EXAM 1 Mastercards Flashcards
What is the primary purpose of using statistics in analytical chemistry?
A. To eliminate variability in measurements
B. To provide tools for drawing conclusions from data
C. To ensure all measurements are the same
D. To increase the number of experimental runs
B. To provide tools for drawing conclusions from data
Statistics help chemists draw conclusions from data that inherently has variability.
What is meant by variability in experimental measurements?
A. All measurements are identical
B. Measurements differ slightly due to random or systematic factors
C. Measurements are completely unpredictable
D. Variability is eliminated by using better equipment
B. Measurements differ slightly due to random or systematic factors
Variability refers to the fact that measurements can differ due to random or systematic factors.
Which statistical tool is commonly used to estimate the precision of an analytical method?
A. Mean
B. Standard deviation
C. Median
D. Range
B. Standard deviation
Standard deviation is a measure of the dispersion or precision of data points around the mean.
What does a low standard deviation indicate in an experiment?
A. High variability in the data
B. Low variability in the data
C. The data is skewed
D. The median is higher than the mean
B. Low variability in the data
A low standard deviation indicates that the data points are close to the mean, meaning low variability.
Which of the following is NOT a source of error in experimental measurements?
A. Systematic error
B. Random error
C. Human error
D. Precise error
D. Precise error
“Precise error” is not a recognized source of error in experimental measurements.
What is a systematic error in the context of analytical chemistry?
A. Error that occurs randomly and unpredictably
B. Error that consistently skews results in one direction
C. Error that reduces variability in the data
D. Error that occurs due to random chance
B. Error that consistently skews results in one direction
A systematic error is a consistent error that skews results in a particular direction.
Which of the following statistical measures is used to describe the central tendency of data?
A. Variance
B. Standard deviation
C. Mean
D. Range
C. Mean
The mean is a measure of central tendency, summarizing the average of data points.
What is the purpose of confidence intervals in statistical analysis?
A. To estimate the likelihood of a random error
B. To provide a range in which the true value is likely to fall
C. To eliminate variability in data
D. To increase the precision of measurements
B. To provide a range in which the true value is likely to fall
Confidence intervals give a range around a sample statistic that is likely to contain the true population parameter.
What does a 95% confidence interval mean?
A. 95% of the data points are within the interval
B. There is a 95% chance that the interval contains the true value
C. 95% of experiments will have no error
D. The interval eliminates 95% of variability
B. There is a 95% chance that the interval contains the true value
A 95% confidence interval means there is a 95% probability that the interval contains the true population parameter.
Which of the following is true about random errors?
A. They can be completely eliminated
B. They affect the precision of measurements
C. They always occur in the same direction
D. They are systematic and predictable
B. They affect the precision of measurements
Random errors affect the precision of measurements but cannot be completely eliminated.
How is the accuracy of an experiment typically assessed?
A. By calculating the mean
B. By comparing the experimental results to a known true value
C. By calculating the standard deviation
D. By minimizing random error
B. By comparing the experimental results to a known true value
Accuracy is assessed by comparing the experimental results to a known or accepted true value.
What is the difference between accuracy and precision?
A. Accuracy refers to consistency, while precision refers to closeness to the true value
B. Precision refers to consistency, while accuracy refers to closeness to the true value
C. Accuracy and precision are the same concept
D. Precision can be measured, but accuracy cannot
B. Precision refers to consistency, while accuracy refers to closeness to the true value
Precision refers to the consistency of repeated measurements, while accuracy refers to how close those measurements are to the true value.
What is the purpose of a null hypothesis in statistical testing?
A. To prove that the experimental hypothesis is correct
B. To provide a statement that can be tested and possibly disproven
C. To eliminate variability in the data
D. To ensure the experiment has no errors
B. To provide a statement that can be tested and possibly disproven
The null hypothesis provides a testable statement that can be rejected or failed to be rejected based on evidence.
When the p-value is less than α (alpha), what decision is made regarding the null hypothesis?
A. Accept the null hypothesis
B. Reject the null hypothesis
C. Fail to reject the null hypothesis
D. Increase the sample size
B. Reject the null hypothesis
When the p-value is less than α, we reject the null hypothesis, indicating a statistically significant result.
Which statistical test is used to compare the means of two independent groups?
A. Paired T-test
B. One-way ANOVA
C. Independent T-test
D. Chi-square test
C. Independent T-test
The independent T-test compares the means of two independent groups.
