尔雅Design and Analysis of Experiments答案(学习通2023完整答案)

Chapter 1 Introduction

Chapter 1 Test

1、尔雅Which of the following method should we use when dealing with experiments with more than one factor?答案
A、Best-guess
B、学习Factorial experiment
C、通完One-factor-at-a-time
D、整答Blocking

2、尔雅Which of the following is 答案not a common experimental strategy?
A、Best-guess
B、学习Quantitative analysis
C、通完One-factor-at-a-time
D、整答Factorial experiment

3、尔雅Statistical methods often assume that the observations (or errors) are independently distributed random variables. Which of the following strategy makes this 答案assumption valid.
A、Replication
B、学习Repeated measurement
C、通完Blocking
D、整答Randomization

4、Which of the following strategy can make the best use of experimental data?
A、One-factor-at-a-time
B、Best-guess
C、Factorial experiment
D、Replication

5、Which of the following can be achieved by using blocking principle?
A、To obtain an estimate of the experimental error
B、To increase the accuracy of the experiment
C、To reduce or eliminate the variability transmitted from nuisance factors
D、To balance out any material or experimental unit effect

6、During the following potential design factors, whose effect are relatively small?
A、Design factors
B、Held-constant factors
C、Allowed-to-vary factors
D、Controllable factors

7、By randomization, we can compensate for the effect of nuisance factors.

8、The fractional factorial experiment interprets the most straightforwardly.

9、Replication reflects sources of variability only within runs.

10、Experiments are used to study the performance of a process or system.

Chapter 1 Homework

1、What are the basic principles of experimental design?

2、What are the advantages of repeated measurement?

3、What are the disadvantages of the best-guess approach?

Chapter 2 Simple comparative experiments

Chapter 2 Test

1、In the two-sample t test, the null hypothesis is that the two samples are equal, and the alternative hypothesis is that the two samples are not equal, and the significance level is α. What quantile should the test statistic t0 be compared with?
A、the upper α/2 percentage point of the t distribution with n1+n2-1 degrees of freedom
B、the upper α/2 percentage point of the t distribution with n1+n2-2 degrees of freedom
C、the lower α/2 percentage point of the t distribution with n1+n2-1 degrees of freedom
D、the lower α/2 percentage point of the t distribution with n1+n2-2 degrees of freedom

2、If is a random sample from the distribution, then (sum of squares of deviations divided by the variance）follows
A、Chi-square distribution with n-1 degrees of freedom
B、Chi-square distribution with n degrees of freedom
C、Normal distribution with mean 0 and variance 1
D、Normal distribution with mean μ and variance 1

3、In semiconductor manufacturing, wet chemical etching is often used to remove silicon from the backs of wafers prior to metalization. The etch rate is an important characteristic of this process. Two different etching solutions are being evaluated. Eight randomly selected wafers have been divided into two pieces and etched in each solution, and the observed etch rates (in mils/min) are as follows. solution 1：9.9，9.4，10.0，10.3，10.6，10.3，9.3，9.8 solution 2：10.2，10.0，10.7，9.5，10.2，9.6，9.4，10.3 Test hypothesis , then when performing paired t-test, the test statistic is equal to:
A、0.169
B、-0.169
C、0.178
D、-0.178

4、When the degree of freedom k is greater than what, the t distribution has mean value μ = 0, and variance σ2 = k/(k-2)?
A、1
B、2
C、3
D、4

5、In the normal probability plot, if the data follow a normal distribution, the plotted points will fall approximately along ( ).
A、A straight line
B、A parabola
C、Normal distribution curve
D、t distribution curve

6、In the paired t test, there are n observations for each sample, by blocking or pairing we have effectively "lost" ( ) degrees of freedom.
A、n
B、n-1
C、n+1
D、n-2

7、Which of the following distributions are symmetric?
A、Normal distribution
B、Chi-square distribution
C、t distribution
D、F distribution

8、Experimental noise is generally controllable and avoidable.

9、The variability or dispersion can be measured by the variance.

10、The sample mean is an unbiased estimator of the population mean.

Chapter 2 Homework

1、Why does blocking serve as a noise reduction design technique?

2、Why is blocking not always the best design strategy?

3、Experimenters want to study the deflection temperature under load for two different formulations of ABS plastic pipe. Two samples of 12 observations each are prepared using each formulation and the deflection temperatures (in °F) are reported below: Formulation 1: 206, 188, 205, 187, 193, 207, 185, 189, 192, 210, 194, 178 Formulation 2: 177, 197, 206, 201, 176, 185, 200, 197, 198, 188, 189, 203 (1) Construct normal probability plots for both samples. Do these plots support assumptions of normality and equal variance for both samples? (write down the statistic and the p-value). Use α=0.05. (2) Do the data support the claim that the mean de?ection temperature under load for formulation 1 exceeds that of formulation 2? Do a test and write down the statistic and the p-value. Use α=0.05.

Chapter 4 Randomized Blocks and Latin Squares

Chapter 4 Test

1、For unknown and uncontrollable nuisance factors, ( ) can be used to eliminate its effect.
A、Covariance analysis
B、Randomization
C、Block design
D、Orthogonalization

2、What does “Randomization” mean in a randomized complete block design（RCBD）?
A、Within a block, the sequence of experiments for all treatments is randomized.
B、Throughout the experiment, the selection of each block is randomized.
C、Within a block, the number of times each treatment appears is randomized.
D、Throughout the experiment, all the numbers appeared are randomized.

3、When period becomes a factor in an experiment, ( ) can be chosen to perform?
A、Factorial design
B、Parallel design
C、Crossover design
D、Replicate design

4、In a Graeco-Latin Square design, if there are four factors each with p levels, how many experiments need to be done?
A、
B、
C、
D、

5、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.
A、
B、
C、
D、

6、In a Latin Square designs, if a standard 5×5 Latin square is used, the quantity of standard Latin squares is ( )
A、25
B、50
C、55
D、56

7、In an experiment, what can be possible nuisance factors?
A、An experimental instrument or machine
B、The batch of raw materials
C、Experimenter
D、Experimental time

8、In a complete randomized block design, the total sum of squares can be written as the sum of the following ( )
A、
B、
C、
D、

9、In a randomized complete block design, block represents a randomization constraint, so is not a meaningful statistic in comparing blocks.

