EDA - Quiz 7

• ANOVA

  A statistical method used to analyze the differences among group means in a sample
• ANOVA

  • Compares the means of two or more groups to determine if they are statistically significantly different from each other
• Characteristics of ANOVA(MOAANPP)

  • Multiple Groups
  • One-Way or Two-Way
  • Assumption of Independence
  • Assumption of Homogeneity of Variances
  • Normal Distribution
  • Provides F-statistic
  • Post-Hoc Tests
• Fixed factors

  ● Factors whose levels are selected in advance and are of specific interest to the researcher.

  ● They represent levels of interest that the researcher wants to generalize about.
• Random Factors

  ● Factors whose levels are randomly selected from a larger population.

  ● They represent a random sample from a larger population, and the researcher is

  interested in generalizing beyond the specific levels included in the study.
• Null hypothesis (ANOVA)

  States that there are no significant differences between the group means. ● It suggests that any observed differences are due to random sampling error
• Alternative hypothesis (ANOVA)

  Contradicts the null hypothesis by proposing that there is at least one group mean that is different from the others
• Design of experiments


  A systematic method used to plan, conduct, analyze, and interpret controlled tests or experiments to evaluate the factors that may affect a particular process, product, or system
• Key Components of DOE(OFLEDRR)

  • Objective
  • Factors
  • Levels
  • Experimental Units
  • Design
  • Replication
  • Randomization
• Factorial experiments


  Experiments that allow researchers to study the effects of TWO OR MORE FACTORS simultaneously
• Factorial experiments without interaction

  Assume that the effects of each factor operate independently of the others
• Two-factor factorial design

  A type of experimental design used to study the effects of TWO independent variables (FACTORS) on a single dependent variable
• Research Topics for 2x2 Factorial Design


  • Effects of Diet and Exercise Regimen on Weight Loss
  • Assessment of Drug Type and Dosage on Patient Recovery Time
• Components 2k Factorial Design

  • k Factors
  • Levels (-1 and +1)
  • Total Number of Runs (2 raised to k)
• Null hypothesis (2k Factorial Design)

  States that there is no effect of changing the level of factor i on the response variable, regardless of the levels of other factors
• Alternative hypothesis (2k Factorial Design)

  States that changing the level of factor i has a significant effect on the response variable
• Blocking


  A TECHNIQUE used in experimental design to CONTROL the variability of EXTRANEOUS factors that may affect the outcome of an experiment
• Confounding


  Occurs when the effects of two or more variables on a response variable cannot be DISTINGUISHED from each other
• Multiple Groups

  • ANOVA is designed to compare means across THREE OR MORE groups simultaneously
• One-Way or Two-Way

  • ANOVA can be one-way (comparing means across one factor) or two-way (comparing means across two factors)
• Assumption of Independence

  • Observations within and between groups should be independent.
• Assumption of Homogeneity of Variances

  • The variances within the different groups should be approximately equal (homoscedasticity)
• Normal Distribution

  • The dependent variable should be approximately normally distributed within each group.
• Provides F-statistic

  • ANOVA provides an F-statistic, which is used to test the null hypothesis that the means of all groups are equal.
• Post-Hoc Tests

  • If ANOVA indicates significant differences among groups, post-hoc tests (e.g., Tukey-Kramer, Bonferroni) can be conducted to identify which specific groups differ from each other.
• In experimental research, confounding can lead to incorrect conclusions about the relationships between variables, as it obscures the true effects of the independent variables on the dependent variable.
• Blocking

  • It helps to improve the precision and validity of the experiment by ensuring that the treatment effects are not confounded with the effects of the blocking variable.
• Objective

  • Clearly define the PURPOSE and GOALS of the experiment.
  • What are you trying to achieve or understand?
• Factors

  • Identify the variables (factors) that may influence the outcome of the experiment.
  • Factors can be classified as: a. Independent Variables (manipulated) b. Dependent Variables (observed)
• Levels

  • Determine the different levels or settings at which each factor will be tested.
• Experimental Units

  • Define the subjects, samples, or items on which the EXPERIMENT will be conducted.
• Design

  • Select an appropriate experimental design that suits the objectives and constraints of the experiment.
• Common designs (CRFR) a. Completely Randomized Design (CRD)

  b. Randomized Complete Block Design (RCBD)

  c. Factorial Design

  d. Response Surface Design
• Replication

  • Decide on the number of REPLICATES or REPETITIONS for each combination of factor levels to enhance the reliability and validity of the results.
• Randomization

  • RANDOMLY ASSIGN experimental units to treatment groups to minimize the effects of extraneous variables and ensure unbiased estimates.