Which of the following best describes the concept of statistical power?
A. The probability of making a Type I error
B. The ability to detect a true effect when one exists
C. The probability of the null hypothesis being true
D. The number of experimental runs required
B. The ability to detect a true effect when one exists
Statistical power refers to the likelihood of detecting a true effect when it exists, reducing the chance of a Type II error.
What does a p-value represent in hypothesis testing?
A. The probability that the null hypothesis is true
B. The probability of obtaining the observed results assuming the null hypothesis is true
C. The probability that the alternative hypothesis is true
D. The probability that a Type I error has occurred
B. The probability of obtaining the observed results assuming the null hypothesis is true
A p-value represents the probability of obtaining the observed data, or more extreme results, assuming the null hypothesis is true.
Which statistical test is used to analyze the relationship between two continuous variables?
A. Chi-square test
B. Correlation analysis
C. Independent t-test
D. One-way ANOVA
B. Correlation analysis
Correlation analysis is used to measure the strength and direction of the relationship between two continuous variables.
What is the primary difference between a population and a sample in statistics?
A. A population includes all possible observations, while a sample includes a subset
B. A sample is always larger than a population
C. A population is used for hypothesis testing, while a sample is not
D. A sample is used to calculate mean, while a population is not
A. A population includes all possible observations, while a sample includes a subset
A population includes all possible observations, while a sample is a subset of the population used for analysis.
Which of the following statements is TRUE about the mean and median in a normal distribution?
A. The mean is always greater than the median
B. The mean and median are equal
C. The median is always greater than the mean
D. The mean and median are unrelated
B. The mean and median are equal
In a normal distribution, the mean and median are equal.
What is the primary purpose of experimental design in scientific research?
A. To eliminate variability in results
B. To ensure that experiments are repeatable
C. To test hypotheses in a controlled and systematic way
D. To increase the complexity of experiments
C. To test hypotheses in a controlled and systematic way
The goal of experimental design is to test hypotheses in a controlled and systematic manner, ensuring the results are valid and interpretable.
In hypothesis testing, which of the following is considered the null hypothesis (H₀)?
A. The hypothesis that there is no effect or no difference
B. The hypothesis that there is a significant effect
C. The hypothesis that experimental results are biased
D. The hypothesis that the experiment has failed
A. The hypothesis that there is no effect or no difference
The null hypothesis is typically the assumption that there is no effect, no difference, or no relationship between variables.
What is the alternative hypothesis (H₁) in hypothesis testing?
A. There is no effect or difference
B. There is a significant effect or difference
C. The hypothesis that the experiment failed
D. The hypothesis that the test was biased
B. There is a significant effect or difference
The alternative hypothesis posits that there is a significant effect or difference between groups or conditions.
Which of the following best describes a Type I error?
A. Failing to reject a false null hypothesis
B. Rejecting a true null hypothesis
C. Accepting the alternative hypothesis when it is false
D. Failing to detect an effect when one exists
B. Rejecting a true null hypothesis
A Type I error occurs when the null hypothesis is erroneously rejected, meaning a false positive result is concluded.
What is a Type II error in hypothesis testing?
A. Rejecting a true null hypothesis
B. Failing to reject a false null hypothesis
C. Accepting the null hypothesis when it is true
D. Accepting the alternative hypothesis when it is false
B. Failing to reject a false null hypothesis
A Type II error occurs when the null hypothesis is false but is not rejected, meaning a false negative result is made.
Which of the following represents a two-tailed hypothesis test?
A. Testing if the mean of a group is greater than a specified value
B. Testing if the mean of a group is less than a specified value
C. Testing if the mean of a group is different from a specified value
D. Testing if the mean of a group is equal to a specified value
C. Testing if the mean of a group is different from a specified value
A two-tailed test examines whether a mean is different from a specified value, allowing for both positive and negative deviations.
In the context of hypothesis testing, what does a p-value represent?
A. The probability that the null hypothesis is true
B. The probability of obtaining the observed results, assuming the null hypothesis is true
C. The probability that the alternative hypothesis is true
D. The probability of making a Type II error
B. The probability of obtaining the observed results, assuming the null hypothesis is true
A p-value is the probability of obtaining the observed results, or more extreme results, under the assumption that the null hypothesis is true.
Which of the following is true when the p-value is less than the significance level (α)?