10、In a randomized complete block design, “complete” means each block (sample) contains all treatments.

Chapter 4 Homework

1、Briefly describe the types of nuisance factors and the corresponding treatment methods.

2、Briefly describe the differences among RCBD, Latin square design and Graeco-Latin Square design.

3、To test the resistance of a particular type of cloth to the chemical erosion, four chemical agents are selected for the experiment. Because there might be variability from one bolt to another, the engineer decides to use a randomized block design, with the bolts of cloth considered as blocks. The engineer selects ?ve bolts and applies all four chemicals in random order to each bolt. Experimental data are shown in the following table. Table：Cloth Experiment Data（raw data-70） Treatments Blocks 1 2 3 4 5 1 3 -1 3 1 -3 2 3 -2 4 2 -1 3 5 2 4 3 -2 4 5 2 7 5 2 Verify whether different chemical agents have the same erosion ability to the cloth (use α=0.05).

Chapter 5 Introduction to Factorial Designs

Chapter 5 Test

1、In a two-factor factorial experiment with factor A at three levels and factor B at four levels, which of the following is the degrees of freedom of factor A, B, and the interaction between them?
A、3; 4; 12
B、2; 3; 11
C、2; 3; 6
D、2; 3; 5

2、An engineer decides to test three materials at two temperature levels (30 and 50℃). Four batteries are tested at each combination of plate material and temperature. This experimental design is called a ( )
A、Latin square design
B、Paired design
C、Factorial design
D、Cross-over Design

3、Factor A has 3 levels and factor B has 4 levels. For each treatment combination 10 replicates are run. =2000，=3000，=1500，=2160. What are the values of 、、?
A、100；100；25
B、50；50；12.5
C、100；50；25
D、50；100；12.5

4、To study the influence of temperature on battery life, the temperature is controlled at three levels. Then we can call it a ( ) variance analysis.
A、single-factor
B、three-factor
C、single-level
D、three-level

5、The parameter estimates from a two-level factorial design (with levels at +1 and -1) are actually least squares estimates.

6、In the single-factor analysis of variance, the numerator of F statistic is the variance within the groups, and the denominator is the variance between groups.

7、In the Latin square design, all treatments occur once and only once on each row and column.

8、It is possible to have a main effect without an interaction, but it is impossible to have an interaction without a main effect.

9、The existence of interaction will affect the test of the main effect of a factor.

10、Within a block in the two-factor factorial design, the treatment combinations are run in a certain order.

Chapter 5 Homework

1、How do you deal with heteroscedasticity in model adequacy checking?

2、Please list two other multiple comparison methods in addition to Tukey's test and describe them.

3、An experiment is conducted to study the influence of operating temperature and three types of faceplate glass in the light output of an oscilloscope tube. The following data are collected: Temperature Glass type 100 125 150 1 790 1177 1306 811 1190 1244 808 1174 1347 2 1506 1071 862 1496 1081 872 1490 1099 865 3 591 1319 1231 693 1210 1207 752 1250 1165 (1) Use a=0.05 in the analysis. Is there a significant interaction effect? Does glass type or temperature affect the response? What conclusions can you draw? (2) Fit an appropriate model relating light output to glass type and temperature. (3) Analyze the residuals from this experiment. Comment on the adequacy of the models you have considered.

Chapter 6 2^k Factorial Design

Chapter 6 Test

1、If we use the method for replicate runs to estimate the MSE of the experiment data of duplicate measurement, it will ( ) the MSE of the run and make those factors that are insignificant appear significant.
A、Under-estimate
B、Over-estimate
C、Correctly estimate
D、None of the above

2、In a factorial design with each run replicated n = 3 times, it is known that the contrast of factor B is , the contrast of interaction effect BD is , then the main effect of B and the interaction effect of BD are _____ respectively.
A、10.67; 15
B、21.33; 30
C、10.67; 30
D、21.33; 15

3、In a factorial design with each run replicated n = 4 times, it is known that the contrast of interaction BC is , then the estimate of the sum of squares of the interaction BC is ______.
A、64
B、2
C、32
D、1

4、The statistical model for a factorial design contains ______ main effects, _______ two-factor interactions, and ________ four-factor interactions.
A、5; 5; 1
B、5; 10; 5
C、5; 20; 5
D、1; 5; 5

5、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 ________
A、"--++--++"
B、"-++--++-"
C、"+--++--+"
D、"++--++--"

6、If in a factorial design with each replicated n = 3 times, without considering the interaction, the effect of factor A is 16, and the effect of factor B is -4, the average value of 12 runs is 24, and and represent the standardized variables of A and B respectively, then the fitted regression model is: _______.
A、
B、
C、
D、

7、Analysis methods for a single replicate of two-level factorial design include ()
A、the normal (or half-normal) plot of the estimated factor effects
B、Lenth's method
C、Conditional inference chart
D、Scatter plot of raw data

8、 is a measure of the proportion of the variance explained by the model to the total variance. increases as more variables are added into the model.

9、The variance of n duplicate measurements at the same level is greater than that of n replicates at the same level.

10、In a two-level factorial design, in order to model the curvature in the response function, we usually fit a second-order response surface model Using the method of adding center points to test its curvature is in actually to test the hypothesis

Chapter 6 Homework

1、Briefly explain why the normal probability plot can be used to detect significant effects in a single replicate of two-level factorial design.

2、In a factorial design, the Pareto principle is usually correct in the screening stage of the experiment. The Pareto principle says that most of the indicator fluctuations are often caused by a small number of factors. The corresponding analysis methods can be divided into graphical methods (normal plot and half-normal graph) and numerical methods (Lenth’s method, etc.). Compare the advantages and disadvantages of the two methods through the following question. The figure below is a half-normal plot of the effect estimates. Since the differences in the absolute values of the effect estimates are not large, it is impossible to determine significant effects by the figure. At this time, which method should be used for factor screening? Compare the advantages and disadvantages of the two methods.

