Question

1. Catfish, which varied in body condition (fat or lean) were given either low or high protein diets.  Did the growth rate vary between body condition and diet?

fish	protein	growth
fat	high	3.55
fat	high	3.36
lean	high	4.15
fat	low	1.90
lean	high	4.34
fat	low	1.99
fat	high	3.59
lean	low	2.77
lean	low	2.83
fat	high	3.89
fat	low	1.83
fat	low	1.95
lean	low	2.94
lean	high	4.44
lean	high	4.32
lean	low	2.74

1. What are the null and alternative hypotheses?
2. What does the data look like?  Please provide appropriate figures and summary statistics (measure of central tendency and variance) to write a sentence or two about the data and discuss the number of levels for each factor.
3. Are the variances equal?
4. Two-way ANOVA
   1. What kind of Two-Way ANOVA?  
   2. What was the outcome of the Two-Way ANOVA? Was there an interaction?
   3. Evaluate the model fit
5. If the Two-Way ANOVA indicates that you may reject the null hypotheses, where do the differences lie?  As a biologist, what can you conclude from this study?

Answer 1

H₀: Variation in Growth Rate due to Body condition and Diet

H1: No Variation in Growth Rate due to Body condition and Diet

std	0.516398	0.516398	0.928857

             sum_sq    df           F        PR(>F)    eta_sq  omega_sq
fish       2.616306   1.0  130.523517  3.758635e-08  0.202162  0.200303
protein   10.064756   1.0  502.115295  9.009098e-12  0.777703  0.774954
Residual   0.260581  13.0         NaN           NaN       NaN       NaN