A. The null hypothesis is rejected
B. The null hypothesis is accepted
C. The alternative hypothesis is rejected
D. A Type II error has occurred
A. The null hypothesis is rejected
When the p-value is less than the significance level, you reject the null hypothesis, suggesting a statistically significant result.
What is the significance level (α) commonly used in hypothesis testing?
A. 0.05
B. 0.01
C. 0.10
D. 0.50
A. 0.05
A significance level of 0.05 is commonly used, meaning there is a 5% risk of rejecting a true null hypothesis (i.e., making a Type I error).
In an experiment, how can randomization help improve the validity of the results?
A. By ensuring all groups receive the same treatment
B. By reducing bias in the assignment of treatments
C. By increasing the sample size
D. By eliminating experimental error
B. By reducing bias in the assignment of treatments
Randomization reduces bias by ensuring that treatment assignments are not influenced by any external factors.
What is meant by the power of a statistical test?
A. The ability to reject the null hypothesis when it is true
B. The ability to detect an effect when one exists
C. The ability to make a Type I error
D. The ability to make a Type II error
B. The ability to detect an effect when one exists
The power of a test refers to its ability to detect a true effect (i.e., to reject the null hypothesis when it is false).
Which of the following increases the power of a hypothesis test?
A. Decreasing the significance level (α)
B. Increasing the sample size
C. Decreasing the effect size
D. Increasing the variability of the data
B. Increasing the sample size
Increasing the sample size improves the power of a test by making it easier to detect a true effect.
What is the effect size in hypothesis testing?
A. The size of the sample used in the experiment
B. The magnitude of the difference between groups or conditions
C. The number of variables tested
D. The number of trials in the experiment
B. The magnitude of the difference between groups or conditions
Effect size refers to the magnitude of the difference or relationship being tested between groups or variables.
Which of the following is an example of a control group in an experiment?
A. A group that receives a higher dose of the treatment
B. A group that receives no treatment or a placebo
C. A group that receives double the treatment
D. A group that is randomly assigned different treatments
B. A group that receives no treatment or a placebo
A control group is a baseline group that receives no treatment or a placebo, allowing for comparison with the experimental groups.
What is the purpose of replication in an experiment?
A. To increase the number of variables tested
B. To reduce bias in the experimental results
C. To estimate experimental error and increase reliability
D. To ensure all participants receive the same treatment
C. To estimate experimental error and increase reliability
Replication allows for the estimation of experimental error and increases the reliability of the results by reducing variability.
Which of the following best describes a one-tailed hypothesis test?
A. Testing whether a group mean is different from a specified value
B. Testing whether a group mean is greater than or less than a specified value
C. Testing whether all group means are equal
D. Testing whether a group mean is equal to a specified value
B. Testing whether a group mean is greater than or less than a specified value
A one-tailed test examines if a group mean is either greater than or less than a specified value, but not both.
Which of the following is a key assumption of parametric tests?
A. The data must be nominal
B. The data must be normally distributed
C. The sample size must be small
D. The data must be ordinal
B. The data must be normally distributed
Parametric tests assume that the data follows a normal distribution.
What is the purpose of using a placebo in an experiment?
A. To reduce the sample size
B. To serve as a control condition
C. To increase the variability in the data
D. To ensure all participants receive the treatment
B. To serve as a control condition
A placebo is used to serve as a control condition, allowing researchers to compare the effects of the treatment with a neutral baseline.
Which of the following is TRUE about non-parametric tests?
A. They assume that the data is normally distributed
B. They are used when parametric assumptions are not met
C. They are only used for large sample sizes
D. They are used to compare means
B. They are used when parametric assumptions are not met
Non-parametric tests are used when the assumptions of parametric tests, such as normal distribution, are not met.
What is the main purpose of blocking in experimental design?
A. To increase the number of treatments
B. To control for the effects of an extraneous variable
C. To eliminate random error
D. To ensure all groups receive the same treatment
B. To control for the effects of an extraneous variable
Blocking is used to control for the effects of an extraneous variable that could influence the outcome of the experiment, thereby reducing unwanted variability.
Which of the following is NOT a key characteristic of a single-factor design?
A. One independent variable
B. Multiple dependent variables
C. Multiple levels of the independent variable
D. Post hoc tests for significant differences
B. Multiple dependent variables
Single-factor designs focus on one dependent variable, not multiple.