3、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 analysis 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?

Chapter 3 Experiments with a single factor

Chapter 3 Test

1、An experimenter has conducted a single-factor experiment with four levels of the factor, and each factor level has been replicated 5,6,7,8 times respectively. How many degrees of freedom does the sum of squared errors has?
A、22
B、23
C、25
D、26

2、For Poisson data, which of the following variance-stabilizing transformation is commonly used?
A、Reciprocal transformation
B、Reciprocal square root transformation
C、Log transformation
D、Square root transformation
E、Arcsine transformation

3、An experimenter has conducted a single-factor experiment with 5 levels of the factor, and each factor level has been replicated 3 times. It is known that the sample mean values at each level are 4, 5, 6, 7, 8 respectively, and the sample variances are 2.1, 3.2, 4.6, 3.4, 2.6. In the contrast where the sum of the mean of level 1 and level 2 is equal to the sum of the mean of level 3 and level 4, what is the test statistic of the t-test?
A、-0.42
B、-2.75
C、-1.05
D、0.23

4、Which of the following statement describes correctly the purpose of analysis of the variance?
A、To analyze whether there is a significant difference in the total variance of each group
B、To analyze whether there is a significant difference in the overall standard deviation of each group
C、To analyze whether there is a significant difference in the overall mean value of each group
D、To analyze whether there is a significant difference in the overall median of each group

5、Does the experimental sequence need to be randomized?

6、An experimenter has conducted a single-factor experiment with four levels of the factor, and each factor level has been replicated six times. The computed value of the F-statistic is =3.26. Then, at a significance level of 0.05, can we reject the null hypothesis that the average at each level is identical?

7、Among the two methods of testing nonconstant variance, Bartlett's test is robust to departures from normality, while the modified Levene test is very sensitive to the normality assumption.

8、We can decide if we should reject the null hypothesis by checking whether the confidence interval of the contrast contains 0.

9、Discovering whether the different factor levels affect variability is called dispersion effects analysis, in which the standard deviation, variance, or some other measure of variability is used as a response variable.

10、If an experimenter randomly selects of a large number of possible levels from the population of factor levels, then we say that the factor is random. Inferences can be valid for the entire population of factor levels.

Chapter 3 Homework

1、What's the difference between a fixed effects model and a random effects model?

2、An article appeared in The Wall Street Journal with the title “Eating Chocolate Is Linked to Depression.” The article reported on a study that examined 931 adults who were not taking antidepressants and did not have known cardiovascular disease or diabetes. The group was about 70% men and the average age of the group was reported to be about 58. The participants were asked about chocolate consumption and then screened for depression using a questionnaire. People who score less than 16 on the questionnaire are not considered depressed, while those with scores above 16 and less than or equal to 22 are considered possibly depressed, while those with scores above 22 are considered likely to be depressed. The survey found that people who were not depressed individuals ate an average of 8.4 servings of chocolate per month, while those individuals who scored above 22 and were likely to be depressed ate the most chocolate, an average of 11.8 servings per month. Other foods were also examined, but no pattern emerged between other foods and depression. Is this study really a designed experiment? Does it establish a cause-and-effect link between chocolate consumption and depression? How would the study have to be conducted to establish such a cause-and-effect link?

3、

Final Exam of Design and Analysis of Experiments

Final Exam of Design and Analysis of Experiments

1、In an experiment, we can use blocking to deal with ( )
A、Designed factors
B、Held-constant factors
C、Controllable factors
D、Uncontrollable factors

2、A four-factor factorial design with two levels of the factor is called ( )
A、 factorial design
B、 factorial design
C、2×4 factorial design
D、2+4 factorial design

3、What's the main contribution of Genichi Taguchi?
A、Developing the insights that lead to the three basic principles of experimental design
B、Developing the response surface method
C、Pointing out the features of industrial experiments
D、Advocating using orthogonal arrays to solve the problems

4、If y obeys N(μ,σ2), then the random variable z=(y-μ)/σ follows ( ).
A、F distribution
B、Chi-square distribution with one degree of freedom
C、Standard normal distribution
D、t distribution

5、With increase of degrees of freedom, the curve of a chi-square distribution tends to be ( ).
A、Steeper
B、Flatter
C、Closer to a normal distribution
D、Independent of the degree of freedom

6、If n is large enough, the sum of n independent and identically distributed random variables will follow
A、F distribution
B、Chi-square distribution
C、t distribution
D、Normal distribution

7、The following are the burning times (in minutes) of chemical flares of two different formulations. Type1：65，81，57，66，82，82，67，59，75，70; Type2：64，71，83，59，65，56，69，74，82，79。 The design engineers are interested in testing the hypothesis ，α=0.05, the statistic
A、0.169
B、-0.169
C、0.978
D、0.988

8、Which of the following hypothesis is not true about single-factor analysis of variance model?
A、The mean of the error is zero
B、The error is a normally distributed random variable
C、The variance of the error is a constant
D、The errors are not independent

9、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
A、Fixed effects model
B、Random effects model
C、Mixed-effects model
D、Mean value model

10、An experimenter has conducted a single-factor experiment with four levels of factor A, and each factor level has been replicated three times. The computed value of the sample standard deviation of each level: 1.5, 2.0, 1.6, 1.2. Find the estimated value of the variance of the error.
A、0.79
B、1.71
C、2.56
D、3.84

11、Plotting the residuals in time order could be used to detect the following except
A、Independence
B、Normality
C、Heteroscedasticity
D、Independence and heteroscedasticity

12、Generally, a residual bigger than ( ) standard deviations from zero is a potential outlier.
A、1
B、2
C、3
D、4

13、Which of the following transformation should we use if the observations follow the binomial distribution?
A、Reciprocal transformation
B、Reciprocal square root transformation
C、Log transformation
D、Square root transformation
E、Arcsine transformation

