Experimental Designs and Statistics

Experimental Design and Statistical Analysis Overview

Importance of Experimental Design

  • Purpose: Necessary to ensure cost-effective collection of appropriate data, valid analysis, and valid conclusions.

Types of Experimental Designs

  • Completely Randomized Design (CRD)

  • Randomized Complete Block Design (RCBD)

  • Latin Square Design (LSD)

Key Concepts

Treatment or Factor

  • Definition: Conditions whose effects are measured and compared.

Response Variable

  • Definition: Characteristic used to measure the effect of a treatment.

Experimental Unit

  • Definition: The unit to which a single treatment is applied.

  • Experimental Error: Occurs when two experimental units treated alike yield different responses.

Examples of Experimental Units

  1. Lowering Costs of Ceramics: Each ceramic tile is an experimental unit.

  2. Chicken Manure as Crab Feeds:

    • Case 1: Crab as the experimental unit.

    • Case 2: Each aquarium as the experimental unit.

  3. Germination Substrates:

    • Case 1: Seed as the experimental unit.

    • Case 2: Each Petri dish as the experimental unit.

Design Specifications

Levels

  • Definition: Pre-set quantity of a treatment.

Layout

  • Definition: Final arrangement of treatment levels.

Lowering Costs of Ceramics Design

  • Levels:

    • No Plastic

    • 20% Hard Plastic

    • 20% Cellophane

    • 10% Cellophane + 10% Hard Plastic

Chicken Manure Experiment Levels

  • Levels:

    • Commercial Feeds

    • Manure from Conventionally Grown Chickens

    • Manure from Organically Grown Chickens

Germination Substrates Levels

  • Levels: 7 different treatments for germination substrates.

Replication

  • Definition: Number of times a treatment level appears in an experiment.

  • Ceramics Experiment Replication: 4

  • Chicken Manure Experiment Replication: 3

  • Germination Substrates Replication: 3

Randomization

  • Definition: Allocating treatment levels to the experimental units using chance mechanisms.

ANOVA (Analysis of Variance)

  • Purpose: Used to compare means across different groups to determine if there is any significant difference.

  • Assumptions: Normal distribution, homogeneity of variances, independence, and additivity of treatment effects.

Tests for Assumptions

  1. Homogeneity of Variances: Hartley's F-max test, Bartlett's Test, Levene's Test.

  2. Normality: Kolmogorov-Smirnov Test, Wilk-Shapiro Test.

  3. Independence: No need to test with proper randomization.

  4. Additivity: No need to test due to the usual nature of research.

Conducting ANOVA

  1. Check if data passes all assumptions.

  2. If passed, proceed to ANOVA calculations.

  3. If p-value < alpha, reject null hypothesis indicating significant differences among treatment means.

  4. Follow up with multiple comparison tests (e.g., Tukey's HSD, Scheffe's Test) to identify which treatments differ.

Conclusion

  • Result Interpretation: ANOVA indicates at least one treatment is different, but further tests are needed to clarify differences.

  • Software Utilized: STAR Statistical Software for data analysis in agricultural research.