Factorial designs: principles and applications

1. Factorial designs: principles and applications

Welcome back! In this video, we'll explore factorial designs.

2. Understanding factorial design

Factorial designs allow for the simultaneous examination of multiple variables. In this setup, every possible combination of factor levels is tested, which not only measures the direct effects of each factor but also the interactions between them. In the example shown of plant growth in different conditions, implementing a factorial design will mean that we can test the effect of different factors on plant growth, including light conditions and fertilizer type, simultaneously, and identify interactions between them. These interactions can illuminate complex dynamics that might be overlooked in simpler experimental setups.

3. Factorial design data example

To explain this concept further, we'll work with this plant growth DataFrame. It has 120 rows and four columns: an identifier column, two factors, and one response/dependent variable. Both factors have two levels: Light_Condition can be Full Sunlight or Partial Shade, and Fertilizer_Type can be either Synthetic or Organic. The Growth_cm column is the numeric response, or dependent variable in the experiment.

4. Organizing data to visualize interactions

We next create a pivot table from the DataFrame using pandas' pivot_table function. It aggregates the Growth_cm values by taking their mean for each combination of Light_Condition and Fertilizer_Type. The resulting table displays these average outcomes, with light values as rows and fertilizer values as columns, illustrating how the growth varies across different levels of the two factors. For example, the value 19.869 represents the average growth for the combination of Full Sunlight from Light_Condition and Synthetic from Fertilizer_Type.

5. Visualize interactions with heatmap

The Seaborn heatmap function paints a picture of how these factors interact, with the color intensity revealing the strength and direction of their interactions. Setting annot to True displays the numerical value of the cell, and 'coolwarm' is a color map that ranges from cooler, or bluer colors, to warmer or redder colors. Lastly, the format argument fmt is set to 'g' to avoid scientific notation.

6. Interpreting interactions

The variation in outcomes when changing levels within a factor indicates an interaction. For instance, the decrease from Organic to Synthetic fertilizer within Full Sunlight (from 20.602 to 19.869) contrasts with the modest change within Partial Shade, illustrating how outcomes differ based on factor levels. The differing changes in outcomes between Full Sunlight and Partial Shade across Fertilizer_Type suggest the factors interact, underscoring the need for nuanced strategies considering the interaction of factors.

7. Factorial designs vs. randomized block designs

Let's conclude by comparing factorial designs to the randomized block design we saw earlier in the course, and that we'll dive deeper into in the next video. Factorial designs investigate multiple treatments and their interactions to understand their combined effects on outcomes. They aim to unravel the effects and interactions of various factors, crucial for complex scenarios with multiple influencing variables. In factorial designs, units experience all treatment combinations, offering thorough exploration but requiring more subjects as treatments grow. Randomized block designs utilize blocks to group similar subjects, minimizing confounding impacts and clearer treatment effects. The focus of randomized block designs is on enhancing experimental precision by managing within-block variability, aiding in the detection of treatment differences. Randomized block designs assign one treatment per unit within blocks, ensuring each treatment's presence in every block to control for block-related variance and bolster treatment effect assessments.

8. Let's practice!

Now it's time to put your knowledge into practice. Let's explore setting up factorial designs and investigating interactions.

This exercise is part of the course

Experimental Design in Python

IntermediateSkill Level

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Building knowledge in experimental design allows you to test hypotheses with best-practice analytical tools and quantify the risk of your work. You’ll begin your journey by setting the foundations of what experimental design is and different experimental design setups such as blocking and stratification. You’ll then learn and apply visual and analytical tests for normality in experimental data.

Exercise 1: Setting up experiments Exercise 2: Non-random assignment of subjects Exercise 3: Random assignment of subjects Exercise 4: Experimental data setup Exercise 5: Blocking experimental data Exercise 6: Stratifying an experiment Exercise 7: Which was stratified?Exercise 8: Normal data Exercise 9: Visual normality in an agricultural experiment Exercise 10: Analytical normality in an agricultural experiment

You'll delve into sophisticated experimental design techniques, focusing on factorial designs, randomized block designs, and covariate adjustments. These methodologies are instrumental in enhancing the accuracy, efficiency, and interpretability of experimental results. Through a combination of theoretical insights and practical applications, you'll acquire the skills needed to design, implement, and analyze complex experiments in various fields of research.

Exercise 1: Factorial designs: principles and applications

Current Exercise

Exercise 2: Understanding marketing campaign effectiveness Exercise 3: Heatmap of campaign interactions Exercise 4: Factorial designs and randomized block designs Exercise 5: Randomized block design: controlling variance Exercise 6: Implementing a randomized block design Exercise 7: Visualizing productivity within blocks by incentive Exercise 8: ANOVA within blocks of employees Exercise 9: Covariate adjustment in experimental design Exercise 10: Importance of covariates Exercise 11: Covariate adjustment with chick growth

Master statistical tests like t-tests, ANOVA, and Chi-Square, and dive deep into post-hoc analyses and power analysis essentials. Learn to select the right test, interpret p-values and errors, and skillfully conduct power analysis to determine sample and effect sizes, all while leveraging Python's powerful libraries to bring your data insights to life.

Exercise 1: Choosing the right statistical test Exercise 2: Choosing the right test: petrochemicals Exercise 3: Choosing the right test: human resources Exercise 4: Choosing the right test: finance Exercise 5: Post-hoc analysis following ANOVA Exercise 6: Anxiety treatments ANOVA Exercise 7: Applying Tukey's HSD Exercise 8: Applying Bonferoni correction Exercise 9: P-values, alpha, and errors Exercise 10: Analyzing toy durability Exercise 11: Visualizing durability differences Exercise 12: Role of significance levels Exercise 13: Power analysis: sample and effect size Exercise 14: Effect size purpose Exercise 15: Estimating required sample size for energy study

Hop into the complexities of experimental data analysis. Learn to synthesize insights using pandas, address data issues like heteroscedasticity with scipy.stats, and apply nonparametric tests like Mann-Whitney U. Learn additional techniques for transforming, visualizing, and interpreting complex data, enhancing your ability to conduct robust analyses in various experimental settings.

Exercise 1: Synthesizing insights from complex experiments Exercise 2: Visualizing loan approval yield Exercise 3: Exploring customer satisfaction Exercise 4: Effectively communicating experimental data Exercise 5: Addressing complexities in experimental data Exercise 6: Check for heteroscedasticity in shelf life Exercise 7: Exploring and transforming shelf life data Exercise 8: Applying nonparametric tests in experimental analysis Exercise 9: Visualizing and testing preservation methods Exercise 10: Further analyzing food preservation techniques Exercise 11: Congratulations!