14、Modified Levene test uses the absolute deviation of the observations in each treatment from the treatment ( ).
A、Median
B、Mode
C、Mean
D、Minimum

15、Which of the following transformation method should we use if the plot of versus is a straight line with slope α=0.5?
A、Log transformation
B、Square root transformation
C、Reciprocal transformation
D、Arcsine transformation
E、Reciprocal square root transformation

16、Which of the following transformation method should we use if the plot of versus is a straight line with slope α=1?
A、Log transformation
B、Square root transformation
C、Reciprocal transformation
D、Reciprocal square root transformation
E、No transformation

17、In a contrast, or a linear combination, the contrast coefficients sum up to ( ).
A、0
B、1
C、-1
D、Not sure

18、Consider 5 hypotheses at the same time, what is the type I error is for each hypothesis when the overall significance level is 0.05?
A、0.05
B、0.95
C、0.01
D、0.50

19、Which of the following method can be used to compare any and all possible contrasts between treatment means?
A、Scheffe's method
B、Tukey's method
C、Bonferroni's method
D、Fisher's LSD method

20、In a single-factor experiment, factor A has 5 levels, and each factor level has been replicated three times. It is known that the sample means at each level is 4, 5, 6, 7 and 8. The sample variance is 6, 7, 7, 2 and 9. The significance level is 0.05. What is the critical value calculated by Fisher's LSD method? Is there a significant difference between the mean of level 1 and the mean of level 5? (The upper 0.025 quantile of the t-distribution with 10 degrees of freedom is 2.228139 and the upper 0.05 quantile of the t-distribution with 10 degrees of freedom is 1.812461.
A、4.53, no significant difference
B、4.53, a significant difference
C、2.58, a significant difference
D、2.58, no significant difference

21、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?
A、6.75
B、5.00
C、10.00
D、7.95

22、The F-statistic of ANOVA is the basis of decision-making. Generally,
A、the larger the statistic F, the more favorable it is to reject the null hypothesis and accept the alternative hypothesis.
B、the larger the statistic F, the more favorable it is to accept the null hypothesis and reject the alternative hypothesis.
C、the lesser the statistic F, the more favorable it is to reject the null hypothesis and accept the alternative hypothesis.
D、the lesser the statistic F, the more favorable it is to accept the null hypothesis and reject the alternative hypothesis.

23、Which of the following statement is not ture about a random effect model with one factor?
A、The variance of the random error is equal to that of processing effect
B、The effects of different treatment levels all follow a normal distribution, the mean is 0, and the variance is the same.
C、The mean of the random error is 0
D、The variance of any observation is the sum of the variance of the random error and the variance of the treatment effect

24、If the block has a large influence on the response variables, but the experimenter does not conduct block design and analysis, then the error effect will be ( ).
A、smaller
B、greater
C、the same
D、not sure

25、In a randomized complete block design, if there is a certain interaction effect, then we can use ( ) to eliminate the interaction.
A、Exponentiation
B、Square-Root Operation
C、Absolute value Operation
D、Logarithm Operation

26、When there are two interference factors, we may consider using
A、Single-Factor Experiment
B、The Randomized Complete Block Design
C、The Latin Square Design
D、None

27、A 4×4 Latin square has ( ) degrees of error freedom
A、4
B、5
C、6
D、7

28、For known but uncontrollable nuisance factors, which of the following method can we use for processing and analysis.
A、Randomization
B、Covariance analysis
C、Block design
D、None

29、How many nuisance factors can exist at most in the Graeco-Latin square design?
A、2
B、3
C、4
D、5

30、For known and controllable nuisance factors, we can systematically eliminate its influence in the comparative processing effect by using ( ).
A、Randomization
B、Covariance analysis
C、Block design
D、None

31、In the Graeco-Latin square design, if every factor has p levels, the error sum of squares is ( ).
A、p-1
B、p-3
C、(p-1)(p-2)
D、(p-1)(p-3)

32、The concept of orthogonal pairs of Latin squares forming a Graeco-Latin square can be extended somewhat. In general, up to p-1 factors could be studied if a complete set of ( ) orthogonal Latin squares is available.
A、p-1
B、p
C、p+1
D、p+2

33、In a randomized complete block design, , then the degrees of freedom of is ( ).
A、(a-1)(b-1)
B、N-1
C、a-1
D、b-1

34、In a randomized complete block design, compared with designing the blocks as fixed factors, the test statistics on whether the mean is equal signing them as random factors will be
A、greater
B、smaller
C、the same
D、not sure

35、If there are 6x6 observations in the Latin square design, the degrees of freedom of the total sum of squares is ( ).
A、5
B、6
C、35
D、36

36、In a Latin square design, if there are 7x7 observations, what are the degrees of freedom of the error sum of squares?
A、6
B、30
C、48
D、49

37、In a Latin square design, if there are 5 treatments with 6 repeat observations, how many observations in total can we get?
A、30
B、150
C、180
D、250

38、In a Graeco-Latin design, if there are 6 treatments and 6 blocks, what are the degrees of freedom of the error sum of squares?
A、15
B、16
C、25
D、36

39、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?
A、a;b;ab
B、a-1;b-1;(a-1)(b-1)
C、a-1;b-1;ab
D、a-1;b-1;ab-1

40、What test method is used in the analysis of variance?
A、t-test
B、F-test
C、Chi-square test
D、Z test

41、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.
A、25；20；5
B、20；25；5
C、5；10；1
D、10；5；1

42、Compared with randomized complete design and analysis of variance, random block design and analysis of variance has( ).
A、more source of variations
B、smaller errors
C、lower efficiency
D、None

43、For data with randomized block, compared with the analysis of random block design, the results using the single-factor analysis of variance ( ).
A、The information applicable to the two methods is different and incomparable
B、The testing effect cannot be determined
C、Both methods can be used
D、Both methods have the same testing effects.