What statistical test is typically used in a single-factor design to test differences between levels?
A. Chi-square
B. One-way ANOVA
C. Two-way ANOVA
D. t-test
B. One-way ANOVA
One-way ANOVA is used to compare means across multiple levels of one factor.
In a completely randomized design (CRD), what ensures the validity of results?
A. Randomly selecting independent variables
B. Randomly assigning treatments to experimental units
C. Randomizing the dependent variable
D. Randomly selecting a hypothesis
B. Randomly assigning treatments to experimental units
CRD ensures each experimental unit has an equal chance of receiving any treatment, reducing bias.
Which of the following represents the model for a completely randomized design with one factor?
A. yᵢⱼ = μ + Aᵢ + ϵᵢⱼ
B. yᵢⱼ = μ + Bⱼ + ϵᵢⱼ
C. yᵢⱼₖ = μ + Aᵢ + Bⱼ + ϵᵢⱼₖ
D. y = μ + ϵ
A. yᵢⱼ = μ + Aᵢ + ϵᵢⱼ
This is the correct model for a single-factor completely randomized design.
Which of the following hypotheses is tested in a one-way ANOVA?
A. H₀: μ₁ = μ₂ = … = μₖ
B. H₀: μ₁ ≠ μ₂
C. H₀: μ₁ = μ₂ + μₖ
D. H₀: μ₁ > μ₂
A. H₀: μ₁ = μ₂ = … = μₖ
The null hypothesis in a one-way ANOVA states that all group means are equal.
If a significant result is found in a one-way ANOVA, what is typically performed next?
A. A t-test
B. A regression analysis
C. Post hoc tests
D. A chi-square test
C. Post hoc tests
Post hoc tests are used to determine which specific group means differ after a significant ANOVA result.
In a single-factor CRD, how is experimental error accounted for?
A. By randomizing the treatment assignment
B. By increasing the sample size
C. By controlling the dependent variable
D. By calculating the error term ϵᵢⱼ
D. By calculating the error term ϵᵢⱼ
The error term ϵᵢⱼ accounts for variability within groups.
Which design is used to control for the effects of extraneous variables?
A. Completely Randomized Block Design (CRBD)
B. Latin-Square Design
C. Full Factorial Design
D. Fractional Factorial Design
A. Completely Randomized Block Design (CRBD)
CRBD controls for extraneous variables by blocking them.
What is the purpose of the Latin-square design in single-factor experiments?
A. To control for two sources of extraneous variation
B. To investigate the interaction of two factors
C. To randomize treatments over all experimental units
D. To test multiple dependent variables
A. To control for two sources of extraneous variation
Latin-square design helps control two sources of variation (rows and columns).
In a one-way ANOVA, what does the F-ratio represent?
A. The ratio of within-group variance to total variance
B. The ratio of between-group variance to within-group variance
C. The ratio of total variance to experimental error
D. The ratio of levels to treatments
B. The ratio of between-group variance to within-group variance
The F-ratio compares the variance between groups to the variance within groups.
Which assumption is required for a one-way ANOVA?
A. The dependent variable is nominal
B. The independent variable is categorical
C. The data across groups have different variances
D. The dependent variable is ordinal
B. The independent variable is categorical
The independent variable in a one-way ANOVA must be categorical with two or more levels.
How are treatments assigned in a completely randomized design?
A. Based on group means
B. Randomly to experimental units
C. Determined by the dependent variable
D. In a systematic order
B. Randomly to experimental units
Treatments are randomly assigned to experimental units in a CRD.
What is the primary advantage of blocking in a CRBD?
A. Reduces the number of levels required
B. Controls for the effects of the blocking variable
C. Increases the number of independent variables
D. Reduces the need for post hoc tests
B. Controls for the effects of the blocking variable
Blocking helps control for the effects of a known extraneous variable.
A researcher is testing three levels of heating time on the absorbance of a sample. What type of design is this?
A. Two-way ANOVA
B. Single-factor CRD
C. Latin-Square Design
D. Multi-factor Design
B. Single-factor CRD
This is a single-factor CRD with three levels of the independent variable (heating time).
Which of the following is NOT a source of variation in a CRD?
A. Treatment effects
B. Block effects
C. Experimental error
D. Total variability
B. Block effects
Blocks are used in CRBD, not CRD.
The variability in a one-way ANOVA is partitioned into which components?
