at the low level, the response (y) is 30; when factor a at the low level and b at the high level, the response (y) is 35; when both a and b at the high level, the response (y) is 60. the main effect of a, the main effect of b, and the interaction effect of ab are ( ) respectively.
compared with randomized complete design and ysis of variance, random block design and ysis of variance has( ).
which of the following statement is not ture?
when we encounter some problems, we take ( ) for the results of n times of repeated measurements.
the statistical model designed by the graeco-latin square design is
in a randomized complete block design, the computational formula for the sum of squares of treatment is
in a randomized complete block design, ( ) is the computational formula for the total sum of squares
the regression model is . observe the following figure, denotes factor a and denotes factor b, then the estimates of are
which of the following are model hypotheses for a two-factor factorial design?
complete the analysis of variance table: question 171 source of variation sum of squares degrees of freedom mean square p-value percentage of carbonation（a） 16.00 1 16.00 q171 0.0862 operating pressure（b） q172 1 100.00 19.06 0.0001 line speed（c） 0.56 1 0.56 0.11 0.7445 ab 0.06 1 q173 0.01 0.9135 ac 0.25 1 0.25 0.05 0.8280 bc 0.25 1 0.25 0.05 0.8280 abc 10.56 q174 10.56 2.01 0.1614 error 293.75 56 5.25 total 421.43 q175
complete the analysis of variance table: question 172 source of variation sum of squares degrees of freedom mean square p-value percentage of carbonation（a） 16.00 1 16.00 q171 0.0862 operating pressure（b） q172 1 100.00 19.06 0.0001 line speed（c） 0.56 1 0.56 0.11 0.7445 ab 0.06 1 q173 0.01 0.9135 ac 0.25 1 0.25 0.05 0.8280 bc 0.25 1 0.25 0.05 0.8280 abc 10.56 q174 10.56 2.01 0.1614 error 293.75 56 5.25 total 421.43 q175
complete the analysis of variance table: question 173 source of variation sum of squares degrees of freedom mean square p-value percentage of carbonation（a） 16.00 1 16.00 q171 0.0862 operating pressure（b） q172 1 100.00 19.06 0.0001 line speed（c） 0.56 1 0.56 0.11 0.7445 ab 0.06 1 q173 0.01 0.9135 ac 0.25 1 0.25 0.05 0.8280 bc 0.25 1 0.25 0.05 0.8280 abc 10.56 q174 10.56 2.01 0.1614 error 293.75 56 5.25 total 421.43 q175
complete the analysis of variance table: question 174 source of variation sum of squares degrees of freedom mean square p-value percentage of carbonation（a） 16.00 1 16.00 q171 0.0862 operating pressure（b） q172 1 100.00 19.06 0.0001 line speed（c） 0.56 1 0.56 0.11 0.7445 ab 0.06 1 q173 0.01 0.9135 ac 0.25 1 0.25 0.05 0.8280 bc 0.25 1 0.25 0.05 0.8280 abc 10.56 q174 10.56 2.01 0.1614 error 293.75 56 5.25 total 421.43 q175
complete the analysis of variance table: question 175 source of variation sum of squares degrees of freedom mean square p-value percentage of carbonation（a） 16.00 1 16.00 q171 0.0862 operating pressure（b） q172 1 100.00 19.06 0.0001 line speed（c） 0.56 1 0.56 0.11 0.7445 ab 0.06 1 q173 0.01 0.9135 ac 0.25 1 0.25 0.05 0.8280 bc 0.25 1 0.25 0.05 0.8280 abc 10.56 q174 10.56 2.01 0.1614 error 293.75 56 5.25 total 421.43 q175
what are the purposes of the experiment design?
which of the following belong to nuisance factors?
which of the following can be shown in a box plot?
in single-factor experimental ysis, what are the advantages of anova over the t-test?
in the ysis of variance, which of the following belong to random error?
some common methods of multiple comparisons include
which of the following can be used as a response variable when studying dispersion effect?
which of the following statement about latin square design is true?
the contents of anova table often contain ( ).
what are the advantages of a factorial design?
the ysis of variance indicated that the basic sources of differences between the means of different treatment groups are:
which of the following graphics can be used for model adequacy checking?
which of the following graphics can be used for detecting the inequality of variance.
what are the characteristics of latin square design?
among nuisance factors, uncontrollable factors can be measured.
the sample variance is an unbiased estimator of the population variance.
in the single-factor experiment, the experiment can be carried out according to the factor levels.
the graphic method can be used for exploratory ysis of experimental data.
the square root transformation is often used for poisson data.
from the results of ysis of variance, it can be concluded which processing means are different from other processing means.
when we think of several hypotheses, we will use multiple comparison method.
the presence of interaction does not affect the test for the main effect of a single factor.
a two-factor factorial design is a completely randomized design
the mean of response plots can be used to tell if there's interaction between two factors.
anova can only determine if there is a difference between the total averages and multiple comparisons can be used to further determine which two averages are different from each other and which are not.
when the interaction is significant, we must fix a factor at all levels and test the other factor.
in a multifactor factorial design, the factors are equally important and all need to be tested for their main effects and their interaction with other factors.
the f-test in anova can be a one-sided test or a two-sided test.
the relative efficiency must increase as the number of factors increases.
interaction is the difference in response between the levels of one factor is not the same at all levels of the other factors.
the p-value in the hypothesis test is the probability of making the type i error.
in a factorial design, (1) represents the treatment combination of both factors at the low level.
in a randomized complete block design, use as the test statistic, when , then reject the original hypothesis.
if a model contains a high-order term (such as ), it should also contain all of the lower order terms that compose it (in this case and ).
in a two-factor factorial design, can all be used to estimate