44、Which of the following statement is not ture?
A、ANOVA can be used to compare the mean of two samples
B、Completely random design is more suitable for the data of the experimental subject's mixed influence is not too big
C、In random block design, the number of columns in each block is equal to the number of treatments
D、In random block design, the smaller the difference within and between blocks, the better

45、One approach to the analysis of an unreplicated factorial is to assume that certain high-order interactions are negligible and combine their mean squares to estimate the error. This is an appeal to ( ).
A、The principle of small probability, the basic principle of hypothesis testing, which means that a small probability event may not happen in an experiment, but it will happen when there are many experiments.
B、The principle of sufficiency, which means that in the presence of sufficient statistics, and statistical inference can be made based on sufficient statistics
C、The effects sparsity principle, which means that most systems are dominated by some of the main effects and low-order interactions, and most high-order interactions are negligible.
D、D. The Lette's criterion is a method for distinguishing outliers under the normal distribution.

46、When we encounter some problems, we take ( ) for the results of n times of repeated measurements.
A、mean
B、minimum
C、maximum
D、95% quantile

47、Compared with the variance of the results of n replicates at the same level, the variance between the results of n tests at the same level in duplicate measurement is ( ).
A、greater
B、smaller
C、the same
D、not sure

48、In a two-level factorial design, with the addition of center points, we test that the pure quadratic is significant. But if the amount of data available is insufficient to estimate all parameters of the second-order response surface model, then several axial runs can be added to the design. The resulting design is called ( ).
A、the randomized complete orthogonal design
B、the addition of center points to the factorial design
C、the central composite design
D、the block design

49、In a factorial design with n replicates, when fitting a regression model, the value of the coefficient in the fitted regression equation is ( ) the value of the corresponding effect estimate.
A、twice
B、the same as
C、one-half
D、three times

50、In a randomized complete block design, if the treatment factors is fixed and the block factor is random, then the variance of is ( )
A、
B、
C、
D、

51、In a randomized complete block design, consider the presence of interaction between treatment factors and block factors. The model containing the interaction between the two is ( ).
A、
B、
C、
D、

52、The statistical model used to analyze the Latin square is ( )
A、
B、
C、
D、

53、In a Latin square design, the analysis of variance consists of partitioning the total sum of squares of the observations into components for rows, columns, treatments, and error, for example, then, the corresponding degrees of freedom of is ( )
A、p-1
B、p
C、p+1
D、

54、In a Latin square design, the analysis of variance consists of partitioning the total sum of squares of the observations into components for rows, columns, treatments, and error, for example, then, the corresponding degrees of freedom of is ( ).
A、p-1
B、p-2
C、p+1
D、(p-1)(p+2)

55、The statistical model designed by the Graeco-Latin square design is
A、
B、
C、
D、

56、In a randomized complete block design, the computational formula for the sum of squares of treatment is
A、
B、
C、
D、

57、In a Latin square, if there are 6x6 observations, we need to compare the statistic to ( ) to determine whether to reject the original hypothesis.
A、
B、
C、
D、

58、In a randomized complete block design, ( ) is the computational formula for the total sum of squares
A、
B、
C、
D、

59、In a Graeco-Latin square design, if there are 6 treatments, we need to compare to ( ) to determine whether to reject the original hypothesis.
A、
B、
C、
D、

60、The response surface and the contour plot below indicate ( ).
A、There is an interaction between the two factors.
B、There is no interaction between the two factors.
C、Unable to make a conclusion.
D、None of the above

61、The regression model is . Observe the following figure, denotes factor A and denotes factor B, then the estimates of are
A、30.5 ，-0.5，-4.5，-14.5
B、30.5，0.5，4.5，-14.5
C、30.5，0.5，-4.5，-14.5
D、30.5，0.5，-4.5，14.5

62、Which of the following are model hypotheses for a two-factor factorial design?
A、
B、
C、
D、

63、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
A、16
B、3.05
C、10
D、5.25

64、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
A、100
B、150
C、200
D、190.6

65、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
A、0.12
B、0.03
C、0.06
D、0.25

66、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
A、1
B、2
C、3
D、4

67、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
A、66
B、65
C、64
D、63

68、In the factorial design with n=4 replicates, the contrast of the known factor A is ，and the main effect of A is ( ).
A、25
B、6.25
C、12.5
D、25

69、In the factorial design with n=5 replicates, the contrast of the known interaction factor AD is ，and the interaction effect of AD is ( ).
A、5
B、20
C、40
D、10

70、In the factorial design with n=3 replicates, the contrast of the known interaction effect AB is ，and the estimate of the sum of squares of interaction effect AB is ( ).
A、1.5
B、0.75
C、13.5
D、27

71、In the factorial design, The treatment combinations in the design are usually represented by lowercase letters. For example, in a factorial design with factors A, B, and D at the high level and factor C at the low level; the treatment combination should be expressed as ( ).
A、(1)
B、abd
C、c
D、bc

72、In the factorial design, when considering the interaction effects between different factors and suppose the number of replicates is n, then the degrees of freedom of (the residual sum of squares ) is ( ).
A、
B、
C、
D、

73、In a single replicate of the factorial design, if all the main effects and interaction effects are considered, (the residual sum of squares) _____. If factor C is not significant and all interactions involving C are negligible, then project the single replicate of the into a _____ factorial design.
A、exists; replicated
B、does not exist; unreplicated
C、exists; unreplicated
D、does not exist; replicated

74、For a general design , the degrees of freedom of the interaction of the n factors is ( ).
A、
B、
C、
D、

75、In a single replicate of a design, the statistic is used to determine the dispersion effect. in this formula represents the variance of ( ) for each treatment combination at the high level.
A、residual error
B、observation
C、fitted value
D、None

76、In a factorial design with n replicates, approximate 95% confidence intervals on the factor effects are: A: ?101.625±54.82 B: 7.375±54.82 C: 306.125±54.82 AB: ?24.875±54.82 AC: 153.625±54.82 BC: ?2.125±54.82 ABC: 5.625±54.82 This analysis indicates that ( ) are important factors.
A、B, C, BC
B、A, B, C, BC
C、A, C, AC
D、None

77、In a single replicate of design, statistic ( ) is often used to judge the magnitude of dispersion effect.
A、
B、
C、
D、None