A. Treatments, blocks, and error
B. Between-groups and within-groups
C. Main effect and interaction
D. Dependent and independent
B. Between-groups and within-groups
In a one-way ANOVA, total variability is partitioned into between-group and within-group components.
What is the difference between a one-way ANOVA and a two-way ANOVA?
A. The number of dependent variables
B. The number of independent variables
C. The number of post hoc tests
D. The type of data analyzed
B. The number of independent variables
A two-way ANOVA involves two independent variables, whereas a one-way ANOVA involves only one.
How are post hoc tests used in a one-way ANOVA?
A. To test the null hypothesis
B. To control for extraneous variables
C. To identify which specific means are different
D. To calculate the F-ratio
C. To identify which specific means are different
Post hoc tests are used to determine which specific group means differ after an ANOVA.
Which of the following is TRUE regarding one-way ANOVA assumptions?
A. The dependent variable must be categorical
B. Groups must have unequal variances
C. Observations within groups must be independent
D. The independent variable must be continuous
C. Observations within groups must be independent
Independence of observations is a key assumption of one-way ANOVA.
In a single-factor design with three levels, how many total levels are analyzed?
A. 1
B. 2
C. 3
D. 4
C. 3
There are three levels of the single independent variable being analyzed.
What is the primary characteristic of a multi-factor design?
A. Only one independent variable is tested
B. Multiple dependent variables are tested
C. Two or more independent variables are tested simultaneously
D. No interactions are analyzed
C. Two or more independent variables are tested simultaneously
Multi-factor designs involve testing two or more independent variables.
Which of the following best describes a factorial design?
A. Testing only one level of each factor
B. Testing all possible combinations of levels across factors
C. Testing interactions without main effects
D. Testing only main effects
B. Testing all possible combinations of levels across factors
Factorial designs test all possible combinations of factor levels.
In a two-factor full factorial design, how many experimental points are there for two factors with two levels each?
A. 2
B. 4
C. 6
D. 8
B. 4
A 2² factorial design has 4 experimental points (2 levels for each of 2 factors).
Which of the following is a key advantage of multi-factor designs over single-factor designs?
A. They are simpler to analyze
B. They reduce the number of experiments required
C. They allow for the study of interactions between factors
D. They eliminate the need for randomization
C. They allow for the study of interactions between factors
Multi-factor designs allow researchers to study interactions between factors.
What is a main effect in a multi-factor design?
A. The combined effect of all factors
B. The effect of one factor independent of other factors
C. The interaction between two factors
D. The error term in the design
B. The effect of one factor independent of other factors
A main effect is the effect of one factor, regardless of the levels of the other factors.
Which of the following describes an interaction in a multi-factor design?
A. The effect of one factor is the same at all levels of another factor
B. The effect of one factor depends on the level of another factor
C. Both factors independently affect the outcome
D. The effect of a factor is negated by the other factor
B. The effect of one factor depends on the level of another factor
An interaction occurs when the effect of one factor depends on the level of another factor.
In a full factorial design, how are the effects of factors calculated?
A. By averaging across all levels of the factor
B. By comparing the highest and lowest responses
C. By calculating the difference between the high and low levels of each factor
D. By random assignment
C. By calculating the difference between the high and low levels of each factor
The effect of a factor is calculated by taking the difference between the high and low levels of that factor.
Why is randomization important in multi-factor designs?
A. It ensures all factors are tested equally
B. It controls for extraneous variables
C. It reduces the complexity of the design
D. It maximizes the impact of the main effects
B. It controls for extraneous variables
Randomization helps control the effects of unwanted extraneous variables.
What is the primary difference between a full factorial and a fractional factorial design?
A. Full factorial designs test all possible combinations, while fractional factorial designs test only a subset
B. Fractional factorial designs test more combinations than full factorial designs
C. Full factorial designs are used for fewer factors
D. Fractional factorial designs do not analyze interactions
A. Full factorial designs test all possible combinations, while fractional factorial designs test only a subset
Fractional factorial designs test only a subset of the possible combinations to reduce experimental runs.
In a fractional factorial design, what is the primary trade-off compared to a full factorial design?
A. Increased accuracy
B. Decreased ability to detect interactions
C. Increased number of experimental runs
D. More precise results
B. Decreased ability to detect interactions
Fractional factorial designs reduce the number of experiments but may miss higher-order interactions.