78、To represent curvature in the response function, we fit a second-order response surface model: . We use the addition of center points to check on curvature, that is, to really test the hypotheses ( ).
A、
B、
C、
D、None

79、In a single replicate of factorial design with the addition of 4 center points, the average of the 16 factorial designs is , and the experimental values at the 4 center points are 134, 162, 146, and 155. Then the sum of squares for the pure quadratic in the ANOVA table is ( ); If the only sources of variance are main effects A, C, D and the interaction effect AC, AD, the sum of squares of error is 284.7, and the F-value of the squared sum of the pure quadratic is ( ).
A、31.752；1.45
B、31.725；2.05
C、35.265；1.45
D、35.265；2.05

80、In a two-level factorial design, in order to estimate all the parameters in a second-order response surface model, a number of axial runs can be added to the design when the number of experimental points is insufficient. The resulting design is called a central composite design. Please determine which of the following 9 experimental points (a -- i) belong to the new experimental points added to the "central composite design" according to its design method.
A、aci
B、ceg
C、bdf
D、bcg

81、To facilitate the computation of a factor effect, we usually list the design matrix shown below. The pattern of filling the design matrix is: the symbol “+” denotes the main effect at the high level, and “-” at the low level. With the symbols of the main effect set, the symbols of each column can be obtained by multiplying those of the preceding columns. Please complete the following design matrix according to its pattern.
A、A: - B: + C: + D: - E: + F: +
B、A: + B: - C: - D: + E: - F: -
C、A: + B: + C: - D: + E: + F: -
D、A: - B: - C: + D: - E: - F: +

82、In a factorial design with n=4 replicates, the degree of freedom of the fitted error in the model is 8 and in the model is 0.87. The value of adjusted is ( ).
A、0.87925
B、0.75625
C、0.88245
D、0.79625

83、In a factorial design, the regression model approach is much more natural and intuitive to express the results of the experiment. V is used to denote the original variable while and are used to denote the high and low levels of the variable, ( ) is the right conversion between the standardized variable and the original variable.
A、
B、
C、
D、

84、What are the purposes of the experiment design?
A、Determining which variables are most influential on the response y
B、Determining where to set the influential x's so that y is almost always near the target
C、Determining where to set the influential x's so that variability in y is small
D、Determining where to set the influential x's so that the effects of the uncontrollable variables are minimized

85、Which of the following belong to nuisance factors?
A、Allowed-to-vary factors
B、Controllable factors
C、Uncontrollable factors
D、Noise factors

86、Which of the following can be shown in a box plot?
A、Minimum value
B、Maximum value
C、Quartile
D、Median

87、Consider testing the equality of the variances of two normal populations. We need to test . The null hypothesis would be rejected if the ratio ( ).
A、
B、
C、
D、

88、In single-factor experimental analysis, what are the advantages of ANOVA over the t-test?
A、It applies to the overall non-normal situation
B、The efficiency is higher.
C、It protects the total type I error rate at the same confidence level.
D、It applies to the heteroscedasticity case.

89、In the analysis of variance, which of the following belong to random error?
A、Variation caused by uncontrollable factors
B、Differences between experimental units
C、Measurement errors
D、Variation caused by noise factors

90、Which of the following residual plots can be used to diagnose inequality of variance in model adequacy checking?
A、The histogram of the residuals
B、The plot of the residuals in time order
C、The normal probability plot of the residuals
D、The plot of residuals versus fitted values

91、Some common methods of multiple comparisons include
A、Bonferroni's method
B、Scheffe's method
C、Tukey's method
D、Fisher's LSD method

92、In many practical situations, we will wish to compare only pairs of means. Frequently, we can determine which means differ by testing the differences between all pairs of treatment means. Methods for making such comparisons include ( ).
A、Scheffe's method
B、Tukey's method
C、Bonferroni's method
D、Fisher's LSD method

93、Which of the following can be used as a response variable when studying dispersion effect?
A、Natural logarithm of the sample variance
B、Sample standard deviation
C、Sample variance
D、Natural logarithm of the sample standard deviation

94、Which of the following belong to random variables in the random-effects model of single-factor experiments?
A、Total mean
B、Treatment effects
C、Random error
D、None

95、Which of the following statement about Latin square design is true?
A、The Latin square is designed to eliminate the sources of variability of the two interfering factors.
B、Generally speaking, a Latin square or p×p Latin square, is a square with rows and columns.
C、Only rows can represent randomization constraints.
D、Each letter appears only once in each row and each column.

96、The contents of ANOVA table often contain ( ).
A、Sum of squares
B、Degree of freedom
C、Mean square
D、F0
E、P-value
F、Source fo variation

97、What are the advantages of a factorial design?
A、A lot of information can be obtained
B、The main effects of each experimental factor can accurately be estimated.
C、The magnitude of the interaction effects between factors can be estimated.
D、it can find the best combination by comparing various combinations
E、More experiments are required

98、The analysis of variance indicated that the basic sources of differences between the means of different treatment groups are:
A、Experimental conditions, that is, the difference caused by different treatments (also known as the difference between groups)
B、Random error
C、Human error
D、None

99、Which of the following graphics can be used for model adequacy checking?
A、The normal probability plot of the residuals
B、The plot of residuals versus fitted values
C、The plot of residuals versus factor of different levels
D、The plot of the relationship between the factors

100、Which of the following graphics can be used for detecting the inequality of variance.
A、The normal probability plot of the residuals
B、The plot of residuals versus fitted values
C、The plot of residuals versus factor of different levels
D、The plot of the relationship between the factors

101、What are the characteristics of Latin square design?
A、Each treatment appears exactly once in each row and each column
B、The number of treatment combinations in a factor factorial design exactly equals the number of restriction levels
C、Regardless of the environmental differences in the row direction or column direction, environmental interference can be overcome through the block to achieve two-way local control
D、There are many kinds of latin square design schemes higher than third order

102、Nuisance factors are factors that may have large effects that must be accounted for, yet we may not be interested in them in the context of the present experiment.