In a 2³ full factorial design, how many experimental points are there?
A. 4
B. 6
C. 8
D. 12
C. 8
A 2³ design has 2 levels for 3 factors, resulting in 8 experimental points.
Which design is best suited for exploring the curvature of a response surface?
A. Fractional factorial design
B. Latin-square design
C. Central composite design
D. Single-factor CRD
C. Central composite design
Central composite designs are used to explore curvature in response surfaces.
How does a central composite design (CCD) enhance a factorial design?
A. By adding center and axial points to explore curvature
B. By reducing the number of experimental points
C. By eliminating the need for randomization
D. By focusing only on main effects
A. By adding center and axial points to explore curvature
CCD adds center and axial points to study both linear and quadratic effects.
Which of the following is NOT a characteristic of a central composite design?
A. Factorial points
B. Axial points
C. Center point
D. Blocking variables
D. Blocking variables
Blocking variables are not a key characteristic of central composite designs.
Why are axial points added in a central composite design?
A. To reduce the number of experimental runs
B. To investigate curvature in the response
C. To focus on main effects only
D. To control for extraneous variables
B. To investigate curvature in the response
Axial points are added to investigate quadratic (curvature) effects in response surface designs.
How are interactions interpreted in a multi-factor design?
A. As the average of all main effects
B. As the difference between the effects of one factor at different levels of another factor
C. As independent of the main effects
D. As the sum of all factor levels
B. As the difference between the effects of one factor at different levels of another factor
Interactions are interpreted as the difference in the effect of one factor depending on the level of another factor.
Which of the following is an example of an interaction in a two-factor design?
A. The effect of one factor is the same regardless of the other factor
B. The effect of one factor changes depending on the level of the other factor
C. Both factors have no effect on the dependent variable
D. Both factors have the same effect on the dependent variable
B. The effect of one factor changes depending on the level of the other factor
An interaction occurs when the effect of one factor depends on the level of the other factor.
Which of the following is TRUE about fractional factorial designs?
A. They require more experimental runs than full factorial designs
B. They test only a subset of possible combinations of factor levels
C. They eliminate the need for randomization
D. They provide exact estimates of all interactions
B. They test only a subset of possible combinations of factor levels
Fractional factorial designs test a subset of the possible combinations to reduce the number of experimental runs.
In a multi-factor design, what does the term “aliasing” refer to?
A. The combination of levels across factors
B. The inability to separate main effects from interactions
C. The addition of extraneous variables
D. The use of axial points to study curvature
B. The inability to separate main effects from interactions
Aliasing occurs in fractional factorial designs when main effects and interactions cannot be separated.
What is the primary benefit of using a multi-factor design?
A. It simplifies data analysis
B. It allows researchers to test multiple factors simultaneously
C. It reduces the number of factors to consider
D. It eliminates the need for post hoc tests
B. It allows researchers to test multiple factors simultaneously
Multi-factor designs allow researchers to study multiple factors at the same time, providing a comprehensive analysis.
In a full factorial design, how are interactions identified?
A. Through random assignment
B. By testing all possible combinations of factors
C. By focusing on the main effects only
D. By eliminating extraneous variables
B. By testing all possible combinations of factors
Full factorial designs involve testing all possible combinations of factor levels, allowing researchers to identify interactions.
In a 2² factorial design, how many experimental points are there?
A. 2
B. 4
C. 6
D. 8
B. 4
A 2² design means there are two factors, each with two levels, resulting in 4 experimental points.
What is a key characteristic of a multi-factor design?
A. Only one independent variable is tested
B. A single dependent variable is measured
C. Two or more independent variables are studied simultaneously
D. One independent variable is tested across multiple levels
C. Two or more independent variables are studied simultaneously
Which of the following is an advantage of multi-factor designs over single-factor designs?
A. Easier analysis
B. Reduced need for randomization
C. Ability to study interactions between factors
D. Less complex data collection
C. Ability to study interactions between factors
Multi-factor designs allow for the study of interactions between the factors.
What does the term “main effect” mean in a multi-factor design?
A. The combined effect of all factors
B. The effect of one factor independent of other factors
C. The interaction between two factors
D. The error term in the design
B. The effect of one factor independent of other factors
A main effect refers to the independent effect of one factor on the dependent variable, regardless of the levels of other factors.
In a full factorial design, what is an interaction effect?