103、In the best-guess approach, when there's already an acceptable result, the experimenter can stop testing and guarantee that the result is the best solution.

104、A fractional factorial experiment is a variation of the basic factorial design in which only a subset of the runs is used.

105、Although noise factors vary naturally and uncontrollably in the process, an analysis procedure called the analysis of covariance can often be used to compensate for its effect.

106、Among nuisance factors, uncontrollable factors can be measured.

107、When conducting t-tests for two sample means, the test statistics t0 are always identical regardless of their total variance.

108、When blocking (or pairing the observations) is needed, but we forgot, the variance estimate in the two-sample t-test will be smaller than the variance estimate in the paired t-test.

109、The sample variance is an unbiased estimator of the population variance.

110、The method of testing variance is insensitive to the normality assumption

111、In the single-factor experiment, the experiment can be carried out according to the factor levels.

112、The graphic method can be used for exploratory analysis of experimental data.

113、In single-factor experimental analysis, the paired t-test can be used to examine whether the mean at multiple levels is equal.

114、Single-factor Analysis of Variance (ANOVA) model is also called the effects model.

115、An experimenter has conducted a single-factor experiment with four levels of factor A, and each factor level has been replicated n times. Then the total sum of squared errors is equal to n times the sum of sample variances.

116、In a single-factor experiment, we could use the mean square of the treatment to estimate the variance of the error if there were differences between the treatment means.

117、In the fixed-effect model of the single-factor experiment with four levels of factor A, each factor level is replicated n times. Then is distributed as chi-square with a(n-1) degrees of freedom

118、In the fixed-effect model of the single-factor experiment with four levels of factor A, each factor level is replicated n times. If there were no differences between the treatment means, then is distributed as chi-square with degrees of freedom.

119、In the fixed-effects model, and are not necessarily independent.

120、If the presence of outliers has an influence on our analysis, we can disregard them directly.

121、If the residual fluctuation changes over time, for example, if the plot of residuals about time is more stretched on one side than the other, it means that there is a correlation between the residuals.

122、In model adequacy checking, the tendency of the normal probability plot to bend upward slightly on the left side and bend down slightly on the right side implies that the tails of the error distribution are somewhat thinner than would be anticipated in a normal distribution.

123、Bartlett test is robust to departures from normality.

124、Modified Levene test is robust to departures from normality.

125、When heteroscedasticity exists, the common solution is to use Variance-Stabilizing Transformations.

126、The alternative hypothesis of Bartlett's test is there are at least two variances are different.

127、In a single-factor experiment, factor A has three levels. The number of replication at each level is 9, 12, 6, and the sample variances are 0.663, 0.574, and 0.752, respectively. Then the three total variances are equal to each other at a significance level of 0.05 using the Bartlett test method.

128、If the observations follow a logarithmic normal distribution we use log transformation.

129、The square root transformation is often used for Poisson data.

130、From the results of analysis of variance, it can be concluded which processing means are different from other processing means.

131、Tests performed on orthogonal contrasts are independent.

132、When we think of several hypotheses, we will use multiple comparison method.

133、In the random-effects model of the single-factor experiment, if the null hypothesis H0 is true, then statistic F follows the chi-square distribution.

134、In the random-effects model, the confidence interval of treatment variance/(treatment variance + random error variance) is relatively narrow because of the small number of looms used in the experiment.

135、The mean squared error (MSE) used in the multiple comparison method is different from that used in the pairwise comparison method, in which only intra-group variations at the two levels of comparison are calculated, whereas the multiple comparison method calculates intra-group variations at all levels.

136、In the random effects model, random error and treatment effect are dependent random variables.

137、If the result of analysis of variance is not to reject the null hypothesis, we should continue to use the multiple comparison method.

138、In the crossover design, the subjects in the first round of experiments are not randomly determined.

139、In the Graeco-Latin square design model, random error follows NID(0,σ2).

140、The common advantage of Latin square design and Graeco-Latin square design is both of them reduce the error sum of squares and error degree of freedom of the experiment.

141、The concept of orthogonal pairs of Latin squares forming a Graeco-Latin square can be extended somewhat. The interaction between the factors will not affect the experiment when using hypersquares.

142、In a randomized complete block design, the experimental error will reflect both random error and variability between coupons.

143、The advantages of a completely randomized block design are to eliminate the variability between blocks, improve the accuracy of comparison between treatments.

144、In a randomized complete block design, the word "randomized" means the sequence in which the treatments are tested is randomly determined.

145、In a randomized complete block design, the order of each treatment is randomly determined during the experiment.

146、In an experiment involving the RCBD, only all the treatment means are different can we reject the null hypothesis.

147、In a randomized complete block design, residual analysis can be performed by making a normal probability plot of residuals, the plot of residuals versus observations, and the residual plot of the blocks and the treatments.

148、In a randomized complete block design, factorial designs must be used in situations where both factors, as well as their possible interaction, are of interest.

149、In a randomized complete block design, if the treatment factor is fixed and the block factor is random, then the covariance between the experimental results of different treatments and different blocks is not 0.

150、In a randomized complete block design, if the treatment factor is fixed and the block factor is random, then the covariance between the experimental results of different treatments and same blocks is 0.

151、Factorial designs allow the effects of a factor to be estimated at several levels of the other factors, yielding conclusions that are valid over a range of experimental conditions.

152、The presence of interaction does not affect the test for the main effect of a single factor.

153、A two-factor factorial design is a completely randomized design

154、In the regression model, if the interaction coefficient is smaller compared to the main effect coefficient, the interaction can be ignored.

155、Response curves and response surfaces can be used to determine the optimal range of quantitative factors.

156、The mean of response plots can be used to tell if there's interaction between two factors.

157、In multiple comparisons, the null hypothesis of Tukey test is the difference between the means is significant.

158、In a Latin square design, row and column represent blocks of two external variables, with each treatment occurring only once in each row or column.

159、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.

160、When the interaction is significant, we must fix a factor at all levels and test the other factor.

161、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.

162、The prerequisite of ANOVA is that there is no significant difference in the total variance of observation variables under different levels of control variables.

163、The F-test in ANOVA can be a one-sided test or a two-sided test.

164、A two-factor factorial design containing blocks assumes that interaction between blocks and treatments is negligible.

165、Factorial designs are most efficient for studying the effects of two or more factors.

166、Due to experimental error, it's desirable to take multiple observations at each treatment combination and estimate the effects of the factors using average responses.

167、The relative efficiency must increase as the number of factors increases.

168、It is not feasible or practical to completely randomize all of the runs in a factorial. Therefore, the presence of a nuisance factor may require that the experiment be run in blocks.

169、Interaction is the difference in response between the levels of one factor is not the same at all levels of the other factors.

170、In the mean of response plots, if the B- and B+ lines don't intersect, there is no interaction between factors A and B.

171、To test the significance of both main effects and their interaction, we can simply divide the corresponding mean square by the error mean square. Small values of this ratio imply that the data do not support the null hypothesis.

172、The p-value in the hypothesis test is the probability of making the type I error.

173、When analyzing data from an unreplicated factorial design, if real higher-order interactions occur, Daniel suggests examining a normal probability plot of the estimates of the effects before establishing the initial model. If the treatment has a significant effect, it will fall on this straight line, and it should be added to the initial model.

174、In an unreplicated factorial design, consider the influence of A and C on the observation y only. If the main effects of factors A and C are both positive, it is considered that when A and C are both at a high level, the value of y reaches the maximum.

175、The straight line on the half-normal plot always passes through the origin

176、In a test with given conditions, when we measure the results for multiple times with other conditions unchanged, these measurements are not replicates but just a form of repeated/duplicate measurements.

177、The MSE of the duplicate measurement will be underestimated if we use replicate method, which makes the originally insignificant factors significant.

178、In a single replicate of the factorial design, since there is only one experimental data at each test point, the variance of the results under this experimental condition cannot be obtained, so we cannot determine the dispersion effect of the single replicate of the factorial design.

179、In a factorial design with n replicates, the response surface plot can be generated by fitting a regression model, and then the potential improvement directions of the two factor levels of the factorial design can be determined by the fitted response surface plot.

180、In a factorial design with n replicates, if the 95% confidence interval of a factor effect contains 0, then we think that the factor effect is significant.

181、In the two-level factorial design, it is unnecessary to consider whether the assumption of linearity holds because we generally assume it to be true.

182、The design is particularly useful in the early stages of experimental work when many factors are likely to be investigated. It provides the smallest number of runs with which k factors can be studied in a complete factorial design. Consequently, these designs are widely used in factor screening experiments.

183、In a factorial design with n replicates, The regression coefficient is one-half the effect estimate because a regression coefficient measures the effect of a one-unit change in x on the mean of y, and the effect estimate is based on a two-unit change (from -1 to 1).

184、 measures the proportion of total variability explained by the model. The greater the is, the better the model explains.

185、Of the general approaches to the statistical analysis of the factorial design, to refine the model usually consists of removing any non-significant variables from the full model.

186、In a factorial design, (1) represents the treatment combination of both factors at the low level.

187、In a single replicate of the design, one way to ensure that reliable effect estimates are obtained is to increase the distance between the levels of the factors.

188、In a randomized complete block design, use as the test statistic, when , then reject the original hypothesis.

189、Suppose we have two factors A and B, each at two levels. We denote the levels of the factors by and . If the one-factor-at-a-time design indicated that and gave better responses than , a logical conclusion would be that would be even better.

190、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 ).

191、In a two-factor factorial design, can all be used to estimate

192、In a factorial design, we generally assume that (1) the factors are fixed, (2) the designs are completely randomized, (3) the usual normality assumptions are satisfied.

193、In a factorial design, there are k factors, each at only two levels. These levels can only be quantitative instead of qualitative.

194、The statistical model for a factorial design would contain effects (interactions considered).

195、In the factorial design, the contrast of BD is .

196、In the factorial design with n replicates, the estimate of interaction effect AB…K can be expressed as .

197、In the factorial design with n replicates, the esti

学习通Design and Analysis of Experiments

Design and Analysis of Experiments是一门应用广泛的实验设计与数据分析课程。在此课程中，学生将学习如何用统计学的方法设计实验、分析实验数据并进行实验结论的推导。它能够为学生提供强大的实验设计和数据分析工具，以便有效地解决现实生活中的问题。

课程学习内容

Design and Analysis of Experiments课程的主要学习内容包括：

实验设计与实验方法论
单因素实验设计
多因素实验设计
统计推断与假设检验
方差分析
回归分析
建模与预测
实验数据的可视化和解释

课程特点

Design and Analysis of Experiments课程的教学特点如下：

全面而深入的教学：课程涵盖了实验设计、数据分析的方方面面，让学生全面掌握实验方法论和数据分析的方法和技巧。
实践与理论相结合：课程既重视理论知识的学习，也注重实践能力的培养。学生将通过大量的实验和案例分析，掌握实际数据分析的方法和技巧。
强调实用性：课程内容注重实用性，强调实验设计和数据分析的应用性。学生将学习如何将理论知识应用到实际问题中。

学习体验

Design and Analysis of Experiments课程采用了互动式教学，通过在线课程视频、练习、作业、案例分析等多种教学方式，帮助学生深入理解实验设计和数据分析的相关知识。此外，学生还可以通过在线讨论、互动问答等方式与教师和其他学生进行交流和学习。

适合人群

Design and Analysis of Experiments课程适合以下人群：

对实验设计和数据分析有兴趣的学生
需要掌握实验设计和数据分析技能的专业人士，如工程师、数据分析师、市场研究员等
需要进行科学研究的科研工作者

结论

综上所述，Design and Analysis of Experiments是一门非常实用和重要的课程，它能够为学生提供实验设计和数据分析的方法和技巧，以解决现实生活中的问题。如果你对实验设计和数据分析感兴趣，或者需要掌握相关技能，那么Design and Analysis of Experiments课程将是一个非常不错的选择。