A. The effect of one factor added to the effect of another factor
B. The effect of one factor depends on the level of another factor
C. The independent effect of one factor
D. The error term in the design
B. The effect of one factor depends on the level of another factor
An interaction effect occurs when the effect of one factor depends on the level of another factor.
What is the purpose of using a central composite design in multi-factor experiments?
A. To investigate the effects of multiple dependent variables
B. To control for extraneous variables
C. To explore both linear and quadratic effects
D. To reduce the number of factors in the design
C. To explore both linear and quadratic effects
The central composite design allows researchers to explore both linear and quadratic effects by adding center and axial points.
Which of the following is NOT a characteristic of a full factorial design?
A. Testing all possible combinations of factor levels
B. Studying both main effects and interactions
C. Randomly assigning subjects to treatments
D. Reducing the number of experimental runs by eliminating interactions
D. Reducing the number of experimental runs by eliminating interactions
Full factorial designs test all possible combinations, including interactions, without reducing experimental runs.
How does a fractional factorial design differ from a full factorial design?
A. It tests all possible combinations of factor levels
B. It tests only a subset of the possible combinations
C. It does not consider interactions between factors
D. It eliminates the need for randomization
B. It tests only a subset of the possible combinations
A fractional factorial design tests only a subset of the possible combinations to reduce the number of experimental runs.
In a 2³ factorial design, how many experimental points are there?
A. 4
B. 6
C. 8
D. 12
C. 8
A 2³ design has 2 levels for each of 3 factors, resulting in 8 experimental points.
What is the primary goal of a factorial design?
A. To test one factor at a time
B. To identify the main effects and interactions between factors
C. To reduce the number of experimental runs by eliminating factors
D. To focus on the dependent variable
B. To identify the main effects and interactions between factors
The goal of a factorial design is to identify the main effects and interactions between multiple factors.
How are the results of a multi-factor experiment typically analyzed?
A. By calculating the sum of all effects
B. By focusing only on main effects
C. By calculating main effects and interaction effects
D. By randomizing the factors
C. By calculating main effects and interaction effects
Multi-factor experiments are analyzed by calculating both main effects and interaction effects.
In a 2² factorial design, how is the interaction effect between two factors calculated?
A. By summing the main effects
B. By averaging the responses for each level
C. By calculating the difference between the effect of one factor at different levels of the other factor
D. By eliminating the error term
C. By calculating the difference between the effect of one factor at different levels of the other factor
Interaction effects are calculated by determining how the effect of one factor changes depending on the level of the other factor.
Which of the following is TRUE about fractional factorial designs?
A. They allow for the study of all possible interactions
B. They reduce the number of experimental runs by testing only a subset of factor combinations
C. They eliminate the need for randomization
D. They do not consider main effects
B. They reduce the number of experimental runs by testing only a subset of factor combinations
Fractional factorial designs reduce the number of experimental runs by testing only a subset of combinations.
Why are center points added in a central composite design?
A. To explore quadratic effects
B. To increase the number of factors
C. To eliminate interactions
D. To reduce the number of experimental runs
A. To explore quadratic effects
Center points are added in a central composite design to explore potential quadratic (curvature) effects.
In a multi-factor design, what is the purpose of randomization?
A. To reduce the complexity of the design
B. To control for extraneous variables
C. To eliminate the need for interactions
D. To focus on the dependent variable
B. To control for extraneous variables
Randomization helps control the effects of extraneous variables.
What does the notation “2ᵏ” represent in a full factorial design?
A. The number of factors and levels
B. The number of dependent variables
C. The type of randomization used
D. The number of experimental units
A. The number of factors and levels
“2ᵏ” represents a factorial design with k factors, each at 2 levels.
Which of the following is TRUE about main effects and interaction effects in multi-factor designs?
A. Main effects are always larger than interaction effects
B. Main effects and interaction effects are analyzed separately
C. Interaction effects occur when the effect of one factor changes depending on the level of another factor
D. Interaction effects are independent of main effects
C. Interaction effects occur when the effect of one factor changes depending on the level of another factor
Interaction effects occur when the effect of one factor depends on the level of another factor.
In a 2² factorial design, the effect of temperature on yield is calculated as +5 units. What is this an example of?
A. Main effect
B. Interaction effect
C. Experimental error
D. Randomization effect
A. Main effect
The main effect refers to the independent effect of temperature on the yield.
